From 15a7345050b404daa40440a70751d2cd45292fc7 Mon Sep 17 00:00:00 2001 From: franciscoeacosta Date: Thu, 12 Sep 2024 20:59:28 -0700 Subject: [PATCH 1/6] create immersion estimator --- neurometry/estimators/geometry/__init__.py | 3 + .../geometry/immersion_estimator.py | 0 .../estimators/geometry/metric_estimator.py | 0 .../estimators/geometry/spherical_vae.py | 174 +++++++++++++++ .../estimators/geometry/toroidal_vae.py | 201 ++++++++++++++++++ 5 files changed, 378 insertions(+) create mode 100644 neurometry/estimators/geometry/__init__.py create mode 100644 neurometry/estimators/geometry/immersion_estimator.py create mode 100644 neurometry/estimators/geometry/metric_estimator.py create mode 100644 neurometry/estimators/geometry/spherical_vae.py create mode 100644 neurometry/estimators/geometry/toroidal_vae.py diff --git a/neurometry/estimators/geometry/__init__.py b/neurometry/estimators/geometry/__init__.py new file mode 100644 index 0000000..8f20503 --- /dev/null +++ b/neurometry/estimators/geometry/__init__.py @@ -0,0 +1,3 @@ +"""Initialize folder as submodule.""" + +__version__ = "0.0.1" diff --git a/neurometry/estimators/geometry/immersion_estimator.py b/neurometry/estimators/geometry/immersion_estimator.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/metric_estimator.py b/neurometry/estimators/geometry/metric_estimator.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/spherical_vae.py b/neurometry/estimators/geometry/spherical_vae.py new file mode 100644 index 0000000..c0414ab --- /dev/null +++ b/neurometry/estimators/geometry/spherical_vae.py @@ -0,0 +1,174 @@ +"""G-manifold deep learning. + +This file gathers deep learning models related to G-manifold learning. +""" + +import torch +from torch.distributions.normal import Normal +from torch.nn import functional as F + +from neurometry.estimators.curvature.hyperspherical.distributions.von_mises_fisher import ( + VonMisesFisher, +) + + +class SphericalVAE(torch.nn.Module): + """VAE with Linear (fully connected) layers. + + Parameters + ---------- + num_neurons : int + Number of neurons in the input data. This is the ambient dimension of the neural state space. + Example: 40 for neural recordings of 40 neurons. + latent_dim : int + Dimension of the latent space. + Example: 2. + """ + + def __init__( + self, + num_neurons, + latent_dim, + sftbeta, + encoder_width=400, + encoder_depth=2, + decoder_width=400, + decoder_depth=2, + drop_out_p=0.0, + ): + super().__init__() + self.num_neurons = num_neurons + self.sftbeta = sftbeta + self.latent_dim = latent_dim + self.drop_out_p = drop_out_p + + decoder_width = encoder_width + decoder_depth = encoder_depth + + self.encoder_fc = torch.nn.Linear(self.num_neurons, encoder_width) + self.encoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(encoder_width, encoder_width) + for _ in range(encoder_depth) + ] + ) + + self.fc_z_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_logvar = torch.nn.Linear(encoder_width, 1) # kappa + + self.decoder_fc = torch.nn.Linear(self.latent_dim, decoder_width) + self.decoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(decoder_width, decoder_width) + for _ in range(decoder_depth) + ] + ) + + self.fc_x_mu = torch.nn.Linear(decoder_width, self.num_neurons) + + self.drop_out = torch.nn.Dropout(p=self.drop_out_p) + + def encode(self, x): + """Encode input into mean and log-variance. + + The parameters mean (mu) and variance (computed + from logvar) defines a multivariate Gaussian + that represents the approximate posterior of the + latent variable z given the input x. + + Parameters + ---------- + x : array-like, shape=[batch_size, num_neurons] + Input data. + + Returns + ------- + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + h = F.softplus(self.encoder_fc(x.double()), beta=self.sftbeta) + + for _i_layer, layer in enumerate(self.encoder_linears): + # h = self.drop_out(h) + h = layer(h) + h = F.softplus(h, beta=self.sftbeta) + + z_mu = self.fc_z_mu(h) + z_kappa = F.softplus(self.fc_z_logvar(h)) + 1 + posterior_params = z_mu, z_kappa + + return posterior_params + + def reparameterize(self, posterior_params): + """ + Apply reparameterization trick. We 'eternalize' the + randomness in z by re-parameterizing the variable as + a deterministic and differentiable function of x, + the encoder weights, and a new random variable eps. + + Parameters + ---------- + posterior_params : tuple + Distributional parameters of approximate posterior. ((e.g.), (z_mu,z_logvar) for Gaussian. + + Returns + ------- + + z: array-like, shape = [batch_size, latent_dim] + Re-parameterized latent variable. + """ + + z_mu, z_kappa = posterior_params + q_z = VonMisesFisher(z_mu, z_kappa) + + return q_z.rsample() + + def decode(self, z): + """Decode latent variable z into data. + + Parameters + ---------- + z : array-like, shape=[batch_size, latent_dim] + Input to the decoder. + + Returns + ------- + _ : array-like, shape=[batch_size, num_neurons] + Reconstructed data corresponding to z. + """ + + h = F.softplus(self.decoder_fc(z), beta=self.sftbeta) + + for _i_layer, layer in enumerate(self.decoder_linears): + # h = self.drop_out(h) + h = layer(h) + h = F.softplus(h, beta=self.sftbeta) + + return self.fc_x_mu(h) + + def forward(self, x): + """Run VAE: Encode, sample and decode. + + Parameters + ---------- + x : array-like, shape=[batch_size, num_neurons] + Input data. + + Returns + ------- + _ : array-like, shape=[batch_size, num_neurons] + Reconstructed data corresponding to z. + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + + posterior_params = self.encode(x) + z = self.reparameterize(posterior_params) + x_mu = self.decode(z) + return z, x_mu, posterior_params diff --git a/neurometry/estimators/geometry/toroidal_vae.py b/neurometry/estimators/geometry/toroidal_vae.py new file mode 100644 index 0000000..191f78c --- /dev/null +++ b/neurometry/estimators/geometry/toroidal_vae.py @@ -0,0 +1,201 @@ +"""G-manifold deep learning. + +This file gathers deep learning models related to G-manifold learning. +""" + +import geomstats.backend as gs +import torch +from torch.nn import functional as F + +from neurometry.estimators.curvature.hyperspherical.distributions.von_mises_fisher import ( + VonMisesFisher, +) + + +class ToroidalVAE(torch.nn.Module): + """VAE with Linear (fully connected) layers. + + Parameters + ---------- + data_dim : int + Dimension of input data. + Example: 40 for neural recordings of 40 units/clusters. + latent_dim : int + Dimension of the latent space. + Example: 2. + """ + + def __init__( + self, + data_dim, + latent_dim, + sftbeta, + encoder_width, + encoder_depth, + decoder_width, + decoder_depth, + posterior_type, + ): + super().__init__() + self.data_dim = data_dim + self.sftbeta = sftbeta + self.latent_dim = latent_dim + self.posterior_type = posterior_type + + # decoder_width = encoder_width + # decoder_depth = encoder_depth + + self.encoder_fc = torch.nn.Linear(self.data_dim, encoder_width) + self.encoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(encoder_width, encoder_width) + for _ in range(encoder_depth) + ] + ) + + self.fc_z_theta_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_theta_kappa = torch.nn.Linear(encoder_width, 1) + + self.fc_z_phi_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_phi_kappa = torch.nn.Linear(encoder_width, 1) + + self.decoder_fc = torch.nn.Linear(3, decoder_width) + self.decoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(decoder_width, decoder_width) + for _ in range(decoder_depth) + ] + ) + + self.fc_x_mu = torch.nn.Linear(decoder_width, self.data_dim) + + def encode(self, x): + """Encode input into mean and log-variance. + + The parameters mean (mu) and variance (computed + from logvar) defines a multivariate Gaussian + that represents the approximate posterior of the + latent variable z given the input x. + + Parameters + ---------- + x : array-like, shape=[batch_size, data_dim] + Input data. + + Returns + ------- + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + h = F.softplus(self.encoder_fc(x), beta=self.sftbeta) + + for layer in self.encoder_linears: + h = F.softplus(layer(h), beta=self.sftbeta) + + z_theta_mu = self.fc_z_theta_mu(h) + z_theta_kappa = F.softplus(self.fc_z_theta_kappa(h)) + 1 + + z_phi_mu = self.fc_z_phi_mu(h) + z_phi_kappa = F.softplus(self.fc_z_phi_kappa(h)) + 1 + + return z_theta_mu, z_theta_kappa, z_phi_mu, z_phi_kappa + + def _build_torus(self, z_theta, z_phi): + # theta = torch.atan2(z_theta[:, 1] / z_theta[:, 0]) + # phi = torch.atan2(z_phi[:, 1] / z_phi[:, 0]) + cos_theta = z_theta[:, 0] + sin_theta = z_theta[:, 1] + + cos_phi = z_phi[:, 0] + sin_phi = z_phi[:, 1] + + major_radius = 2 + minor_radius = 1 + + x = (major_radius - minor_radius * cos_theta) * cos_phi + y = (major_radius - minor_radius * cos_theta) * sin_phi + z = minor_radius * sin_theta + + return gs.stack([x, y, z], axis=-1) + + def reparameterize(self, posterior_params): + """ + Apply reparameterization trick. We 'eternalize' the + randomness in z by re-parameterizing the variable as + a deterministic and differentiable function of x, + the encoder weights, and a new random variable eps. + + Parameters + ---------- + posterior_params : tuple + Distributional parameters of approximate posterior. ((e.g.), (z_mu,z_logvar) for Gaussian. + + Returns + ------- + + z: array-like, shape = [batch_size, latent_dim] + Re-parameterized latent variable. + """ + + z_theta_mu, z_theta_kappa, z_phi_mu, z_phi_kappa = posterior_params + + q_z_theta = VonMisesFisher(z_theta_mu, z_theta_kappa) + + q_z_phi = VonMisesFisher(z_phi_mu, z_phi_kappa) + + z_theta = q_z_theta.rsample() + + z_phi = q_z_phi.rsample() + + return self._build_torus(z_theta, z_phi) + + def decode(self, z): + """Decode latent variable z into data. + + Parameters + ---------- + z : array-like, shape=[batch_size, latent_dim] + Input to the decoder. + + Returns + ------- + _ : array-like, shape=[batch_size, data_dim] + Reconstructed data corresponding to z. + """ + + h = F.softplus(self.decoder_fc(z), beta=self.sftbeta) + + for layer in self.decoder_linears: + h = F.softplus(layer(h), beta=self.sftbeta) + + return self.fc_x_mu(h) + + def forward(self, x): + """Run VAE: Encode, sample and decode. + + Parameters + ---------- + x : array-like, shape=[batch_size, data_dim] + Input data. + + Returns + ------- + _ : array-like, shape=[batch_size, data_dim] + Reconstructed data corresponding to z. + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + + posterior_params = self.encode(x) + + z = self.reparameterize(posterior_params) + + x_mu = self.decode(z) + + return z, x_mu, posterior_params From 759652e93fe38051d7ab69d4c810963461adbc22 Mon Sep 17 00:00:00 2001 From: franciscoeacosta Date: Fri, 13 Sep 2024 08:25:37 -0700 Subject: [PATCH 2/6] ruff --- .../estimators/geometry/immersion_estimator.py | 17 +++++++++++++++++ neurometry/estimators/geometry/spherical_vae.py | 4 +--- 2 files changed, 18 insertions(+), 3 deletions(-) diff --git a/neurometry/estimators/geometry/immersion_estimator.py b/neurometry/estimators/geometry/immersion_estimator.py index e69de29..e93d8ed 100644 --- a/neurometry/estimators/geometry/immersion_estimator.py +++ b/neurometry/estimators/geometry/immersion_estimator.py @@ -0,0 +1,17 @@ + +from sklearn.base import BaseEstimator + + +class ImmersionEstimator(BaseEstimator): + def __init__(self, num_neurons, intrinsic_dimension, topology): + + self.estimate_ = None + self.num_neurons = num_neurons + self.intrinsic_dimension = intrinsic_dimension + self.topology = topology + + + + + + diff --git a/neurometry/estimators/geometry/spherical_vae.py b/neurometry/estimators/geometry/spherical_vae.py index c0414ab..fd32f77 100644 --- a/neurometry/estimators/geometry/spherical_vae.py +++ b/neurometry/estimators/geometry/spherical_vae.py @@ -4,7 +4,6 @@ """ import torch -from torch.distributions.normal import Normal from torch.nn import functional as F from neurometry.estimators.curvature.hyperspherical.distributions.von_mises_fisher import ( @@ -98,9 +97,8 @@ def encode(self, x): z_mu = self.fc_z_mu(h) z_kappa = F.softplus(self.fc_z_logvar(h)) + 1 - posterior_params = z_mu, z_kappa - return posterior_params + return z_mu, z_kappa def reparameterize(self, posterior_params): """ From b1ef0558e10117951f6f680628380bd36f618088 Mon Sep 17 00:00:00 2001 From: franciscoeacosta Date: Fri, 13 Sep 2024 17:37:09 -0700 Subject: [PATCH 3/6] implement ImmersionEstimator for hypersphere --- neurometry/datasets/synthetic.py | 17 +- .../geometry/immersion_estimator.py | 83 +- .../estimators/geometry/metric_estimator.py | 24 + .../estimators/geometry/models/__init__.py | 3 + .../models/hyperspherical/__init__.py | 0 .../hyperspherical/distributions/__init__.py | 0 .../distributions/hyperspherical_uniform.py | 56 + .../distributions/von_mises_fisher.py | 213 + .../models/hyperspherical/ops/__init__.py | 0 .../geometry/models/hyperspherical/ops/ive.py | 76 + .../estimators/geometry/models/losses.py | 176 + .../geometry/models/spherical_vae.py | 263 + .../geometry/{ => models}/toroidal_vae.py | 40 +- .../estimators/geometry/models/train.py | 107 + .../geometry/models/train_config.py | 13 + .../estimators/geometry/models/utils.py | 248 + .../estimators/geometry/spherical_vae.py | 172 - .../topology/topology_classifier.py | 11 +- .../topology/test_topology_classifier.py | 1 - ..._methods_estimate_manifold_immersion.ipynb | 9026 +++++++++++++++++ 20 files changed, 10320 insertions(+), 209 deletions(-) create mode 100644 neurometry/estimators/geometry/models/__init__.py create mode 100644 neurometry/estimators/geometry/models/hyperspherical/__init__.py create mode 100644 neurometry/estimators/geometry/models/hyperspherical/distributions/__init__.py create mode 100644 neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py create mode 100644 neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py create mode 100644 neurometry/estimators/geometry/models/hyperspherical/ops/__init__.py create mode 100644 neurometry/estimators/geometry/models/hyperspherical/ops/ive.py create mode 100644 neurometry/estimators/geometry/models/losses.py create mode 100644 neurometry/estimators/geometry/models/spherical_vae.py rename neurometry/estimators/geometry/{ => models}/toroidal_vae.py (85%) create mode 100644 neurometry/estimators/geometry/models/train.py create mode 100644 neurometry/estimators/geometry/models/train_config.py create mode 100644 neurometry/estimators/geometry/models/utils.py delete mode 100644 neurometry/estimators/geometry/spherical_vae.py create mode 100644 tutorials/04_methods_estimate_manifold_immersion.ipynb diff --git a/neurometry/datasets/synthetic.py b/neurometry/datasets/synthetic.py index d9613c1..32c8ed2 100644 --- a/neurometry/datasets/synthetic.py +++ b/neurometry/datasets/synthetic.py @@ -75,7 +75,9 @@ def hypersphere(intrinsic_dim, num_points, radius=1): """ unit_hypersphere = Hypersphere(dim=intrinsic_dim) unit_hypersphere_points = unit_hypersphere.random_point(n_samples=num_points) - intrinsic_coords = unit_hypersphere.extrinsic_to_intrinsic_coords(unit_hypersphere_points) + intrinsic_coords = unit_hypersphere.extrinsic_to_intrinsic_coords( + unit_hypersphere_points + ) return radius * unit_hypersphere_points, intrinsic_coords @@ -110,9 +112,14 @@ def hypertorus(intrinsic_dim, num_points, radii=None, parameterization="flat"): hypertorus_points[:, _, :] = radii[_] * unit_hypertorus_points[:, _, :] intrinsic_coords = torch.zeros(num_points, intrinsic_dim) for i, factor in enumerate(unit_hypertorus.factors): - intrinsic_coords[:, i] = factor.extrinsic_to_intrinsic_coords(hypertorus_points[:, i, :]).squeeze() + intrinsic_coords[:, i] = factor.extrinsic_to_intrinsic_coords( + hypertorus_points[:, i, :] + ).squeeze() - return gs.reshape(hypertorus_points, (num_points, intrinsic_dim * 2)), intrinsic_coords + return ( + gs.reshape(hypertorus_points, (num_points, intrinsic_dim * 2)), + intrinsic_coords, + ) def cylinder(num_points, radius=1): @@ -132,7 +139,9 @@ def cylinder(num_points, radius=1): cylinder = ProductManifold(factors=factors) cylinder_points = cylinder.random_point(n_samples=num_points, bound=1) intrinsic_coords = torch.zeros(num_points, 2) - intrinsic_coords[:, 0] = factors[0].extrinsic_to_intrinsic_coords(cylinder_points[:, :2]).squeeze() + intrinsic_coords[:, 0] = ( + factors[0].extrinsic_to_intrinsic_coords(cylinder_points[:, :2]).squeeze() + ) intrinsic_coords[:, 1] = cylinder_points[:, 2] cylinder_points[:, :2] = radius * cylinder_points[:, :2] return cylinder_points, intrinsic_coords diff --git a/neurometry/estimators/geometry/immersion_estimator.py b/neurometry/estimators/geometry/immersion_estimator.py index e93d8ed..a8efba4 100644 --- a/neurometry/estimators/geometry/immersion_estimator.py +++ b/neurometry/estimators/geometry/immersion_estimator.py @@ -1,17 +1,92 @@ +import os +os.environ["GEOMSTATS_BACKEND"] = "pytorch" +import geomstats.backend as gs +import torch from sklearn.base import BaseEstimator +from sklearn.model_selection import train_test_split +from torch.utils.data import DataLoader, TensorDataset +import neurometry.estimators.geometry.models.train_config as train_config +from neurometry.estimators.geometry.models.spherical_vae import SphericalVAE +from neurometry.estimators.geometry.models.toroidal_vae import ToroidalVAE +from neurometry.estimators.geometry.models.train import train_test -class ImmersionEstimator(BaseEstimator): - def __init__(self, num_neurons, intrinsic_dimension, topology): +class ImmersionEstimator(BaseEstimator): + def __init__(self, extrinsic_dim, topology, device): self.estimate_ = None - self.num_neurons = num_neurons - self.intrinsic_dimension = intrinsic_dimension + self.device = device + self.extrinsic_dim = extrinsic_dim self.topology = topology + self.latent_dims = {"circle": 2, "sphere": 3, "torus": 3} + self.model = self._get_model() + def _get_model(self): + if self.topology == "circle" or self.topology == "sphere": + return SphericalVAE( + extrinsic_dim=self.extrinsic_dim, + latent_dim=self.latent_dims[self.topology], + ).to(self.device) + if self.topology == "torus": + return ToroidalVAE( + extrinsic_dim=self.extrinsic_dim, + latent_dim=self.latent_dims[self.topology], + ).to(self.device) + raise ValueError("Topology not supported") + def _intrinsic_to_extrinsic(self): + if self.topology == "circle": + return lambda x: gs.array([gs.cos(x), gs.sin(x)]) + if self.topology == "sphere": + return lambda x: gs.array( + [ + gs.sin(x[0]) * gs.cos(x[1]), + gs.sin(x[0]) * gs.sin(x[1]), + gs.cos(x[0]), + ] + ) + if self.topology == "torus": + return lambda x: gs.array( + [ + (1 - gs.cos(x[0])) * gs.cos(x[1]), + (1 - gs.cos(x[0])) * gs.sin(x[1]), + gs.sin(x[0]), + ] + ) + raise ValueError("Topology not supported") + def fit(self, X, y=None): + X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2) + X_train = torch.tensor(X_train).to(self.device) + X_test = torch.tensor(X_test).to(self.device) + y_train = torch.tensor(y_train).to(self.device) + y_test = torch.tensor(y_test).to(self.device) + train_loader = DataLoader( + TensorDataset(X_train, y_train), + batch_size=train_config.batch_size, + shuffle=True, + ) + test_loader = DataLoader( + TensorDataset(X_test, y_test), + batch_size=train_config.batch_size, + shuffle=True, + ) + optimizer = torch.optim.Adam( + self.model.parameters(), lr=train_config.lr, amsgrad=True + ) + train_losses, test_losses, best_model = train_test( + model=self.model, + train_loader=train_loader, + test_loader=test_loader, + optimizer=optimizer, + scheduler=None, + config=train_config, + ) + self.estimate_ = lambda task_variable: best_model.decode( + self._intrinsic_to_extrinsic()(task_variable).T + ) + return self diff --git a/neurometry/estimators/geometry/metric_estimator.py b/neurometry/estimators/geometry/metric_estimator.py index e69de29..e4cd230 100644 --- a/neurometry/estimators/geometry/metric_estimator.py +++ b/neurometry/estimators/geometry/metric_estimator.py @@ -0,0 +1,24 @@ +# import os + +# os.environ["GEOMSTATS_BACKEND"] = "pytorch" +# from geomstats.geometry.base import ImmersedSet +# from geomstats.geometry.euclidean import Euclidean +# from geomstats.geometry.pullback_metric import PullbackMetric + + +# class NeuralManifoldIntrinsic(ImmersedSet): +# def __init__(self, dim, neural_embedding_dim, neural_immersion, equip=True): +# self.neural_embedding_dim = neural_embedding_dim +# super().__init__(dim=dim, equip=equip) +# self.neural_immersion = neural_immersion + +# def immersion(self, point): +# return self.neural_immersion(point) + +# def _define_embedding_space(self): +# return Euclidean(dim=self.neural_embedding_dim) + +# neural_manifold = NeuralManifoldIntrinsic( +# dim, embedding_dim, immersion, equip=False +# ) +# neural_manifold.equip_with_metric(PullbackMetric) diff --git a/neurometry/estimators/geometry/models/__init__.py b/neurometry/estimators/geometry/models/__init__.py new file mode 100644 index 0000000..8f20503 --- /dev/null +++ b/neurometry/estimators/geometry/models/__init__.py @@ -0,0 +1,3 @@ +"""Initialize folder as submodule.""" + +__version__ = "0.0.1" diff --git a/neurometry/estimators/geometry/models/hyperspherical/__init__.py b/neurometry/estimators/geometry/models/hyperspherical/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/models/hyperspherical/distributions/__init__.py b/neurometry/estimators/geometry/models/hyperspherical/distributions/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py b/neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py new file mode 100644 index 0000000..20f8a41 --- /dev/null +++ b/neurometry/estimators/geometry/models/hyperspherical/distributions/hyperspherical_uniform.py @@ -0,0 +1,56 @@ +import math + +import torch + + +class HypersphericalUniform(torch.distributions.Distribution): + arg_constraints = {} + support = torch.distributions.constraints.real + has_rsample = False + _mean_carrier_measure = 0 + + @property + def dim(self): + return self._dim + + @property + def device(self): + return self._device + + @device.setter + def device(self, val): + self._device = val if isinstance(val, torch.device) else torch.device(val) + + def __init__(self, dim, validate_args=None, device=None): + super().__init__(torch.Size([dim]), validate_args=validate_args) + self._dim = dim + self.device = device + + def sample(self, shape=None): + if shape is None: + shape = torch.Size() + output = ( + torch.distributions.Normal(0, 1) + .sample( + (shape if isinstance(shape, torch.Size) else torch.Size([shape])) + + torch.Size([self._dim + 1]) + ) + .to(self.device) + ) + + return output / output.norm(dim=-1, keepdim=True) + + def entropy(self): + return self.__log_surface_area() + + def log_prob(self, x): + return -torch.ones(x.shape[:-1], device=self.device) * self.__log_surface_area() + + def __log_surface_area(self): + if torch.__version__ >= "1.0.0": + lgamma = torch.lgamma(torch.tensor([(self._dim + 1) / 2]).to(self.device)) + else: + lgamma = torch.lgamma( + torch.Tensor([(self._dim + 1) / 2], device=self.device) + ) + return math.log(2) + ((self._dim + 1) / 2) * math.log(math.pi) - lgamma diff --git a/neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py b/neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py new file mode 100644 index 0000000..1ea089b --- /dev/null +++ b/neurometry/estimators/geometry/models/hyperspherical/distributions/von_mises_fisher.py @@ -0,0 +1,213 @@ +import math + +import torch +from torch.distributions.kl import register_kl + +from neurometry.estimators.geometry.models.hyperspherical.ops.ive import ive + +from .hyperspherical_uniform import ( + HypersphericalUniform, +) + + +class VonMisesFisher(torch.distributions.Distribution): + arg_constraints = { + "loc": torch.distributions.constraints.real, + "scale": torch.distributions.constraints.positive, + } + support = torch.distributions.constraints.real + has_rsample = True + _mean_carrier_measure = 0 + + @property + def mean(self): + # option 1: + return self.loc * ( + ive(self.__m / 2, self.scale) / ive(self.__m / 2 - 1, self.scale) + ) + # option 2: + # return self.loc * ive_fraction_approx(torch.tensor(self.__m / 2), self.scale) + # options 3: + # return self.loc * ive_fraction_approx2(torch.tensor(self.__m / 2), self.scale) + + @property + def stddev(self): + return self.scale + + def __init__(self, loc, scale, validate_args=None, k=1): + self.dtype = loc.dtype + self.loc = loc + self.scale = scale + self.device = loc.device + self.__m = loc.shape[-1] + self.__e1 = (torch.Tensor([1.0] + [0] * (loc.shape[-1] - 1))).to(self.device) + self.k = k + + super().__init__(self.loc.size(), validate_args=validate_args) + + def sample(self, shape=None): + if shape is None: + shape = torch.Size() + with torch.no_grad(): + return self.rsample(shape) + + def rsample(self, shape=None): + if shape is None: + shape = torch.Size() + shape = shape if isinstance(shape, torch.Size) else torch.Size([shape]) + + w = ( + self.__sample_w3(shape=shape) + if self.__m == 3 + else self.__sample_w_rej(shape=shape) + ) + + v = ( + torch.distributions.Normal(0, 1) + .sample(shape + torch.Size(self.loc.shape)) + .to(self.device) + .transpose(0, -1)[1:] + ).transpose(0, -1) + v = v / v.norm(dim=-1, keepdim=True) + + w_ = torch.sqrt(torch.clamp(1 - (w**2), 1e-10)) + x = torch.cat((w, w_ * v), -1) + z = self.__householder_rotation(x) + + return z.type(self.dtype) + + def __sample_w3(self, shape): + shape = shape + torch.Size(self.scale.shape) + u = torch.distributions.Uniform(0, 1).sample(shape).to(self.device) + self.__w = ( + 1 + + torch.stack( + [torch.log(u), torch.log(1 - u) - 2 * self.scale], dim=0 + ).logsumexp(0) + / self.scale + ) + return self.__w + + def __sample_w_rej(self, shape): + c = torch.sqrt((4 * (self.scale**2)) + (self.__m - 1) ** 2) + b_true = (-2 * self.scale + c) / (self.__m - 1) + + # using Taylor approximation with a smooth swift from 10 < scale < 11 + # to avoid numerical errors for large scale + b_app = (self.__m - 1) / (4 * self.scale) + s = torch.min( + torch.max( + torch.tensor([0.0], dtype=self.dtype, device=self.device), + self.scale - 10, + ), + torch.tensor([1.0], dtype=self.dtype, device=self.device), + ) + b = b_app * s + b_true * (1 - s) + + a = (self.__m - 1 + 2 * self.scale + c) / 4 + d = (4 * a * b) / (1 + b) - (self.__m - 1) * math.log(self.__m - 1) + + self.__b, (self.__e, self.__w) = b, self.__while_loop(b, a, d, shape, k=self.k) + return self.__w + + @staticmethod + def first_nonzero(x, dim, invalid_val=-1): + mask = x > 0 + return torch.where( + mask.any(dim=dim), + mask.float().argmax(dim=1).squeeze(), + torch.tensor(invalid_val, device=x.device), + ) + + def __while_loop(self, b, a, d, shape, k=20, eps=1e-20): + # matrix while loop: samples a matrix of [A, k] samples, to avoid looping all together + b, a, d = ( + e.repeat(*shape, *([1] * len(self.scale.shape))).reshape(-1, 1) + for e in (b, a, d) + ) + w, e, bool_mask = ( + torch.zeros_like(b).to(self.device), + torch.zeros_like(b).to(self.device), + (torch.ones_like(b) == 1).to(self.device), + ) + + sample_shape = torch.Size([b.shape[0], k]) + shape = shape + torch.Size(self.scale.shape) + + while bool_mask.sum() != 0: + con1 = torch.tensor((self.__m - 1) / 2, dtype=torch.float64) + con2 = torch.tensor((self.__m - 1) / 2, dtype=torch.float64) + e_ = ( + torch.distributions.Beta(con1, con2) + .sample(sample_shape) + .to(self.device) + .type(self.dtype) + ) + + u = ( + torch.distributions.Uniform(0 + eps, 1 - eps) + .sample(sample_shape) + .to(self.device) + .type(self.dtype) + ) + + w_ = (1 - (1 + b) * e_) / (1 - (1 - b) * e_) + t = (2 * a * b) / (1 - (1 - b) * e_) + + accept = ((self.__m - 1.0) * t.log() - t + d) > torch.log(u) + accept_idx = self.first_nonzero(accept, dim=-1, invalid_val=-1).unsqueeze(1) + accept_idx_clamped = accept_idx.clamp(0) + # we use .abs(), in order to not get -1 index issues, the -1 is still used afterwards + w_ = w_.gather(1, accept_idx_clamped.view(-1, 1)) + e_ = e_.gather(1, accept_idx_clamped.view(-1, 1)) + + reject = accept_idx < 0 + accept = ~reject if torch.__version__ >= "1.2.0" else 1 - reject + + w[bool_mask * accept] = w_[bool_mask * accept] + e[bool_mask * accept] = e_[bool_mask * accept] + + bool_mask[bool_mask * accept] = reject[bool_mask * accept] + + return e.reshape(shape), w.reshape(shape) + + def __householder_rotation(self, x): + u = self.__e1 - self.loc + u = u / (u.norm(dim=-1, keepdim=True) + 1e-5) + return x - 2 * (x * u).sum(-1, keepdim=True) * u + + def entropy(self): + # option 1: + output = ( + -self.scale + * ive(self.__m / 2, self.scale) + / ive((self.__m / 2) - 1, self.scale) + ) + # option 2: + # output = - self.scale * ive_fraction_approx(torch.tensor(self.__m / 2), self.scale) + # option 3: + # output = - self.scale * ive_fraction_approx2(torch.tensor(self.__m / 2), self.scale) + + return output.view(*(output.shape[:-1])) + self._log_normalization() + + def log_prob(self, x): + return self._log_unnormalized_prob(x) - self._log_normalization() + + def _log_unnormalized_prob(self, x): + output = self.scale * (self.loc * x).sum(-1, keepdim=True) + + return output.view(*(output.shape[:-1])) + + def _log_normalization(self): + output = -( + (self.__m / 2 - 1) * torch.log(self.scale) + - (self.__m / 2) * math.log(2 * math.pi) + - (self.scale + torch.log(ive(self.__m / 2 - 1, self.scale))) + ) + + return output.view(*(output.shape[:-1])) + + +@register_kl(VonMisesFisher, HypersphericalUniform) +def _kl_vmf_uniform(vmf, hyu): + return -vmf.entropy() + hyu.entropy() diff --git a/neurometry/estimators/geometry/models/hyperspherical/ops/__init__.py b/neurometry/estimators/geometry/models/hyperspherical/ops/__init__.py new file mode 100644 index 0000000..e69de29 diff --git a/neurometry/estimators/geometry/models/hyperspherical/ops/ive.py b/neurometry/estimators/geometry/models/hyperspherical/ops/ive.py new file mode 100644 index 0000000..62ce49b --- /dev/null +++ b/neurometry/estimators/geometry/models/hyperspherical/ops/ive.py @@ -0,0 +1,76 @@ +from numbers import Number + +import numpy as np +import scipy.special +import torch + + +class IveFunction(torch.autograd.Function): + @staticmethod + def forward(self, v, z): + assert isinstance(v, Number), "v must be a scalar" + + self.save_for_backward(z) + self.v = v + z_cpu = z.data.cpu().numpy() + + if np.isclose(v, 0): + output = scipy.special.i0e(z_cpu, dtype=z_cpu.dtype) + elif np.isclose(v, 1): + output = scipy.special.i1e(z_cpu, dtype=z_cpu.dtype) + else: # v > 0 + output = scipy.special.ive(v, z_cpu, dtype=z_cpu.dtype) + # else: + # print(v, type(v), np.isclose(v, 0)) + # raise RuntimeError('v must be >= 0, it is {}'.format(v)) + + return torch.Tensor(output).to(z.device) + + @staticmethod + def backward(self, grad_output): + z = self.saved_tensors[-1] + return ( + None, + grad_output * (ive(self.v - 1, z) - ive(self.v, z) * (self.v + z) / z), + ) + + +class Ive(torch.nn.Module): + def __init__(self, v): + super().__init__() + self.v = v + + def forward(self, z): + return ive(self.v, z) + + +ive = IveFunction.apply + + +########## +# The below provided approximations were provided in the +# respective source papers, to improve the stability of +# the Bessel fractions. +# I_(v/2)(k) / I_(v/2 - 1)(k) + + +# source: https://arxiv.org/pdf/1606.02008.pdf +def ive_fraction_approx(v, z): + # I_(v/2)(k) / I_(v/2 - 1)(k) >= z / (v-1 + ((v+1)^2 + z^2)^0.5 + return z / (v - 1 + torch.pow(torch.pow(v + 1, 2) + torch.pow(z, 2), 0.5)) + + +# source: https://arxiv.org/pdf/1902.02603.pdf +def ive_fraction_approx2(v, z, eps=1e-20): + def delta_a(a): + lamb = v + (a - 1.0) / 2.0 + return (v - 0.5) + lamb / ( + 2 * torch.sqrt((torch.pow(lamb, 2) + torch.pow(z, 2)).clamp(eps)) + ) + + delta_0 = delta_a(0.0) + delta_2 = delta_a(2.0) + B_0 = z / (delta_0 + torch.sqrt(torch.pow(delta_0, 2) + torch.pow(z, 2)).clamp(eps)) + B_2 = z / (delta_2 + torch.sqrt(torch.pow(delta_2, 2) + torch.pow(z, 2)).clamp(eps)) + + return (B_0 + B_2) / 2.0 diff --git a/neurometry/estimators/geometry/models/losses.py b/neurometry/estimators/geometry/models/losses.py new file mode 100644 index 0000000..21fb2a8 --- /dev/null +++ b/neurometry/estimators/geometry/models/losses.py @@ -0,0 +1,176 @@ +"""Losses.""" + +import torch + +from neurometry.estimators.curvature.hyperspherical.distributions import ( + hyperspherical_uniform, + von_mises_fisher, +) + + +def elbo(x, x_mu, posterior_params, z, labels, config): + """Compute the ELBO for the VAE loss. + + The VAE elbo loss is defined as: + = reconstruction loss + Kl divergence + over all elements and batch + + Notes + ----- + see Appendix B from VAE paper: + Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014 + https://arxiv.org/abs/1312.6114 + 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2) + + Parameters + ---------- + x : array-like, shape=[batch_size, data_dim] + Input data. + gen_likelihood_params : tuple + Learned distributional parameters of generative model. + (e.g., (x_mu,x_logvar) for Gaussian). + posterior_params : tuple + Learned distributional parameters of approximate posterior. + (e.g., (z_mu,z_logvar) for Gaussian). + config : module + Module specifying various model hyperparameters + + Returns + ------- + _ : array-like, shape=[batch_size,] + VAE elbo loss function on each batch element. + """ + + if config.posterior_type == "gaussian": + z_mu, z_logvar = posterior_params + z_var = torch.exp(z_logvar) + kld = -0.5 * torch.sum(1 + z_logvar - z_mu.pow(2) - z_var) + + if config.posterior_type == "hyperspherical": + z_mu, z_kappa = posterior_params + q_z = von_mises_fisher.VonMisesFisher(z_mu, z_kappa) + p_z = hyperspherical_uniform.HypersphericalUniform( + config.latent_dim - 1, device=config.device + ) + kld = torch.distributions.kl.kl_divergence(q_z, p_z).mean() + + if config.posterior_type == "toroidal": + z_theta_mu, z_theta_kappa, z_phi_mu, z_phi_kappa = posterior_params + q_z_theta = von_mises_fisher.VonMisesFisher(z_theta_mu, z_theta_kappa) + q_z_phi = von_mises_fisher.VonMisesFisher(z_phi_mu, z_phi_kappa) + p_z = hyperspherical_uniform.HypersphericalUniform( + config.latent_dim - 1, device=config.device + ) + kld_theta = torch.distributions.kl.kl_divergence(q_z_theta, p_z).mean() + kld_phi = torch.distributions.kl.kl_divergence(q_z_phi, p_z).mean() + kld = kld_theta + kld_phi + + if config.gen_likelihood_type == "gaussian": + recon_loss = torch.mean((x - x_mu).pow(2)) + else: + raise NotImplementedError + + if config.dataset_name == "s1_synthetic": + recon_loss = recon_loss / (config.radius**2) + + latent_loss = latent_regularization_loss(labels, z, config) + moving_loss = moving_forward_loss(z, config) + + elbo_loss = ( + config.alpha * recon_loss + + config.beta * kld + + config.gamma * latent_loss + + config.gamma_moving * moving_loss + ) + return elbo_loss, recon_loss, kld, latent_loss, moving_loss + + +def latent_regularization_loss(labels, z, config): + """Compute squared geodesic distance between outside and inside's variables. + + For example, this computes the squared difference in angles between the lab's + angle and the latent angle. + + Parameters + ---------- + labels : array-like, shape=[batch_size, latent_dim] + Task variables recorded. + z : array-like, shape=[batch_size, latent_dim] + Latent variables on the template manifold. + config : object-like + Configuration of the experiment in wandb format. + + Returns + ------- + _ : array-like, shape=[batch_size, 1] + Squared geodesic distance, i.e. the loss. + """ + if config.dataset_name == "s1_synthetic": + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + angle_loss = torch.mean(1 - torch.cos(latent_angles - labels)) + latent_loss = angle_loss + elif config.dataset_name in ("experimental", "three_place_cells_synthetic"): + labels = labels * (torch.pi / 180) + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + angle_loss = torch.mean(1 - torch.cos(latent_angles - labels)) + latent_loss = angle_loss + elif config.dataset_name == "s2_synthetic": + latent_thetas = torch.arccos(z[:, 2]) + latent_phis = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + thetas_loss = torch.mean(1 - torch.cos(latent_thetas - labels[:, 0])) + phis_loss = torch.mean( + torch.sin(latent_thetas) + * torch.sin(labels[:, 0]) + * (1 - torch.cos(latent_phis - labels[:, 1])) + ) + latent_loss = thetas_loss + phis_loss + elif config.dataset_name == "t2_synthetic": + latent_thetas = ( + torch.atan2(z[:, 2], 2 - torch.sqrt(z[:, 0] ** 2 + z[:, 1] ** 2)) + + 2 * torch.pi + ) % (2 * torch.pi) + latent_phis = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + thetas_loss = torch.mean(1 - torch.cos(latent_thetas - labels[:, 0])) + phis_loss = torch.mean(1 - torch.cos(latent_phis - labels[:, 1])) + latent_loss = thetas_loss + phis_loss + elif config.dataset_name == "grid_cells": + return 0 + + return latent_loss**2 + + +def moving_forward_loss(z, config): + """Compute difference between two consecutive z's. + + This loss will enforce that the latent variable (the angles) only increase + when the rat moves forward. + + In order to enforce increasing values of z's, the loss is not squared. + minimizing -(z_t+1 - z_t) will force it to be negative, i.e. z_t+1 > z_t. + + We remove the situation where the rat crosses the angles 360 --> 0. + Note that atol=0.089 radians corresponds to 5 degrees, which is the max degree + difference observed in the rat's labelled lab angles. + + Parameters + ---------- + """ + if config.dataset_name != "experimental": + # print( + # "WARNING: Moving forward loss only implemented for experimental data + # --> Skipped." + # ) + return torch.zeros(1).to(config.device) + if len(z) == 1: + return torch.zeros(1).to(config.device) + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % (2 * torch.pi) + diff = latent_angles[1:] - latent_angles[:-1] + # only keep angles where the rat is not crossing 360 --> 0 + mask = ~torch.isclose( + 2 * torch.pi - latent_angles[:-1], torch.tensor(0.0), atol=0.089 + ) + loss = -diff[mask] + if len(loss) == 0: + return torch.zeros(1).to(config.device) + return torch.mean(loss) + diff --git a/neurometry/estimators/geometry/models/spherical_vae.py b/neurometry/estimators/geometry/models/spherical_vae.py new file mode 100644 index 0000000..cc79c39 --- /dev/null +++ b/neurometry/estimators/geometry/models/spherical_vae.py @@ -0,0 +1,263 @@ +"""G-manifold deep learning. + +This file gathers deep learning models related to G-manifold learning. +""" + +import torch +from torch.nn import functional as F + +from neurometry.estimators.geometry.models import train_config as train_config +from neurometry.estimators.geometry.models.hyperspherical.distributions import ( + hyperspherical_uniform, + von_mises_fisher, +) + + +class SphericalVAE(torch.nn.Module): + """VAE with Linear (fully connected) layers. + + Parameters + ---------- + extrinsic_dim : int + Extrinsic dimension of neural data. + This is the dimension of a hyperplane in which neural activity lies within neural state space. + latent_dim : int + Dimension of the latent space. This is the dimension of the minimal euclidean embedding of the task-relevant variables. + """ + + def __init__( + self, + extrinsic_dim, + latent_dim, + sftbeta=4.5, + encoder_width=400, + encoder_depth=2, + decoder_width=400, + decoder_depth=2, + drop_out_p=0.0, + ): + super().__init__() + self.extrinsic_dim = extrinsic_dim + self.sftbeta = sftbeta + self.latent_dim = latent_dim + self.drop_out_p = drop_out_p + + decoder_width = encoder_width + decoder_depth = encoder_depth + + self.encoder_fc = torch.nn.Linear(self.extrinsic_dim, encoder_width) + self.encoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(encoder_width, encoder_width) + for _ in range(encoder_depth) + ] + ) + + self.fc_z_mu = torch.nn.Linear(encoder_width, self.latent_dim) + self.fc_z_logvar = torch.nn.Linear(encoder_width, 1) # kappa + + self.decoder_fc = torch.nn.Linear(self.latent_dim, decoder_width) + self.decoder_linears = torch.nn.ModuleList( + [ + torch.nn.Linear(decoder_width, decoder_width) + for _ in range(decoder_depth) + ] + ) + + self.fc_x_mu = torch.nn.Linear(decoder_width, self.extrinsic_dim) + + self.drop_out = torch.nn.Dropout(p=self.drop_out_p) + + def encode(self, x): + """Encode input into mean and log-variance. + + The parameters mean (mu) and variance (computed + from logvar) defines a multivariate Gaussian + that represents the approximate posterior of the + latent variable z given the input x. + + Parameters + ---------- + x : array-like, shape=[batch_size, extrinsic_dim] + Input data. + + Returns + ------- + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + h = F.softplus(self.encoder_fc(x.double()), beta=self.sftbeta) + + for _i_layer, layer in enumerate(self.encoder_linears): + # h = self.drop_out(h) + h = layer(h) + h = F.softplus(h, beta=self.sftbeta) + + z_mu = self.fc_z_mu(h) + z_kappa = F.softplus(self.fc_z_logvar(h)) + 1 + + return z_mu, z_kappa + + def reparameterize(self, posterior_params): + """ + Apply reparameterization trick. We 'externalize' the + randomness in z by re-parameterizing the variable as + a deterministic and differentiable function of x, + the encoder weights, and a new random variable eps. + + Parameters + ---------- + posterior_params : tuple + Distributional parameters of approximate posterior. ((e.g.), (z_mu,z_logvar) for Gaussian. + + Returns + ------- + + z: array-like, shape = [batch_size, latent_dim] + Re-parameterized latent variable. + """ + + z_mu, z_kappa = posterior_params + q_z = von_mises_fisher.VonMisesFisher(z_mu, z_kappa) + + return q_z.rsample() + + def decode(self, z): + """Decode latent variable z into data. + + Parameters + ---------- + z : array-like, shape=[batch_size, latent_dim] + Input to the decoder. + + Returns + ------- + _ : array-like, shape=[batch_size, extrinsic_dim] + Reconstructed data corresponding to z. + """ + + h = F.softplus(self.decoder_fc(z), beta=self.sftbeta) + + for _i_layer, layer in enumerate(self.decoder_linears): + # h = self.drop_out(h) + h = layer(h) + h = F.softplus(h, beta=self.sftbeta) + + return self.fc_x_mu(h) + + def forward(self, x): + """Run VAE: Encode, sample and decode. + + Parameters + ---------- + x : array-like, shape=[batch_size, extrinsic_dim] + Input data. + + Returns + ------- + _ : array-like, shape=[batch_size, extrinsic_dim] + Reconstructed data corresponding to z. + mu : array-like, shape=[batch_size, latent_dim] + Mean of multivariate Gaussian in latent space. + logvar : array-like, shape=[batch_size, latent_dim] + Vector representing the diagonal covariance of the + multivariate Gaussian in latent space. + """ + + posterior_params = self.encode(x) + z = self.reparameterize(posterior_params) + x_mu = self.decode(z) + return z, x_mu, posterior_params + + def _elbo(self, x, x_mu, posterior_params): + """Compute the ELBO for the VAE loss. + + The VAE elbo loss is defined as: + = reconstruction loss + Kl divergence + over all elements and batch + + Notes + ----- + see Appendix B from VAE paper: + Kingma and Welling. Auto-Encoding Variational Bayes. ICLR, 2014 + https://arxiv.org/abs/1312.6114 + 0.5 * sum(1 + log(sigma^2) - mu^2 - sigma^2) + + Parameters + ---------- + x : array-like, shape=[batch_size, data_dim] + Input data. + gen_likelihood_params : tuple + Learned distributional parameters of generative model. + (e.g., (x_mu,x_logvar) for Gaussian). + posterior_params : tuple + Learned distributional parameters of approximate posterior. + (e.g., (z_mu,z_logvar) for Gaussian). + + Returns + ------- + _ : array-like, shape=[batch_size,] + VAE elbo loss function on each batch element. + """ + + z_mu, z_kappa = posterior_params + q_z = von_mises_fisher.VonMisesFisher(z_mu, z_kappa) + p_z = hyperspherical_uniform.HypersphericalUniform( + self.latent_dim - 1, device=train_config.device + ) + kld = torch.distributions.kl.kl_divergence(q_z, p_z).mean() + + recon_loss = torch.mean((x - x_mu).pow(2)) + + + return train_config.recon_weight * recon_loss + train_config.kld_weight * kld + + def _latent_regularization_loss(self, labels, z): + """Compute squared geodesic distance between outside and inside's variables. + + For example, this computes the squared difference in angles between the lab's + angle and the latent angle. + + Parameters + ---------- + labels : array-like, shape=[batch_size, latent_dim] + Task variables recorded. + z : array-like, shape=[batch_size, latent_dim] + Latent variables on the template manifold. + config : object-like + Configuration of the experiment in wandb format. + + Returns + ------- + _ : array-like, shape=[batch_size, 1] + Squared geodesic distance, i.e. the loss. + """ + if self.latent_dim == 2: + latent_angles = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % ( + 2 * torch.pi + ) + angle_loss = torch.mean(1 - torch.cos(latent_angles - labels)) + latent_loss = angle_loss + elif self.latent_dim == 3: + latent_thetas = torch.arccos(z[:, 2]) + latent_phis = (torch.atan2(z[:, 1], z[:, 0]) + 2 * torch.pi) % ( + 2 * torch.pi + ) + thetas_loss = torch.mean(1 - torch.cos(latent_thetas - labels[:, 0])) + phis_loss = torch.mean( + torch.sin(latent_thetas) + * torch.sin(labels[:, 0]) + * (1 - torch.cos(latent_phis - labels[:, 1])) + ) + latent_loss = thetas_loss + phis_loss + + return latent_loss**2 + + def criterion(self, x, x_mu, posterior_params, labels, z): + elbo_loss = self._elbo(x, x_mu, posterior_params) + latent_loss = self._latent_regularization_loss(labels, z) + + return elbo_loss + train_config.latent_weight * latent_loss diff --git a/neurometry/estimators/geometry/toroidal_vae.py b/neurometry/estimators/geometry/models/toroidal_vae.py similarity index 85% rename from neurometry/estimators/geometry/toroidal_vae.py rename to neurometry/estimators/geometry/models/toroidal_vae.py index 191f78c..e3eb2b7 100644 --- a/neurometry/estimators/geometry/toroidal_vae.py +++ b/neurometry/estimators/geometry/models/toroidal_vae.py @@ -17,35 +17,29 @@ class ToroidalVAE(torch.nn.Module): Parameters ---------- - data_dim : int - Dimension of input data. - Example: 40 for neural recordings of 40 units/clusters. + extrinsic_dim : int + Extrinsic dimension of neural data. + This is the dimension of a hyperplane in which neural activity lies within neural state space. latent_dim : int - Dimension of the latent space. - Example: 2. + Dimension of the latent space. This is the dimension of the minimal euclidean embedding of the task-relevant variables. """ def __init__( self, - data_dim, + extrinsic_dim, latent_dim, - sftbeta, - encoder_width, - encoder_depth, - decoder_width, - decoder_depth, - posterior_type, + sftbeta=4.5, + encoder_width=400, + encoder_depth=2, + decoder_width=400, + decoder_depth=2, ): super().__init__() - self.data_dim = data_dim + self.extrinsic_dim = extrinsic_dim self.sftbeta = sftbeta self.latent_dim = latent_dim - self.posterior_type = posterior_type - # decoder_width = encoder_width - # decoder_depth = encoder_depth - - self.encoder_fc = torch.nn.Linear(self.data_dim, encoder_width) + self.encoder_fc = torch.nn.Linear(self.extrinsic_dim, encoder_width) self.encoder_linears = torch.nn.ModuleList( [ torch.nn.Linear(encoder_width, encoder_width) @@ -67,7 +61,7 @@ def __init__( ] ) - self.fc_x_mu = torch.nn.Linear(decoder_width, self.data_dim) + self.fc_x_mu = torch.nn.Linear(decoder_width, self.extrinsic_dim) def encode(self, x): """Encode input into mean and log-variance. @@ -79,7 +73,7 @@ def encode(self, x): Parameters ---------- - x : array-like, shape=[batch_size, data_dim] + x : array-like, shape=[batch_size, extrinsic_dim] Input data. Returns @@ -162,7 +156,7 @@ def decode(self, z): Returns ------- - _ : array-like, shape=[batch_size, data_dim] + _ : array-like, shape=[batch_size, extrinsic_dim] Reconstructed data corresponding to z. """ @@ -178,12 +172,12 @@ def forward(self, x): Parameters ---------- - x : array-like, shape=[batch_size, data_dim] + x : array-like, shape=[batch_size, extrinsic_dim] Input data. Returns ------- - _ : array-like, shape=[batch_size, data_dim] + _ : array-like, shape=[batch_size, extrinsic_dim] Reconstructed data corresponding to z. mu : array-like, shape=[batch_size, latent_dim] Mean of multivariate Gaussian in latent space. diff --git a/neurometry/estimators/geometry/models/train.py b/neurometry/estimators/geometry/models/train.py new file mode 100644 index 0000000..36db748 --- /dev/null +++ b/neurometry/estimators/geometry/models/train.py @@ -0,0 +1,107 @@ +"""Training and testing functions for VAE model.""" + +import copy + +# import wandb +import numpy as np + + +def train_test(model, train_loader, test_loader, optimizer, scheduler, config): + train_losses = [] + test_losses = [] + lowest_test_loss = np.inf + for epoch in range(1, config.num_epochs + 1): + train_loss = run_one_epoch( + epoch=epoch, + model=model, + data_loader=train_loader, + device=config.device, + optimizer=optimizer, + train=True, + ) + train_losses.append(train_loss) + + test_loss = run_one_epoch( + epoch=epoch, + model=model, + data_loader=test_loader, + device=config.device, + optimizer=optimizer, + train=False, + ) + + if scheduler is not None: + scheduler.step(test_loss) + + test_losses.append(test_loss) + + if epoch == 1 or test_loss < lowest_test_loss: + lowest_test_loss = test_loss + best_model = copy.deepcopy(model) + + return train_losses, test_losses, best_model + + +def run_one_epoch(epoch, model, data_loader, device, optimizer, train=True): + """Run one epoch on the train or test set. + + Parameters + ---------- + epoch : int + Index of current epoch. + train : bool, optional + Whether this is a training epoch (default is True). + + Returns + ------- + loss : float + Loss on epoch. + """ + if train: + model.train() + mode = "Train" + else: + model.eval() + mode = "Test" + + epoch_loss = 0 + + for batch_idx, batch_data in enumerate(data_loader): + x_batch, labels = batch_data + x_batch = x_batch.to(device) + labels = labels.float().to(device) + + if train: + optimizer.zero_grad() + + # Forward pass + z_batch, x_mu_batch, posterior_params = model(x_batch) + + # Compute loss + loss = model.criterion(x_batch, x_mu_batch, posterior_params, labels, z_batch) + epoch_loss += loss.item() + + # Backpropagation and optimizer step only during training + if train: + loss.backward() + optimizer.step() + + # Logging during training + if train and batch_idx % 20 == 0: + print( + f"{mode} Epoch: {epoch} [{batch_idx * len(x_batch)}/{len(data_loader.dataset)} " + f"({100.0 * batch_idx / len(data_loader):.0f}%)]\tLoss: {loss.item() / len(x_batch):.6f}" + ) + + epoch_loss /= len(data_loader.dataset) + + # # Logging with wandb + # wandb.log( + # { + # f"{mode.lower()}_loss": epoch_loss, + # }, + # step=epoch, + # ) + + print(f"====> {mode} Epoch: {epoch} Average loss: {epoch_loss:.4f}") + return epoch_loss diff --git a/neurometry/estimators/geometry/models/train_config.py b/neurometry/estimators/geometry/models/train_config.py new file mode 100644 index 0000000..4bb241a --- /dev/null +++ b/neurometry/estimators/geometry/models/train_config.py @@ -0,0 +1,13 @@ +import torch + +# hardware +device = "cuda" if torch.cuda.is_available() else "cpu" + +# training +num_epochs = 500 +batch_size = 64 +lr = 1e-3 + +recon_weight = 1.0 # weight for the reconstruction loss +kld_weight = 0.03 # 0.03 # weight for KL loss +latent_weight = 10 # weight for latent regularization loss diff --git a/neurometry/estimators/geometry/models/utils.py b/neurometry/estimators/geometry/models/utils.py new file mode 100644 index 0000000..ef0f6f3 --- /dev/null +++ b/neurometry/estimators/geometry/models/utils.py @@ -0,0 +1,248 @@ +"""Utils to import data from matlab.""" + +import mat73 +import numpy as np +import scipy.io +import torch +from scipy.signal import savgol_filter + +from neurometry.estimators.curvature.datasets.experimental import load_neural_activity +from neurometry.estimators.curvature.datasets.synthetic import ( + load_place_cells, + load_points, + load_s1_synthetic, + load_s2_synthetic, + load_t2_synthetic, +) + + +def load(config): + """Load dataset according to configuration in config. + + Parameters + ---------- + config + + Returns + ------- + dataset_torch : torch.Tensor + Dataset (without labels) as a torch tensor. + Each row represents one data point. + labels : pd.DataFrame + Dataframe of labels corresponding to dataset_torch + train_loader : torch.DataLoader + Loader that yields minibatches (data and labels) from the + train dataset. + test_loader : torch.DataLoader + Loader that yields minibatches (data and labels) from the + test dataset. + """ + if config.dataset_name == "experimental": + dataset, labels = load_neural_activity( + expt_id=config.expt_id, timestep_microsec=config.timestep_microsec + ) + dataset = dataset[labels["velocities"] > 5] + labels = labels[labels["velocities"] > 5] + dataset = np.log(dataset.astype(np.float32) + 1) + + if config.smooth is True: + dataset_smooth = np.zeros_like(dataset) + for _ in range(dataset.shape[1]): + dataset_smooth[:, _] = savgol_filter( + dataset[:, _], window_length=40, polyorder=2 + ) + dataset = dataset_smooth + dataset = (dataset - np.min(dataset)) / (np.max(dataset) - np.min(dataset)) + + gain_counts = labels["gains"].value_counts() + gain_1 = 1 + one_gain = labels["gains"].value_counts().is_unique + if one_gain: + print(f"The dataset contains only one gain value: {gain_counts.index[0]}") + gain = gain_1 + else: + print( + "The dataset transitions between two gains:" + f" {gain_counts.index[0]:4f} and {gain_counts.index[1]:4f}." + ) + if config.select_gain_1: + gain = gain_1 + print(f"We select gain 1: gain = {gain_1}.") + else: + other_gain = gain_counts.index[0] + if other_gain == gain_1: + other_gain = gain_counts.index[1] + gain = other_gain + print(f"We select the other gain: gain = {other_gain:4f}.") + config.update({"gain": gain}) + dataset = dataset[labels["gains"] == gain] + labels = labels[labels["gains"] == gain] + + elif config.dataset_name == "synthetic": + dataset, labels = load_place_cells() + dataset = np.log(dataset.astype(np.float32) + 1) + dataset = (dataset - np.min(dataset)) / (np.max(dataset) - np.min(dataset)) + elif config.dataset_name == "points": + dataset, labels = load_points() + dataset = dataset.astype(np.float32) + elif config.dataset_name == "s1_synthetic": + dataset, labels = load_s1_synthetic( + synthetic_rotation=config.synthetic_rotation, + n_times=config.n_times, + radius=config.radius, + n_wiggles=config.n_wiggles, + geodesic_distortion_amp=config.geodesic_distortion_amp, + embedding_dim=config.embedding_dim, + noise_var=config.noise_var, + geodesic_distortion_func=config.geodesic_distortion_func, + ) + elif config.dataset_name == "s2_synthetic": + dataset, labels = load_s2_synthetic( + synthetic_rotation=config.synthetic_rotation, + n_times=config.n_times, + radius=config.radius, + geodesic_distortion_amp=config.geodesic_distortion_amp, + embedding_dim=config.embedding_dim, + noise_var=config.noise_var, + ) + elif config.dataset_name == "t2_synthetic": + dataset, labels = load_t2_synthetic( + synthetic_rotation=config.synthetic_rotation, + n_times=config.n_times, + major_radius=config.major_radius, + minor_radius=config.minor_radius, + geodesic_distortion_amp=config.geodesic_distortion_amp, + embedding_dim=config.embedding_dim, + noise_var=config.noise_var, + ) + print(f"Dataset shape: {dataset.shape}.") + if isinstance(dataset, np.ndarray): + dataset_torch = torch.from_numpy(dataset) + else: + dataset_torch = dataset + # dataset_torch = dataset_torch - torch.mean(dataset_torch, dim=0) + + train_num = int(round(0.7 * len(dataset))) # 70% training + indices = np.arange(len(dataset)) + + train_indices = np.arange(train_num) + rng = np.random.default_rng(seed=0) + if config.batch_shuffle: + # Note: this breaks the temporal ordering. + train_indices = rng.choice(indices, train_num, replace=False) + + test_indices = np.delete(indices, train_indices) + train_dataset = dataset[train_indices] + train_labels = labels.iloc[train_indices] + + test_dataset = dataset[test_indices] + test_labels = labels.iloc[test_indices] + + train_dataset = dataset[train_indices] + train_labels = labels.iloc[train_indices] + test_dataset = dataset[test_indices] + test_labels = labels.iloc[test_indices] + + # The angles are positional angles in the lab frame + if config.dataset_name in ( + "experimental", + "s1_synthetic", + ) or config.dataset_name in ("three_place_cells_synthetic"): + train = [] + for data, label in zip(train_dataset, train_labels["angles"], strict=False): + train.append([data, float(label)]) + test = [] + for data, label in zip(test_dataset, test_labels["angles"], strict=False): + test.append([data, float(label)]) + elif config.dataset_name in ("s2_synthetic", "t2_synthetic"): + train = [] + for data, theta, phi in zip( + train_dataset, train_labels["thetas"], train_labels["phis"], strict=False + ): + train.append([data, torch.tensor([float(theta), float(phi)])]) + test = [] + for data, theta, phi in zip( + test_dataset, test_labels["thetas"], test_labels["phis"], strict=False + ): + test.append([data, torch.tensor([float(theta), float(phi)])]) + + train_loader = torch.utils.data.DataLoader(train, batch_size=config.batch_size) + test_loader = torch.utils.data.DataLoader(test, batch_size=config.batch_size) + return dataset_torch, labels, train_loader, test_loader + + +def loadmat(filename): + """Improved loadmat (replacement for scipy.io.loadmat). + + Ensures correct loading of python dictionaries from mat files. + + Inspired by: https://stackoverflow.com/a/29126361/572908. + + Parameters + ---------- + filename : str + Name of the file containing matlab data. + Example: expt34.mat + """ + + def _has_struct(elem): + """Check if elem is an array & if its first item is a struct.""" + return ( + isinstance(elem, np.ndarray) + and (elem.size > 0) + and isinstance(elem[0], scipy.io.matlab.mio5_params.mat_struct) + ) + + def _check_keys(d): + """Check if entries in dictionary are mat-objects. + + If they are mat-objects, then todict is called to change + them to nested dictionaries. + """ + for key in d: + elem = d[key] + if isinstance(elem, scipy.io.matlab.mio5_params.mat_struct): + d[key] = _todict(elem) + elif _has_struct(elem): + d[key] = _tolist(elem) + return d + + def _todict(matobj): + """Build nested dictionaries from mat-objects. + + This is a recursive function. + """ + d = {} + for strg in matobj._fieldnames: + elem = matobj.__dict__[strg] + if isinstance(elem, scipy.io.matlab.mio5_params.mat_struct): + d[strg] = _todict(elem) + elif _has_struct(elem): + d[strg] = _tolist(elem) + else: + d[strg] = elem + return d + + def _tolist(ndarray): + """Build lists from cellarays. + + This is a recursive function that constructs lists from + cellarrays (which are loaded as numpy ndarrays). + + It is recursing into the elements if they contain matobjects. + """ + elem_list = [] + for sub_elem in ndarray: + if isinstance(sub_elem, scipy.io.matlab.mio5_params.mat_struct): + elem_list.append(_todict(sub_elem)) + elif _has_struct(sub_elem): + elem_list.append(_tolist(sub_elem)) + else: + elem_list.append(sub_elem) + return elem_list + + try: + data = scipy.io.loadmat(filename, struct_as_record=False, squeeze_me=True) + except Exception: + data = mat73.loadmat(filename) + return _check_keys(data) diff --git a/neurometry/estimators/geometry/spherical_vae.py b/neurometry/estimators/geometry/spherical_vae.py deleted file mode 100644 index fd32f77..0000000 --- a/neurometry/estimators/geometry/spherical_vae.py +++ /dev/null @@ -1,172 +0,0 @@ -"""G-manifold deep learning. - -This file gathers deep learning models related to G-manifold learning. -""" - -import torch -from torch.nn import functional as F - -from neurometry.estimators.curvature.hyperspherical.distributions.von_mises_fisher import ( - VonMisesFisher, -) - - -class SphericalVAE(torch.nn.Module): - """VAE with Linear (fully connected) layers. - - Parameters - ---------- - num_neurons : int - Number of neurons in the input data. This is the ambient dimension of the neural state space. - Example: 40 for neural recordings of 40 neurons. - latent_dim : int - Dimension of the latent space. - Example: 2. - """ - - def __init__( - self, - num_neurons, - latent_dim, - sftbeta, - encoder_width=400, - encoder_depth=2, - decoder_width=400, - decoder_depth=2, - drop_out_p=0.0, - ): - super().__init__() - self.num_neurons = num_neurons - self.sftbeta = sftbeta - self.latent_dim = latent_dim - self.drop_out_p = drop_out_p - - decoder_width = encoder_width - decoder_depth = encoder_depth - - self.encoder_fc = torch.nn.Linear(self.num_neurons, encoder_width) - self.encoder_linears = torch.nn.ModuleList( - [ - torch.nn.Linear(encoder_width, encoder_width) - for _ in range(encoder_depth) - ] - ) - - self.fc_z_mu = torch.nn.Linear(encoder_width, self.latent_dim) - self.fc_z_logvar = torch.nn.Linear(encoder_width, 1) # kappa - - self.decoder_fc = torch.nn.Linear(self.latent_dim, decoder_width) - self.decoder_linears = torch.nn.ModuleList( - [ - torch.nn.Linear(decoder_width, decoder_width) - for _ in range(decoder_depth) - ] - ) - - self.fc_x_mu = torch.nn.Linear(decoder_width, self.num_neurons) - - self.drop_out = torch.nn.Dropout(p=self.drop_out_p) - - def encode(self, x): - """Encode input into mean and log-variance. - - The parameters mean (mu) and variance (computed - from logvar) defines a multivariate Gaussian - that represents the approximate posterior of the - latent variable z given the input x. - - Parameters - ---------- - x : array-like, shape=[batch_size, num_neurons] - Input data. - - Returns - ------- - mu : array-like, shape=[batch_size, latent_dim] - Mean of multivariate Gaussian in latent space. - logvar : array-like, shape=[batch_size, latent_dim] - Vector representing the diagonal covariance of the - multivariate Gaussian in latent space. - """ - h = F.softplus(self.encoder_fc(x.double()), beta=self.sftbeta) - - for _i_layer, layer in enumerate(self.encoder_linears): - # h = self.drop_out(h) - h = layer(h) - h = F.softplus(h, beta=self.sftbeta) - - z_mu = self.fc_z_mu(h) - z_kappa = F.softplus(self.fc_z_logvar(h)) + 1 - - return z_mu, z_kappa - - def reparameterize(self, posterior_params): - """ - Apply reparameterization trick. We 'eternalize' the - randomness in z by re-parameterizing the variable as - a deterministic and differentiable function of x, - the encoder weights, and a new random variable eps. - - Parameters - ---------- - posterior_params : tuple - Distributional parameters of approximate posterior. ((e.g.), (z_mu,z_logvar) for Gaussian. - - Returns - ------- - - z: array-like, shape = [batch_size, latent_dim] - Re-parameterized latent variable. - """ - - z_mu, z_kappa = posterior_params - q_z = VonMisesFisher(z_mu, z_kappa) - - return q_z.rsample() - - def decode(self, z): - """Decode latent variable z into data. - - Parameters - ---------- - z : array-like, shape=[batch_size, latent_dim] - Input to the decoder. - - Returns - ------- - _ : array-like, shape=[batch_size, num_neurons] - Reconstructed data corresponding to z. - """ - - h = F.softplus(self.decoder_fc(z), beta=self.sftbeta) - - for _i_layer, layer in enumerate(self.decoder_linears): - # h = self.drop_out(h) - h = layer(h) - h = F.softplus(h, beta=self.sftbeta) - - return self.fc_x_mu(h) - - def forward(self, x): - """Run VAE: Encode, sample and decode. - - Parameters - ---------- - x : array-like, shape=[batch_size, num_neurons] - Input data. - - Returns - ------- - _ : array-like, shape=[batch_size, num_neurons] - Reconstructed data corresponding to z. - mu : array-like, shape=[batch_size, latent_dim] - Mean of multivariate Gaussian in latent space. - logvar : array-like, shape=[batch_size, latent_dim] - Vector representing the diagonal covariance of the - multivariate Gaussian in latent space. - """ - - posterior_params = self.encode(x) - z = self.reparameterize(posterior_params) - x_mu = self.decode(z) - return z, x_mu, posterior_params diff --git a/neurometry/estimators/topology/topology_classifier.py b/neurometry/estimators/topology/topology_classifier.py index a4657e4..cf01c2a 100644 --- a/neurometry/estimators/topology/topology_classifier.py +++ b/neurometry/estimators/topology/topology_classifier.py @@ -60,7 +60,7 @@ def _generate_ref_data(self, input_data): points=circle_task_points, encoding_dim=encoding_dim, nonlinearity="sigmoid", - scales=5*gs.random.rand(encoding_dim), + scales=5 * gs.random.rand(encoding_dim), fano_factor=self.fano_factor, ) circle_point_clouds.append(circle_noisy_points) @@ -72,7 +72,7 @@ def _generate_ref_data(self, input_data): points=sphere_task_points, encoding_dim=encoding_dim, nonlinearity="sigmoid", - scales=5*gs.random.rand(encoding_dim), + scales=5 * gs.random.rand(encoding_dim), fano_factor=self.fano_factor, ) sphere_point_clouds.append(sphere_noisy_points) @@ -84,7 +84,7 @@ def _generate_ref_data(self, input_data): points=torus_task_points, encoding_dim=encoding_dim, nonlinearity="sigmoid", - scales=5*gs.random.rand(encoding_dim), + scales=5 * gs.random.rand(encoding_dim), fano_factor=self.fano_factor, ) torus_point_clouds.append(torus_noisy_points) @@ -143,7 +143,9 @@ def fit(self, X, y=None): """ if not isinstance(X, np.ndarray | torch.Tensor): - raise ValueError(f"Expected array-like input for X, but got {type(X).__name__}.") + raise ValueError( + f"Expected array-like input for X, but got {type(X).__name__}." + ) ref_point_clouds, ref_labels = self._generate_ref_data(X) self.ref_labels = ref_labels @@ -270,4 +272,3 @@ def compute_diagrams_shuffle(X, num_shuffles, seed=0, homology_dimensions=(0, 1) return compute_persistence_diagrams( [X, *shuffled_Xs], homology_dimensions=homology_dimensions ) - diff --git a/tests/neurometry/estimators/topology/test_topology_classifier.py b/tests/neurometry/estimators/topology/test_topology_classifier.py index 203b80a..c20fa11 100644 --- a/tests/neurometry/estimators/topology/test_topology_classifier.py +++ b/tests/neurometry/estimators/topology/test_topology_classifier.py @@ -112,4 +112,3 @@ def test_not_fitted_error(self): ) with pytest.raises(NotFittedError): classifier.predict(self.circle_data) - diff --git a/tutorials/04_methods_estimate_manifold_immersion.ipynb b/tutorials/04_methods_estimate_manifold_immersion.ipynb new file mode 100644 index 0000000..7f24cec --- /dev/null +++ b/tutorials/04_methods_estimate_manifold_immersion.ipynb @@ -0,0 +1,9026 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Working directory: /home/facosta/neurometry/neurometry\n", + "Directory added to path: /home/facosta/neurometry\n", + "Directory added to path: /home/facosta/neurometry/neurometry\n", + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n", + "The jupyter_black extension is already loaded. To reload it, use:\n", + " %reload_ext jupyter_black\n" + ] + } + ], + "source": [ + "import setup\n", + "\n", + "setup.main()\n", + "%load_ext autoreload\n", + "%autoreload 2\n", + "%load_ext jupyter_black\n", + "\n", + "import neurometry.datasets.synthetic as synthetic\n", + "import numpy as np\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "import os\n", + "\n", + "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n", + "import geomstats.backend as gs" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [], + "source": [ + "task_points, intrinsic_coords = synthetic.hypersphere(1, 1000)\n", + "noisy_points, manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=task_points,\n", + " encoding_dim=3,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.array([5, 3, 1]),\n", + ")\n", + "\n", + "X = manifold_points\n", + "labels = intrinsic_coords" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [], + "source": [ + "from neurometry.estimators.geometry.immersion_estimator import ImmersionEstimator" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [], + "source": [ + "extrinsic_dim = 3\n", + "topology = \"circle\"\n", + "device = \"cuda\"\n", + "\n", + "immersion_estimator = ImmersionEstimator(extrinsic_dim, topology, device=device)" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Train Epoch: 1 [0/800 (0%)]\tLoss: 202.562974\n", + "====> Train Epoch: 1 Average loss: 188.1801\n", + "====> Test Epoch: 1 Average loss: 165.0614\n", + "Train Epoch: 2 [0/800 (0%)]\tLoss: 134.526717\n", + "====> Train Epoch: 2 Average loss: 74.1690\n", + "====> Test Epoch: 2 Average loss: 70.4762\n", + "Train Epoch: 3 [0/800 (0%)]\tLoss: 56.325479\n", + "====> Train Epoch: 3 Average loss: 47.7297\n", + "====> Test Epoch: 3 Average loss: 57.2686\n", + "Train Epoch: 4 [0/800 (0%)]\tLoss: 42.957465\n", + "====> Train Epoch: 4 Average loss: 44.2286\n", + "====> Test Epoch: 4 Average loss: 54.5528\n", + "Train Epoch: 5 [0/800 (0%)]\tLoss: 42.971686\n", + "====> Train Epoch: 5 Average loss: 44.1926\n", + "====> Test Epoch: 5 Average loss: 53.0346\n", + "Train Epoch: 6 [0/800 (0%)]\tLoss: 45.222545\n", + "====> Train Epoch: 6 Average loss: 43.8985\n", + "====> Test Epoch: 6 Average loss: 53.7503\n", + "Train Epoch: 7 [0/800 (0%)]\tLoss: 42.859619\n", + "====> Train Epoch: 7 Average loss: 43.8415\n", + "====> Test Epoch: 7 Average loss: 55.3904\n", + "Train Epoch: 8 [0/800 (0%)]\tLoss: 43.091515\n", + "====> Train Epoch: 8 Average loss: 43.9621\n", + "====> Test Epoch: 8 Average loss: 57.2641\n", + "Train Epoch: 9 [0/800 (0%)]\tLoss: 44.604582\n", + "====> Train Epoch: 9 Average loss: 43.0592\n", + "====> Test Epoch: 9 Average loss: 56.2048\n", + "Train Epoch: 10 [0/800 (0%)]\tLoss: 43.722002\n", + "====> Train Epoch: 10 Average loss: 41.9819\n", + "====> Test Epoch: 10 Average loss: 47.0864\n", + "Train Epoch: 11 [0/800 (0%)]\tLoss: 40.527655\n", + "====> Train Epoch: 11 Average loss: 32.4589\n", + "====> Test Epoch: 11 Average loss: 24.6105\n", + "Train Epoch: 12 [0/800 (0%)]\tLoss: 20.672960\n", + "====> Train Epoch: 12 Average loss: 11.0092\n", + "====> Test Epoch: 12 Average loss: 3.7723\n", + "Train Epoch: 13 [0/800 (0%)]\tLoss: 2.635911\n", + "====> Train Epoch: 13 Average loss: 1.5510\n", + "====> Test Epoch: 13 Average loss: 1.2765\n", + "Train Epoch: 14 [0/800 (0%)]\tLoss: 0.891321\n", + "====> Train Epoch: 14 Average loss: 0.8177\n", + "====> Test Epoch: 14 Average loss: 0.6365\n", + "Train Epoch: 15 [0/800 (0%)]\tLoss: 0.475057\n", + "====> Train Epoch: 15 Average loss: 0.5230\n", + "====> Test Epoch: 15 Average loss: 0.6178\n", + "Train Epoch: 16 [0/800 (0%)]\tLoss: 0.478396\n", + "====> Train Epoch: 16 Average loss: 0.4701\n", + "====> Test Epoch: 16 Average loss: 0.5698\n", + "Train Epoch: 17 [0/800 (0%)]\tLoss: 0.432256\n", + "====> Train Epoch: 17 Average loss: 0.4701\n", + "====> Test Epoch: 17 Average loss: 0.5922\n", + "Train Epoch: 18 [0/800 (0%)]\tLoss: 0.370971\n", + "====> Train Epoch: 18 Average loss: 0.4501\n", + "====> Test Epoch: 18 Average loss: 0.5178\n", + "Train Epoch: 19 [0/800 (0%)]\tLoss: 0.414358\n", + "====> Train Epoch: 19 Average loss: 0.4366\n", + "====> Test Epoch: 19 Average loss: 0.4987\n", + "Train Epoch: 20 [0/800 (0%)]\tLoss: 0.409152\n", + "====> Train Epoch: 20 Average loss: 0.4115\n", + "====> Test Epoch: 20 Average loss: 0.5795\n", + "Train Epoch: 21 [0/800 (0%)]\tLoss: 0.358589\n", + "====> Train Epoch: 21 Average loss: 0.4051\n", + "====> Test Epoch: 21 Average loss: 0.5097\n", + "Train Epoch: 22 [0/800 (0%)]\tLoss: 0.340934\n", + "====> Train Epoch: 22 Average loss: 0.4006\n", + "====> Test Epoch: 22 Average loss: 0.5227\n", + "Train Epoch: 23 [0/800 (0%)]\tLoss: 0.364239\n", + "====> Train Epoch: 23 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ImmersionEstimator(device='cuda', extrinsic_dim=3, topology='circle')
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "ImmersionEstimator(device='cuda', extrinsic_dim=3, topology='circle')" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "immersion_estimator.fit(X, labels)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [], + "source": [ + "immersion = immersion_estimator.estimate_" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [], + "source": [ + "import torch\n", + "\n", + "intrinsic_coords = torch.tensor(intrinsic_coords, device=device)" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [], + "source": [ + "recon_points = immersion(intrinsic_coords).detach().cpu().numpy().squeeze()" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import plotly.graph_objects as go\n", + "from plotly.subplots import make_subplots\n", + "\n", + "# plot manifold points in 3d and recon points in 3d in separate subplots\n", + "\n", + "fig = make_subplots(\n", + " rows=1, cols=2, specs=[[{\"type\": \"scatter3d\"}, {\"type\": \"scatter3d\"}]]\n", + ")\n", + "\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=manifold_points[:, 0],\n", + " y=manifold_points[:, 1],\n", + " z=manifold_points[:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3),\n", + " ),\n", + " row=1,\n", + " col=1,\n", + ")\n", + "\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=recon_points[:, 0],\n", + " y=recon_points[:, 1],\n", + " z=recon_points[:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3),\n", + " ),\n", + " row=1,\n", + " col=2,\n", + ")\n", + "\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "neurometry", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From fe16028a870575cf264b0cbfa353ab208ccb513a Mon Sep 17 00:00:00 2001 From: franciscoeacosta Date: Sun, 22 Sep 2024 02:40:53 -0700 Subject: [PATCH 4/6] implement ablated immersion estimator, reorg tutorials --- .../geometry/immersion_estimator.py | 151 +- .../estimators/geometry/metric_estimator.py | 32 +- .../estimators/geometry/models/losses.py | 1 - .../geometry/models/spherical_vae.py | 1 - .../geometry/models/train_config.py | 6 +- ...4_methods_estimate_manifold_geometry.ipynb | 52554 ++++++++-------- ..._methods_estimate_manifold_immersion.ipynb | 9026 --- ...nb => 05_analyze_task_optimized_rnn.ipynb} | 50 +- ...ipynb => 06_analyze_digital_twin_V4.ipynb} | 2 +- .../07_analyze_electrophys_hippocampus.ipynb | 25 + .../04_explore_hyperbolic_geometry.ipynb | 0 ...4_methods_estimate_manifold_geometry.ipynb | 29839 +++++++++ .../05_explore_diffeomorphisms_of_space.ipynb | 0 .../06_application_synthetic_v1.ipynb | 0 .../071_application_dual_agent_rnns.ipynb | 0 .../07_application_rnns_grid_cells.ipynb | 0 ...08_applications_synthetic_grid_cells.ipynb | 0 ..._methods_estimate_manifold_curvature.ipynb | 0 tutorials/{ => move}/11_visualize_rnn.ipynb | 0 tutorials/{ => move}/plot_klein_bottle.py | 0 tutorials/{ => old_curvature}/load_runs.py | 0 21 files changed, 55084 insertions(+), 36603 deletions(-) delete mode 100644 tutorials/04_methods_estimate_manifold_immersion.ipynb rename tutorials/{09_application_rnns_grid_cells_xu.ipynb => 05_analyze_task_optimized_rnn.ipynb} (99%) rename tutorials/{12_application_digitaltwin_v4.ipynb => 06_analyze_digital_twin_V4.ipynb} (99%) create mode 100644 tutorials/07_analyze_electrophys_hippocampus.ipynb rename tutorials/{ => move}/04_explore_hyperbolic_geometry.ipynb (100%) create mode 100644 tutorials/move/04_methods_estimate_manifold_geometry.ipynb rename tutorials/{ => move}/05_explore_diffeomorphisms_of_space.ipynb (100%) rename tutorials/{ => move}/06_application_synthetic_v1.ipynb (100%) rename tutorials/{ => move}/071_application_dual_agent_rnns.ipynb (100%) rename tutorials/{ => move}/07_application_rnns_grid_cells.ipynb (100%) rename tutorials/{ => move}/08_applications_synthetic_grid_cells.ipynb (100%) rename tutorials/{ => move}/10_methods_estimate_manifold_curvature.ipynb (100%) rename tutorials/{ => move}/11_visualize_rnn.ipynb (100%) rename tutorials/{ => move}/plot_klein_bottle.py (100%) rename tutorials/{ => old_curvature}/load_runs.py (100%) diff --git a/neurometry/estimators/geometry/immersion_estimator.py b/neurometry/estimators/geometry/immersion_estimator.py index a8efba4..7272276 100644 --- a/neurometry/estimators/geometry/immersion_estimator.py +++ b/neurometry/estimators/geometry/immersion_estimator.py @@ -3,57 +3,49 @@ os.environ["GEOMSTATS_BACKEND"] = "pytorch" import geomstats.backend as gs import torch +import torch.optim as optim from sklearn.base import BaseEstimator from sklearn.model_selection import train_test_split from torch.utils.data import DataLoader, TensorDataset import neurometry.estimators.geometry.models.train_config as train_config -from neurometry.estimators.geometry.models.spherical_vae import SphericalVAE -from neurometry.estimators.geometry.models.toroidal_vae import ToroidalVAE -from neurometry.estimators.geometry.models.train import train_test class ImmersionEstimator(BaseEstimator): - def __init__(self, extrinsic_dim, topology, device): + def __init__(self, extrinsic_dim, topology, device, verbose=False): self.estimate_ = None + self.verbose = verbose self.device = device self.extrinsic_dim = extrinsic_dim self.topology = topology - self.latent_dims = {"circle": 2, "sphere": 3, "torus": 3} + self.latent_dims = {"circle": 2, "sphere": 3, "torus": 4} self.model = self._get_model() def _get_model(self): - if self.topology == "circle" or self.topology == "sphere": - return SphericalVAE( - extrinsic_dim=self.extrinsic_dim, - latent_dim=self.latent_dims[self.topology], - ).to(self.device) - if self.topology == "torus": - return ToroidalVAE( - extrinsic_dim=self.extrinsic_dim, - latent_dim=self.latent_dims[self.topology], - ).to(self.device) - raise ValueError("Topology not supported") + return NeuralEmbedding( + latent_dim=self.latent_dims[self.topology], extrinsic_dim=self.extrinsic_dim + ).to(self.device) - def _intrinsic_to_extrinsic(self): + def intrinsic_to_extrinsic(self, x): if self.topology == "circle": - return lambda x: gs.array([gs.cos(x), gs.sin(x)]) + return gs.array([gs.cos(x), gs.sin(x)]).T if self.topology == "sphere": - return lambda x: gs.array( + return gs.array( [ - gs.sin(x[0]) * gs.cos(x[1]), - gs.sin(x[0]) * gs.sin(x[1]), - gs.cos(x[0]), + gs.sin(x[:, 0]) * gs.cos(x[:, 1]), + gs.sin(x[:, 0]) * gs.sin(x[:, 1]), + gs.cos(x[:, 0]), ] - ) + ).T if self.topology == "torus": - return lambda x: gs.array( + return gs.array( [ - (1 - gs.cos(x[0])) * gs.cos(x[1]), - (1 - gs.cos(x[0])) * gs.sin(x[1]), - gs.sin(x[0]), + gs.cos(x[:, 0]), + gs.sin(x[:, 0]), + gs.cos(x[:, 1]), + gs.sin(x[:, 1]), ] - ) + ).T raise ValueError("Topology not supported") def fit(self, X, y=None): @@ -73,20 +65,99 @@ def fit(self, X, y=None): shuffle=True, ) - optimizer = torch.optim.Adam( - self.model.parameters(), lr=train_config.lr, amsgrad=True - ) - train_losses, test_losses, best_model = train_test( - model=self.model, - train_loader=train_loader, - test_loader=test_loader, - optimizer=optimizer, - scheduler=None, - config=train_config, + trainer = Trainer( + self.model, + train_loader, + test_loader, + criterion=torch.nn.MSELoss(), + learning_rate=train_config.lr, + scheduler=False, + verbose=self.verbose, ) + trainer.train(train_config.num_epochs) + + self.trainer = trainer - self.estimate_ = lambda task_variable: best_model.decode( - self._intrinsic_to_extrinsic()(task_variable).T + self.model.eval() + self.estimate_ = lambda task_variable: self.model( + self.intrinsic_to_extrinsic(task_variable) ) return self + + +class NeuralEmbedding(torch.nn.Module): + def __init__( + self, latent_dim, extrinsic_dim, hidden_dims=64, num_hidden=4, sft_beta=4.5 + ): + super().__init__() + + self.fc1 = torch.nn.Linear(latent_dim, hidden_dims) + self.fc_hidden = torch.nn.ModuleList( + [torch.nn.Linear(hidden_dims, hidden_dims) for _ in range(num_hidden)] + ) + self.fc_output = torch.nn.Linear(hidden_dims, extrinsic_dim) + self.softplus = torch.nn.Softplus(beta=sft_beta) + + def forward(self, x): + h = self.softplus(self.fc1(x)) + for fc in self.fc_hidden: + h = self.softplus(fc(h)) + return self.fc_output(h) + + +class Trainer: + def __init__( + self, + model, + train_loader, + test_loader, + criterion, + learning_rate, + scheduler=False, + verbose=False, + ): + self.model = model + self.train_loader = train_loader + self.test_loader = test_loader + self.criterion = criterion + self.optimizer = optim.Adam(model.parameters(), lr=learning_rate) + if scheduler: + self.scheduler = optim.lr_scheduler.StepLR( + self.optimizer, step_size=10, gamma=0.1 + ) + self.verbose = verbose + + def train(self, num_epochs=10): + train_losses = [] + test_losses = [] + for epoch in range(num_epochs): + self.model.train() + train_loss = 0.0 + for inputs, targets in self.train_loader: + self.optimizer.zero_grad() + outputs = self.model(inputs) + loss = self.criterion(outputs, targets) + loss.backward() + self.optimizer.step() + train_loss += loss.item() + avg_train_loss = train_loss / len(self.train_loader) + train_losses.append(avg_train_loss) + avg_test_loss = self.evaluate() + test_losses.append(avg_test_loss) + if self.verbose: + print( + f"Epoch {epoch+1}/{num_epochs}, Train Loss: {avg_train_loss}, Test Loss: {avg_test_loss}" + ) + self.train_losses = train_losses + self.test_losses = test_losses + + def evaluate(self): + self.model.eval() + test_loss = 0.0 + with torch.no_grad(): + for inputs, targets in self.test_loader: + outputs = self.model(inputs) + loss = self.criterion(outputs, targets) + test_loss += loss.item() + return test_loss / len(self.test_loader) diff --git a/neurometry/estimators/geometry/metric_estimator.py b/neurometry/estimators/geometry/metric_estimator.py index e4cd230..cc1d5be 100644 --- a/neurometry/estimators/geometry/metric_estimator.py +++ b/neurometry/estimators/geometry/metric_estimator.py @@ -1,24 +1,18 @@ -# import os +import os -# os.environ["GEOMSTATS_BACKEND"] = "pytorch" -# from geomstats.geometry.base import ImmersedSet -# from geomstats.geometry.euclidean import Euclidean -# from geomstats.geometry.pullback_metric import PullbackMetric +os.environ["GEOMSTATS_BACKEND"] = "pytorch" +from geomstats.geometry.base import ImmersedSet +from geomstats.geometry.euclidean import Euclidean -# class NeuralManifoldIntrinsic(ImmersedSet): -# def __init__(self, dim, neural_embedding_dim, neural_immersion, equip=True): -# self.neural_embedding_dim = neural_embedding_dim -# super().__init__(dim=dim, equip=equip) -# self.neural_immersion = neural_immersion +class NeuralManifoldIntrinsic(ImmersedSet): + def __init__(self, dim, neural_embedding_dim, neural_immersion, equip=True): + self.neural_embedding_dim = neural_embedding_dim + super().__init__(dim=dim, equip=equip) + self.neural_immersion = neural_immersion -# def immersion(self, point): -# return self.neural_immersion(point) + def immersion(self, point): + return self.neural_immersion(point) -# def _define_embedding_space(self): -# return Euclidean(dim=self.neural_embedding_dim) - -# neural_manifold = NeuralManifoldIntrinsic( -# dim, embedding_dim, immersion, equip=False -# ) -# neural_manifold.equip_with_metric(PullbackMetric) + def _define_embedding_space(self): + return Euclidean(dim=self.neural_embedding_dim) diff --git a/neurometry/estimators/geometry/models/losses.py b/neurometry/estimators/geometry/models/losses.py index 21fb2a8..c331feb 100644 --- a/neurometry/estimators/geometry/models/losses.py +++ b/neurometry/estimators/geometry/models/losses.py @@ -173,4 +173,3 @@ def moving_forward_loss(z, config): if len(loss) == 0: return torch.zeros(1).to(config.device) return torch.mean(loss) - diff --git a/neurometry/estimators/geometry/models/spherical_vae.py b/neurometry/estimators/geometry/models/spherical_vae.py index cc79c39..62b4870 100644 --- a/neurometry/estimators/geometry/models/spherical_vae.py +++ b/neurometry/estimators/geometry/models/spherical_vae.py @@ -212,7 +212,6 @@ def _elbo(self, x, x_mu, posterior_params): recon_loss = torch.mean((x - x_mu).pow(2)) - return train_config.recon_weight * recon_loss + train_config.kld_weight * kld def _latent_regularization_loss(self, labels, z): diff --git a/neurometry/estimators/geometry/models/train_config.py b/neurometry/estimators/geometry/models/train_config.py index 4bb241a..44b37be 100644 --- a/neurometry/estimators/geometry/models/train_config.py +++ b/neurometry/estimators/geometry/models/train_config.py @@ -4,10 +4,10 @@ device = "cuda" if torch.cuda.is_available() else "cpu" # training -num_epochs = 500 -batch_size = 64 +num_epochs = 200 +batch_size = 32 lr = 1e-3 recon_weight = 1.0 # weight for the reconstruction loss kld_weight = 0.03 # 0.03 # weight for KL loss -latent_weight = 10 # weight for latent regularization loss +latent_weight = 100 # weight for latent regularization loss diff --git a/tutorials/04_methods_estimate_manifold_geometry.ipynb b/tutorials/04_methods_estimate_manifold_geometry.ipynb index 88a2ee8..a966073 100644 --- a/tutorials/04_methods_estimate_manifold_geometry.ipynb +++ b/tutorials/04_methods_estimate_manifold_geometry.ipynb @@ -4,19 +4,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Classify Neural Manifold Topology" + "# Estimate Neural Manifold Immersion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### Set-up + Imports" + "## Set Up + Imports" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 238, "metadata": {}, "outputs": [ { @@ -41,25681 +41,707 @@ "%autoreload 2\n", "%load_ext jupyter_black\n", "\n", - "import os\n", + "import neurometry.datasets.synthetic as synthetic\n", + "import numpy as np\n", "\n", "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import torch\n", + "\n", + "\n", + "import os\n", "\n", "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n", "import geomstats.backend as gs\n", - "import neurometry.datasets.synthetic as synthetic" + "import torch" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Synthetic circle analysis" ] }, { "cell_type": "code", - "execution_count": 59, + "execution_count": 312, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], + "outputs": [], "source": [ - "import neurometry.datasets.synthetic as synthetic\n", - "\n", - "circle_task_points = synthetic.hypersphere(1, 1000)\n", - "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=circle_task_points,\n", - " encoding_dim=10,\n", + "task_points, intrinsic_coords = synthetic.hypersphere(1, 1000)\n", + "noisy_points, manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=task_points,\n", + " encoding_dim=3,\n", " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(10),\n", - " poisson_multiplier=100,\n", + " scales=gs.array([5, 3, 1]),\n", + " fano_factor=0.1,\n", ")" ] }, { "cell_type": "code", - "execution_count": 60, + "execution_count": 313, + "metadata": {}, + "outputs": [], + "source": [ + "from neurometry.estimators.geometry.immersion_estimator import ImmersionEstimator\n", + "\n", + "extrinsic_dim = 3\n", + "topology = \"circle\"\n", + "device = \"cuda\"\n", + "\n", + "immersion_estimator = ImmersionEstimator(\n", + " extrinsic_dim, topology, device=device, verbose=True\n", + ")\n", + "\n", + "latents = immersion_estimator.intrinsic_to_extrinsic(intrinsic_coords).squeeze()" + ] + }, + { + "cell_type": "code", + "execution_count": 314, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/200, Train Loss: 13022.06607155235, Test Loss: 11866.508007193383\n", + "Epoch 2/200, Train Loss: 8618.303601918711, Test Loss: 4035.902180384047\n", + "Epoch 3/200, Train Loss: 3506.947428379754, Test Loss: 2918.8028884944165\n", + "Epoch 4/200, Train Loss: 2998.2627454944236, Test Loss: 2960.5285708899637\n", + "Epoch 5/200, Train Loss: 2943.1006402080316, Test Loss: 2854.7209811061157\n", + "Epoch 6/200, Train Loss: 2931.749965913282, Test Loss: 2906.7113782873034\n", + "Epoch 7/200, Train Loss: 2936.539423533661, Test Loss: 2869.982490885765\n", + "Epoch 8/200, Train Loss: 2924.5017225906395, Test Loss: 2927.270978193271\n", + "Epoch 9/200, Train Loss: 2925.263847975524, Test Loss: 2780.0403350470656\n", + "Epoch 10/200, Train Loss: 2921.043327633271, Test Loss: 2839.904050959253\n", + "Epoch 11/200, Train Loss: 2905.3423914164487, Test Loss: 2866.2912308967966\n", + "Epoch 12/200, Train Loss: 2876.427814198662, Test Loss: 2829.4151015565185\n", + "Epoch 13/200, Train Loss: 2779.8973905041703, Test Loss: 2673.4944191285686\n", + "Epoch 14/200, Train Loss: 2228.9491204374194, Test Loss: 1400.3976173857802\n", + "Epoch 15/200, Train Loss: 581.9834140784118, Test Loss: 347.7742810896095\n", + "Epoch 16/200, Train Loss: 279.0328247109313, Test Loss: 267.3305055635849\n", + "Epoch 17/200, Train Loss: 245.75622916679703, Test Loss: 263.6164780319128\n", + "Epoch 18/200, Train Loss: 240.68186166147058, Test Loss: 246.66219983676436\n", + "Epoch 19/200, Train Loss: 237.38749625808438, Test Loss: 279.4329071476583\n", + "Epoch 20/200, Train Loss: 234.5714734116473, Test Loss: 265.0156918540006\n", + "Epoch 21/200, Train Loss: 231.79229446742386, Test Loss: 279.2706086243095\n", + "Epoch 22/200, Train Loss: 229.0386950753332, Test Loss: 249.94186853725634\n", + "Epoch 23/200, Train Loss: 227.31539005782253, Test Loss: 268.75888290801004\n", + "Epoch 24/200, Train Loss: 224.451204087807, Test Loss: 248.40102634320124\n", + "Epoch 25/200, Train Loss: 221.43353973405112, Test Loss: 261.67802879136224\n", + "Epoch 26/200, Train Loss: 220.20762645825585, Test Loss: 273.82256446995797\n", + "Epoch 27/200, Train Loss: 216.8689131767153, Test Loss: 237.06024181351796\n", + "Epoch 28/200, Train Loss: 213.77894809375042, Test Loss: 240.26168916206117\n", + "Epoch 29/200, Train Loss: 211.60635354746665, Test Loss: 252.11766448825193\n", + "Epoch 30/200, Train Loss: 209.21178646748385, Test Loss: 260.092256280038\n", + "Epoch 31/200, Train Loss: 202.79718661209427, Test Loss: 241.52946227609323\n", + "Epoch 32/200, Train Loss: 194.87351492525858, Test Loss: 230.76113112748914\n", + "Epoch 33/200, Train Loss: 181.05125346479946, Test Loss: 192.13371221101397\n", + "Epoch 34/200, Train Loss: 153.56953441472442, Test Loss: 156.07161616470881\n", + "Epoch 35/200, Train Loss: 91.97569775646785, Test Loss: 56.56133262001696\n", + "Epoch 36/200, Train Loss: 26.815740785373166, Test Loss: 19.558717344291274\n", + "Epoch 37/200, Train Loss: 16.52103507874917, Test Loss: 15.952853481531998\n", + "Epoch 38/200, Train Loss: 13.58144190250396, Test Loss: 14.01960901155492\n", + "Epoch 39/200, Train Loss: 12.836103158344738, Test Loss: 13.863664165425158\n", + "Epoch 40/200, Train Loss: 12.315041795453169, Test Loss: 11.806134492512886\n", + "Epoch 41/200, Train Loss: 11.76138155573257, Test Loss: 12.063178828959058\n", + "Epoch 42/200, Train Loss: 11.179732268351385, Test Loss: 11.508513510793687\n", + "Epoch 43/200, Train Loss: 11.189405334737547, Test Loss: 11.760025788343384\n", + "Epoch 44/200, Train Loss: 10.93132931872994, Test Loss: 10.761865696993798\n", + "Epoch 45/200, Train Loss: 10.838990171532553, Test Loss: 11.41829957247278\n", + "Epoch 46/200, Train Loss: 10.71024981766642, Test Loss: 10.848896291883566\n", + "Epoch 47/200, Train Loss: 10.634998890933032, Test Loss: 10.895327969624399\n", + "Epoch 48/200, Train Loss: 10.68274010705295, Test Loss: 11.32860870929207\n", + "Epoch 49/200, Train Loss: 10.421924024059225, Test Loss: 11.571128517912175\n", + "Epoch 50/200, Train Loss: 10.409696850767475, Test Loss: 11.736795351597083\n", + "Epoch 51/200, Train Loss: 11.102182471691105, Test Loss: 12.956047146141959\n", + "Epoch 52/200, Train Loss: 10.994703279510636, Test Loss: 13.17528889908434\n", + "Epoch 53/200, Train Loss: 10.482852547091355, Test Loss: 11.898595168607349\n", + "Epoch 54/200, Train Loss: 10.416190271918822, Test Loss: 10.924367498999512\n", + "Epoch 55/200, Train Loss: 10.210945332522176, Test Loss: 11.43018198040949\n", + "Epoch 56/200, Train Loss: 10.782676653098546, Test Loss: 11.04902838432696\n", + "Epoch 57/200, Train Loss: 10.763412235093108, Test Loss: 10.859743072117222\n", + "Epoch 58/200, Train Loss: 10.339436268494127, Test Loss: 10.490132593006257\n", + "Epoch 59/200, Train Loss: 10.542175790212186, Test Loss: 11.062322965313768\n", + "Epoch 60/200, Train Loss: 10.515446976184366, Test Loss: 10.643298152949187\n", + "Epoch 61/200, Train Loss: 10.129465570403294, Test Loss: 10.874929821086694\n", + "Epoch 62/200, Train Loss: 10.33095289254145, Test Loss: 11.038826062315238\n", + "Epoch 63/200, Train Loss: 10.607780176477222, Test Loss: 11.117567014450696\n", + "Epoch 64/200, Train Loss: 10.19363055203544, Test Loss: 11.502888288373672\n", + "Epoch 65/200, Train Loss: 10.395164764760532, Test Loss: 12.286309922334661\n", + "Epoch 66/200, Train Loss: 10.489277835265082, Test Loss: 12.147076416175407\n", + "Epoch 67/200, Train Loss: 10.297389446751724, Test Loss: 11.487427999800166\n", + "Epoch 68/200, Train Loss: 10.0532093981172, Test Loss: 10.783335880098052\n", + "Epoch 69/200, Train Loss: 10.00805927965536, Test Loss: 10.517746803451905\n", + "Epoch 70/200, Train Loss: 10.038053454807573, Test Loss: 10.524892050300585\n", + "Epoch 71/200, Train Loss: 10.249230543577973, Test Loss: 11.073625057481442\n", + "Epoch 72/200, Train Loss: 10.45075518826603, Test Loss: 11.42113223852472\n", + "Epoch 73/200, Train Loss: 10.487131999981225, Test Loss: 10.570602616595844\n", + "Epoch 74/200, Train Loss: 10.220835674571193, Test Loss: 10.895753993079435\n", + "Epoch 75/200, Train Loss: 10.169529125904287, Test Loss: 10.883637800501536\n", + "Epoch 76/200, Train Loss: 10.268290528991837, Test Loss: 11.839045803259603\n", + "Epoch 77/200, Train Loss: 10.841278901725104, Test Loss: 13.286651308136339\n", + "Epoch 78/200, Train Loss: 10.78742451158501, Test Loss: 10.868974746991341\n", + "Epoch 79/200, Train Loss: 10.184991181320887, Test Loss: 11.489565595819442\n", + "Epoch 80/200, Train Loss: 9.927987072603319, Test Loss: 11.906069808679359\n", + "Epoch 81/200, Train Loss: 10.229912019206585, Test Loss: 11.056351778753053\n", + "Epoch 82/200, Train Loss: 10.224477222643996, Test Loss: 10.983212042660464\n", + "Epoch 83/200, Train Loss: 10.534749195451557, Test Loss: 10.981141283742133\n", + "Epoch 84/200, Train Loss: 10.03709890637773, Test Loss: 11.091489528134302\n", + "Epoch 85/200, Train Loss: 10.099075219602044, Test Loss: 10.215108201629263\n", + "Epoch 86/200, Train Loss: 9.957683713049423, Test Loss: 10.696675303985618\n", + "Epoch 87/200, Train Loss: 10.548157830056248, Test Loss: 10.841509217747175\n", + "Epoch 88/200, Train Loss: 11.518595731549267, Test Loss: 12.169079221187564\n", + "Epoch 89/200, Train Loss: 10.042051033225153, Test Loss: 11.729942718219364\n", + "Epoch 90/200, Train Loss: 10.119450966510573, Test Loss: 11.207343911274242\n", + "Epoch 91/200, Train Loss: 10.41091179659802, Test Loss: 10.694221713934525\n", + "Epoch 92/200, Train Loss: 10.56489884217293, Test Loss: 12.265211287976276\n", + "Epoch 93/200, Train Loss: 10.458070270826122, Test Loss: 11.641027302346824\n", + "Epoch 94/200, Train Loss: 10.504942763502745, Test Loss: 11.058611111962534\n", + "Epoch 95/200, Train Loss: 10.548172735467055, Test Loss: 11.000239800035514\n", + "Epoch 96/200, Train Loss: 10.245151854108455, Test Loss: 11.04323252110764\n", + "Epoch 97/200, Train Loss: 10.191355638964907, Test Loss: 11.36048088953506\n", + "Epoch 98/200, Train Loss: 9.924821653795432, Test Loss: 11.75451218909611\n", + "Epoch 99/200, Train Loss: 10.330173887084506, Test Loss: 13.351181120901066\n", + "Epoch 100/200, Train Loss: 10.838888420624166, Test Loss: 13.823539535519176\n", + "Epoch 101/200, Train Loss: 10.453439593661505, Test Loss: 11.017190055960508\n", + "Epoch 102/200, Train Loss: 10.36379832834558, Test Loss: 10.153877488902717\n", + "Epoch 103/200, Train Loss: 10.261569604917467, Test Loss: 11.63506595178647\n", + "Epoch 104/200, Train Loss: 10.030633530976703, Test Loss: 12.98612818928918\n", + "Epoch 105/200, Train Loss: 10.516783408807225, Test Loss: 12.411771616249382\n", + "Epoch 106/200, Train Loss: 11.723875801195627, Test Loss: 14.518145701813138\n", + "Epoch 107/200, Train Loss: 10.953136398023542, Test Loss: 11.480414953544896\n", + "Epoch 108/200, Train Loss: 10.490797649613818, Test Loss: 12.078476891010268\n", + "Epoch 109/200, Train Loss: 10.574833275822863, Test Loss: 11.29328176777963\n", + "Epoch 110/200, Train Loss: 10.618192868035145, Test Loss: 12.077397393585514\n", + "Epoch 111/200, Train Loss: 10.659403823924361, Test Loss: 11.75574367947267\n", + "Epoch 112/200, Train Loss: 10.136886238475372, Test Loss: 12.441191867571947\n", + "Epoch 113/200, Train Loss: 10.42011253567286, Test Loss: 11.143815747493239\n", + "Epoch 114/200, Train Loss: 11.008284384802122, Test Loss: 11.46021107680554\n", + "Epoch 115/200, Train Loss: 10.817967284863048, Test Loss: 11.915131627573961\n", + "Epoch 116/200, Train Loss: 10.153092769335945, Test Loss: 10.568478333836405\n", + "Epoch 117/200, Train Loss: 10.645266961321623, Test Loss: 11.236809955086718\n", + "Epoch 118/200, Train Loss: 10.531840968945703, Test Loss: 13.324285602372624\n", + "Epoch 119/200, Train Loss: 10.219342748924332, Test Loss: 11.83394631601235\n", + "Epoch 120/200, Train Loss: 10.508616401148757, Test Loss: 14.55446090382992\n", + "Epoch 121/200, Train Loss: 10.541280977049324, Test Loss: 10.582763624228578\n", + "Epoch 122/200, Train Loss: 10.656432892575117, Test Loss: 10.803629422166404\n", + "Epoch 123/200, Train Loss: 10.151317978603426, Test Loss: 10.581207787907042\n", + "Epoch 124/200, Train Loss: 10.336319523696458, Test Loss: 11.344743150047892\n", + "Epoch 125/200, Train Loss: 10.166030341868, Test Loss: 13.813791344556348\n", + "Epoch 126/200, Train Loss: 10.092743927755372, Test Loss: 10.776318576583618\n", + "Epoch 127/200, Train Loss: 10.113921768874539, Test Loss: 11.404366889515973\n", + "Epoch 128/200, Train Loss: 10.924066937889807, Test Loss: 9.971519365672515\n", + "Epoch 129/200, Train Loss: 10.446296324875595, Test Loss: 10.594064106762302\n", + "Epoch 130/200, Train Loss: 11.167741104478774, Test Loss: 12.793943451311602\n", + "Epoch 131/200, Train Loss: 10.521995408035934, Test Loss: 10.49897520536827\n", + "Epoch 132/200, Train Loss: 10.428246720334194, Test Loss: 13.231898942024616\n", + "Epoch 133/200, Train Loss: 10.793708156397104, Test Loss: 12.60166338113954\n", + "Epoch 134/200, Train Loss: 11.021249109847336, Test Loss: 11.260395768368387\n", + "Epoch 135/200, Train Loss: 10.952955900195018, Test Loss: 14.230480686985752\n", + "Epoch 136/200, Train Loss: 11.503802173193101, Test Loss: 12.949232517923068\n", + "Epoch 137/200, Train Loss: 10.822156605041187, Test Loss: 11.822374905189267\n", + "Epoch 138/200, Train Loss: 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot noisy_points and manifold_points in 3D with plotly\n", - "\n", - "import plotly.graph_objects as go\n", - "\n", - "fig = go.Figure()\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=circle_noisy_points[:, 0],\n", - " y=circle_noisy_points[:, 1],\n", - " z=circle_noisy_points[:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3),\n", - " )\n", - ")\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=circle_manifold_points[:, 0],\n", - " y=circle_manifold_points[:, 1],\n", - " z=circle_manifold_points[:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3),\n", - " )\n", - ")\n", - "\n", - "fig.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [], - "source": [ - "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", - "\n", - "\n", - "import neurometry.datasets.synthetic as synthetic\n", - "\n", - "circle_task_points = synthetic.hypersphere(1, 1000)\n", - "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=circle_task_points,\n", - " encoding_dim=10,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(10),\n", - " poisson_multiplier=100,\n", - ")\n", - "\n", - "num_shuffles = 100\n", - "\n", - "circle_noisy_diagrams = compute_diagrams_shuffle(\n", - " circle_noisy_points, num_shuffles=num_shuffles, homology_dimensions=[0, 1, 2]\n", - ")\n", - "\n", - "\n", - "from gtda.diagrams import PersistenceEntropy\n", - "\n", - "circle_PE = PersistenceEntropy()\n", - "\n", - "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)\n", - "\n", - "# manifold_diagrams = compute_diagrams_shuffle(manifold_points, num_shuffles=num_shuffles)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [], - "source": [ - "X = noisy_points\n", - "\n", - "\n", - "def _shuffle_entries(data, rng):\n", - 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+ "/* Toggleable content - dropdown */\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content {\n", + " max-height: 0;\n", + " max-width: 0;\n", + " overflow: hidden;\n", + " text-align: left;\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content.fitted {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content pre {\n", + " margin: 0.2em;\n", + " border-radius: 0.25em;\n", + " color: var(--sklearn-color-text);\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-toggleable__content.fitted pre {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-fitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n", + " /* Expand drop-down */\n", + " max-height: 200px;\n", + " max-width: 100%;\n", + " overflow: auto;\n", + "}\n", + "\n", + "#sk-container-id-15 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n", + " content: \"▾\";\n", + "}\n", + "\n", + "/* Pipeline/ColumnTransformer-specific style */\n", + "\n", + "#sk-container-id-15 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " color: var(--sklearn-color-text);\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "/* Estimator-specific style */\n", + "\n", + "/* Colorize estimator box */\n", + "#sk-container-id-15 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-label label.sk-toggleable__label,\n", + "#sk-container-id-15 div.sk-label label {\n", + " /* The background is the default theme color */\n", + " color: var(--sklearn-color-text-on-default-background);\n", + "}\n", + "\n", + "/* On hover, darken the color of the background */\n", + "#sk-container-id-15 div.sk-label:hover label.sk-toggleable__label {\n", + " color: var(--sklearn-color-text);\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "/* Label box, darken color on hover, fitted */\n", + "#sk-container-id-15 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n", + " color: var(--sklearn-color-text);\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "/* Estimator label */\n", + "\n", + "#sk-container-id-15 div.sk-label label {\n", + " font-family: monospace;\n", + " font-weight: bold;\n", + " display: inline-block;\n", + " line-height: 1.2em;\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-label-container {\n", + " text-align: center;\n", + "}\n", + "\n", + "/* Estimator-specific */\n", + "#sk-container-id-15 div.sk-estimator {\n", + " font-family: monospace;\n", + " border: 1px dotted var(--sklearn-color-border-box);\n", + " border-radius: 0.25em;\n", + " box-sizing: border-box;\n", + " margin-bottom: 0.5em;\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-0);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-estimator.fitted {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-0);\n", + "}\n", + "\n", + "/* on hover */\n", + "#sk-container-id-15 div.sk-estimator:hover {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-2);\n", + "}\n", + "\n", + "#sk-container-id-15 div.sk-estimator.fitted:hover {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-2);\n", + "}\n", + "\n", + "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n", + "\n", + "/* Common style for \"i\" and \"?\" */\n", + "\n", + ".sk-estimator-doc-link,\n", + "a:link.sk-estimator-doc-link,\n", + "a:visited.sk-estimator-doc-link {\n", + " float: right;\n", + " font-size: smaller;\n", + " line-height: 1em;\n", + " font-family: monospace;\n", + " background-color: var(--sklearn-color-background);\n", + " border-radius: 1em;\n", + " height: 1em;\n", + " width: 1em;\n", + " text-decoration: none !important;\n", + " margin-left: 1ex;\n", + " /* unfitted */\n", + " border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n", + " color: var(--sklearn-color-unfitted-level-1);\n", + "}\n", + "\n", + ".sk-estimator-doc-link.fitted,\n", + "a:link.sk-estimator-doc-link.fitted,\n", + "a:visited.sk-estimator-doc-link.fitted {\n", + " /* fitted */\n", + " border: var(--sklearn-color-fitted-level-1) 1pt solid;\n", + " color: var(--sklearn-color-fitted-level-1);\n", + "}\n", + "\n", + "/* On hover */\n", + "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n", + ".sk-estimator-doc-link:hover,\n", + "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n", + ".sk-estimator-doc-link:hover {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-3);\n", + " color: var(--sklearn-color-background);\n", + " text-decoration: none;\n", + "}\n", + "\n", + "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n", + ".sk-estimator-doc-link.fitted:hover,\n", + "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n", + ".sk-estimator-doc-link.fitted:hover {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-3);\n", + " color: var(--sklearn-color-background);\n", + " text-decoration: none;\n", + "}\n", + "\n", + "/* Span, style for the box shown on hovering the info icon */\n", + ".sk-estimator-doc-link span {\n", + " display: none;\n", + " z-index: 9999;\n", + " position: relative;\n", + " font-weight: normal;\n", + " right: .2ex;\n", + " padding: .5ex;\n", + " margin: .5ex;\n", + " width: min-content;\n", + " min-width: 20ex;\n", + " max-width: 50ex;\n", + " color: var(--sklearn-color-text);\n", + " box-shadow: 2pt 2pt 4pt #999;\n", + " /* unfitted */\n", + " background: var(--sklearn-color-unfitted-level-0);\n", + " border: .5pt solid var(--sklearn-color-unfitted-level-3);\n", + "}\n", + "\n", + ".sk-estimator-doc-link.fitted span {\n", + " /* fitted */\n", + " background: var(--sklearn-color-fitted-level-0);\n", + " border: var(--sklearn-color-fitted-level-3);\n", + "}\n", + "\n", + ".sk-estimator-doc-link:hover span {\n", + " display: block;\n", + "}\n", + "\n", + "/* \"?\"-specific style due to the `` HTML tag */\n", + "\n", + "#sk-container-id-15 a.estimator_doc_link {\n", + " float: right;\n", + " font-size: 1rem;\n", + " line-height: 1em;\n", + " font-family: monospace;\n", + " background-color: var(--sklearn-color-background);\n", + " border-radius: 1rem;\n", + " height: 1rem;\n", + " width: 1rem;\n", + " text-decoration: none;\n", + " /* unfitted */\n", + " color: var(--sklearn-color-unfitted-level-1);\n", + " border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n", + "}\n", + "\n", + "#sk-container-id-15 a.estimator_doc_link.fitted {\n", + " /* fitted */\n", + " border: var(--sklearn-color-fitted-level-1) 1pt solid;\n", + " color: var(--sklearn-color-fitted-level-1);\n", + "}\n", + "\n", + "/* On hover */\n", + "#sk-container-id-15 a.estimator_doc_link:hover {\n", + " /* unfitted */\n", + " background-color: var(--sklearn-color-unfitted-level-3);\n", + " color: var(--sklearn-color-background);\n", + " text-decoration: none;\n", + "}\n", + "\n", + "#sk-container-id-15 a.estimator_doc_link.fitted:hover {\n", + " /* fitted */\n", + " background-color: var(--sklearn-color-fitted-level-3);\n", + "}\n", + "
ImmersionEstimator(device='cuda', extrinsic_dim=3, topology='circle',\n",
+       "                   verbose=True)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], "text/plain": [ - "
" + "ImmersionEstimator(device='cuda', extrinsic_dim=3, topology='circle',\n", + " verbose=True)" ] }, + "execution_count": 314, "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from neurometry.estimators.topology.plotting import plot_all_barcodes_with_null\n", - "\n", - "plot_all_barcodes_with_null(\n", - " noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n", - ");" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [], - "source": [ - "def _get_lifespan_from_diagram(diagram):\n", - " birth = diagram[:, 0]\n", - " death = diagram[:, 1]\n", - " if np.isfinite(death).any():\n", - " inf_value = 3 * np.max(death[death != np.inf])\n", - " else:\n", - " inf_value = 1000\n", - " death[death == np.inf] = inf_value\n", - " lifespan = death - birth\n", - " indices = np.argsort(-lifespan)[:20]\n", - "\n", - " return lifespan[indices]" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [], - "source": [ - "def estimate_betti_numbers(points, num_shuffles, homology_dimensions=(0, 1, 2)):\n", - " all_diagrams = compute_diagrams_shuffle(\n", - " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", - " )\n", - " diagram = all_diagrams[0]\n", - " shuffled_diagrams = all_diagrams[1:]\n", - "\n", - " betti_numbers = {dim: None for dim in homology_dimensions}\n", - "\n", - " for dim in homology_dimensions:\n", - " filtered_diagram = diagram[diagram[:, 2] == dim]\n", - " lifespan = _get_lifespan_from_diagram(filtered_diagram)\n", - " filtered_shuffled_diagrams = np.array(\n", - " [\n", - " shuffled_diagrams[i, shuffled_diagrams[i, :, 2] == 1]\n", - " for i in range(shuffled_diagrams.shape[0])\n", - " ]\n", - " )\n", - " betti_number = []\n", - " for diag in filtered_shuffled_diagrams:\n", - " shuffled_lifespan = _get_lifespan_from_diagram(diag)\n", - " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", - " betti_number.append(sum(significant_features))\n", - " betti_numbers[dim] = (np.mean(betti_number), np.std(betti_number))\n", - "\n", - " return betti_numbers" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "{0: (1.28, 2.209434316742636), 1: (1.0, 0.0), 2: (0.0, 0.0)}\n" - ] + "output_type": "execute_result" } ], "source": [ - "betti_numbers = estimate_betti_numbers(\n", - " manifold_points, num_shuffles=100, homology_dimensions=(0, 1, 2)\n", - ")\n", - "print(betti_numbers)" + "immersion_estimator.fit(X=latents, y=noisy_points)" ] }, { "cell_type": "code", - "execution_count": 67, + "execution_count": 267, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, "metadata": {}, @@ -25723,218 +749,34 @@ } ], "source": [ - "homology_dimensions = (0, 1)\n", - "points = manifold_points\n", - "num_shuffles = 100\n", - "\n", - "all_diagrams = compute_diagrams_shuffle(\n", - " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", - ")\n", - "\n", - "plot_all_barcodes_with_null(all_diagrams, \"manifold\")\n", - "\n", - "\n", - "diagram = all_diagrams[0]\n", - "lifespan = _get_lifespan_from_diagram(diagram)\n", - "shuffled_diagrams = all_diagrams[1:]\n", - "\n", - "betti_numbers = {dim: None for dim in homology_dimensions}\n", - "\n", - "for dim in homology_dimensions:\n", - " betti_number = []\n", - " for shuffled_diagram in shuffled_diagrams:\n", - " shuffled_lifespan = _get_lifespan_from_diagram(shuffled_diagram)\n", - " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", - " betti_number.append(sum(significant_features))\n", - " betti_numbers[dim] = np.mean(betti_number)" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [], - "source": [ - "def get_betti_numbers(diagrams):\n", - " original_diagram = diagrams[0]\n", - " shuffled_diagrams = diagrams[1:]\n", - "\n", - " dims = np.unique(original_diagram[:, 2]).astype(int)\n", - "\n", - " betti_numbers = {dim: None for dim in dims}\n", - " for i, dim in enumerate(dims):\n", - " diagram_dim = original_diagram[original_diagram[:, 2] == dim]\n", - " null_diagram_dim = shuffled_diagrams[:, :, 2] == dim\n", - " null_diagram = shuffled_diagrams[null_diagram_dim]\n", - "\n", - " null_lifespans_dim = _get_lifespan_from_diagram(null_diagram)\n", - " lifespans_dim = _get_lifespan_from_diagram(diagram_dim)\n", - "\n", - " comparison = (lifespans_dim > null_lifespans_dim).astype(int)\n", - "\n", - " betti_numbers[dim] = sum(comparison)\n", - "\n", - " return betti_numbers" + "plt.plot(immersion_estimator.trainer.train_losses)\n", + "plt.plot(immersion_estimator.trainer.test_losses);" ] }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 303, "metadata": {}, "outputs": [], "source": [ - "betti = get_betti_numbers(noisy_diagrams)" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: 0, 1: 5, 2: 2}" - ] - }, - "execution_count": 34, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "betti" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Classify circle, sphere, torus point clouds" + "immersion_estimator.model.to(\"cpu\")\n", + "immersion = immersion_estimator.estimate_" ] }, { "cell_type": "code", - "execution_count": 68, + "execution_count": 269, "metadata": {}, "outputs": [], "source": [ - "import neurometry.datasets.synthetic as synthetic\n", - "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", - "from gtda.diagrams import PersistenceEntropy\n", - "\n", - "num_points = 1000\n", - "encoding_dim = 10\n", - "poisson_multiplier = 100\n", - "homology_dimensions = [0, 1, 2]\n", - "num_shuffles = 100" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], - "source": [ - "circle_task_points = synthetic.hypersphere(1, num_points)\n", - "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=circle_task_points,\n", - " encoding_dim=encoding_dim,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(encoding_dim),\n", - " poisson_multiplier=poisson_multiplier,\n", - ")\n", - "\n", - "\n", - "circle_noisy_diagrams = compute_diagrams_shuffle(\n", - " circle_noisy_points,\n", - " num_shuffles=num_shuffles,\n", - " homology_dimensions=homology_dimensions,\n", - ")\n", - "\n", - "circle_PE = PersistenceEntropy()\n", - "\n", - "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], - "source": [ - "sphere_task_points = synthetic.hypersphere(2, num_points)\n", - "sphere_noisy_points, sphere_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=sphere_task_points,\n", - " encoding_dim=encoding_dim,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(encoding_dim),\n", - " poisson_multiplier=poisson_multiplier,\n", - ")\n", - "\n", - "sphere_noisy_diagrams = compute_diagrams_shuffle(\n", - " sphere_noisy_points,\n", - " num_shuffles=num_shuffles,\n", - " homology_dimensions=homology_dimensions,\n", - ")\n", - "\n", - "sphere_PE = PersistenceEntropy()\n", - "sphere_features = sphere_PE.fit_transform(sphere_noisy_diagrams)" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "noise level: 0.71%\n" - ] - } - ], - "source": [ - "torus_task_points = synthetic.hypertorus(2, num_points)\n", - "torus_noisy_points, torus_manifold_points = synthetic.synthetic_neural_manifold(\n", - " points=torus_task_points,\n", - " encoding_dim=encoding_dim,\n", - " nonlinearity=\"sigmoid\",\n", - " scales=gs.ones(encoding_dim),\n", - " poisson_multiplier=poisson_multiplier,\n", - ")\n", - "\n", - "torus_noisy_diagrams = compute_diagrams_shuffle(\n", - " torus_noisy_points,\n", - " num_shuffles=num_shuffles,\n", - " homology_dimensions=homology_dimensions,\n", - ")\n", - "\n", - "torus_PE = PersistenceEntropy()\n", + "intrinsic_coords = torch.tensor(intrinsic_coords, device=device)\n", "\n", - "torus_features = torus_PE.fit_transform(torus_noisy_diagrams)" + "recon_points = immersion(intrinsic_coords).detach().cpu().numpy().squeeze()" ] }, { "cell_type": "code", - "execution_count": 72, + "execution_count": 270, "metadata": {}, "outputs": [ { @@ 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "import plotly.graph_objects as go\n", - "from plotly.subplots import make_subplots\n", - "\n", - "# plot manifold points in 3d and recon points in 3d in separate subplots\n", - "\n", - "fig = make_subplots(\n", - " rows=1, cols=2, specs=[[{\"type\": \"scatter3d\"}, {\"type\": \"scatter3d\"}]]\n", - ")\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=manifold_points[:, 0],\n", - " y=manifold_points[:, 1],\n", - " z=manifold_points[:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3),\n", - " ),\n", - " row=1,\n", - " col=1,\n", - ")\n", - "\n", - "fig.add_trace(\n", - " go.Scatter3d(\n", - " x=recon_points[:, 0],\n", - " y=recon_points[:, 1],\n", - " z=recon_points[:, 2],\n", - " mode=\"markers\",\n", - " marker=dict(size=3),\n", - " ),\n", - " row=1,\n", - " col=2,\n", - ")\n", - "\n", - "fig.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "neurometry", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.3" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/tutorials/09_application_rnns_grid_cells_xu.ipynb b/tutorials/05_analyze_task_optimized_rnn.ipynb similarity index 99% rename from tutorials/09_application_rnns_grid_cells_xu.ipynb rename to tutorials/05_analyze_task_optimized_rnn.ipynb index 1a052b5..a6bac84 100644 --- a/tutorials/09_application_rnns_grid_cells_xu.ipynb +++ b/tutorials/05_analyze_task_optimized_rnn.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Analyze Representations in Path-Integrating RNN\n", + "# Analyze a Task-Optimized RNN model of Medial Entorhinal Cortex\n", "\n", - "Model from \"Conformal Isometry of Lie Group Representation in Recurrent Network of Grid Cells\" Xu, et al. 2022. (https://arxiv.org/abs/2210.02684)" + "Model from \"Global Distortions from Local Rewards: Neural Coding Strategies in Path-Integrating Neural Systems\" (Acosta, et al. 2024)" ] }, { @@ -5370,7 +5370,7 @@ 0.7443443850961186, 0.5335202760982172, 0.24113993732822775, - -1.3682012603804389e-05, + -0.000013682012603804389, -0.3033129326391612, -0.5569430706714704, -0.8256463124162846, @@ -11817,7 +11817,7 @@ 0.02560628578066826, 0.01852361485362053, 0.008083760738372803, - 5.028516170568764e-05, + 0.00005028516170568764, 0.0026055434718728065, 0.0025169490836560726, 0.012283924035727978, @@ -11847,7 +11847,7 @@ 0.043918464332818985, 0.022042324766516685, 0.011334008537232876, - 2.338462400075514e-05, + 0.00002338462400075514, 0.011400146409869194, 0.00028882070910185575, 0, @@ -11899,7 +11899,7 @@ 0, 0, 0, - 4.476889444049448e-05, + 0.00004476889444049448, 0.0032937396317720413, 0.0018493246752768755, 0.0036336251068860292, @@ -11907,7 +11907,7 @@ 0.0028639091178774834, 0.002532734302803874, 0.0010890428675338626, - 8.220231393352151e-05, + 0.00008220231393352151, 0, 0, 0.0030053616501390934, @@ -11943,7 +11943,7 @@ 0.009876681491732597, 0.0020584804005920887, 0, - 3.318797462270595e-05, + 0.00003318797462270595, 0, 0, 0, @@ -12000,7 +12000,7 @@ 0, 0, 0.0006767080049030483, - 3.1347757612820715e-05, + 0.000031347757612820715, 0.0037735109217464924, 0.009763515554368496, 0.011874261312186718, @@ -12073,7 +12073,7 @@ 0.029602648690342903, 0.009325867518782616, 0, - 7.046433165669441e-05, + 0.00007046433165669441, 0.0039690397679805756, 0.008116052486002445, 0.015035456046462059, @@ -12217,7 +12217,7 @@ 0.00024178068269975483, 0.000310216419165954, 0.00015290986630134284, - 1.583690391271375e-05, + 0.00001583690391271375, 0.005117141176015139, 0.006794402841478586, 0.005132411140948534, @@ -12298,7 +12298,7 @@ 0.004861349705606699, 0, 0, - 2.8017200293106725e-07, + 2.8017200293106725e-7, 0.00219922699034214, 0.0033365830313414335, 0.006072622258216143, @@ -12366,7 +12366,7 @@ 0.01037217304110527, 0.013310388661921024, 0.00950609240680933, - 3.0475432595267193e-06, + 0.0000030475432595267193, 0.0027488062623888254, 0.008986018598079681, 0.024930628016591072, @@ -12571,8 +12571,8 @@ 0.016063859686255455, 0.006869303062558174, 0, - 4.36862392234616e-05, - 4.605479625752196e-05, + 0.0000436862392234616, + 0.00004605479625752196, 0, 0.0025435504503548145, 0.008932068943977356, @@ -12610,7 +12610,7 @@ 0.0011874311603605747, 0.03220932558178902, 0.0009610020206309855, - 1.0785831364046317e-05, + 0.000010785831364046317, 0, 0, 0.0015135452849790454, @@ -12620,7 +12620,7 @@ 0.025296663865447044, 0.014601591974496841, 0.002030174480751157, - 3.934487176593393e-05, + 0.00003934487176593393, 0.00043734433711506426, 0.0038455717731267214, 0.0034299069084227085, @@ -12652,7 +12652,7 @@ 0.010176997631788254, 0.004731710534542799, 0.00023628040798939764, - 3.4099302865797654e-05, + 0.000034099302865797654, 0.00997556746006012, 0.03170761093497276, 0.0509360209107399, @@ -12719,7 +12719,7 @@ 0.03663862124085426, 0.02172727882862091, 0.00837465189397335, - 2.1194051441852935e-05, + 0.000021194051441852935, 0, 0.0011375406756997108, 0.011287457309663296, @@ -12861,7 +12861,7 @@ 0.005713008809834719, 0.001924386015161872, 0, - 1.8789161231325124e-06, + 0.0000018789161231325124, 0.0006248669815249741, 0.0046332706697285175, 0.00908583216369152, @@ -12962,8 +12962,8 @@ 0, 0.004411284811794758, 0.0017078923992812634, - 3.0413501008297317e-05, - 1.1602993254200555e-05, + 0.000030413501008297317, + 0.000011602993254200555, 0.002275587059557438, 0.007443869952112436, 0.003325021592900157, @@ -13001,7 +13001,7 @@ 0.007172558456659317, 0.0012941695749759674, 0.0022711646743118763, - 2.3564927687402815e-05, + 0.000023564927687402815, 0, 0, 0, @@ -13075,7 +13075,7 @@ 0.028236834332346916, 0.008330672048032284, 0, - 4.509258815232897e-07, + 4.509258815232897e-7, 0.0142352981492877, 0.029934925958514214, 0.03995843604207039, @@ -13765,7 +13765,7 @@ -1.3973425704910003, -1.265250473345472, -0.6972569609826321, - 7.210046424716754e-05, + 0.00007210046424716754, 0.2759193759679177, 0.6007969902842584, 1.1094660690062637, diff --git a/tutorials/12_application_digitaltwin_v4.ipynb b/tutorials/06_analyze_digital_twin_V4.ipynb similarity index 99% rename from tutorials/12_application_digitaltwin_v4.ipynb rename to tutorials/06_analyze_digital_twin_V4.ipynb index 165e90f..d54d60c 100644 --- a/tutorials/12_application_digitaltwin_v4.ipynb +++ b/tutorials/06_analyze_digital_twin_V4.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# V4 Digital Twins" + "# Analyze a Digital Twin model of Macaque Visual Cortex area V4" ] }, { diff --git a/tutorials/07_analyze_electrophys_hippocampus.ipynb b/tutorials/07_analyze_electrophys_hippocampus.ipynb new file mode 100644 index 0000000..1b08c3b --- /dev/null +++ b/tutorials/07_analyze_electrophys_hippocampus.ipynb @@ -0,0 +1,25 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Analyze Electrophysiological Recordings of Rodent Hippocampus\n", + "\n", + "We would like to thank James Knierim, Noah Cowan and Ravikrishnan Jayakumar at Johns Hopkins University for providing experimental data. The rodent place cell data analyzed in this tutorial was collected in the Knierim and Cowan labs by R. Jayakumar and M. Madhav." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "language_info": { + "name": "python" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/04_explore_hyperbolic_geometry.ipynb b/tutorials/move/04_explore_hyperbolic_geometry.ipynb similarity index 100% rename from tutorials/04_explore_hyperbolic_geometry.ipynb rename to tutorials/move/04_explore_hyperbolic_geometry.ipynb diff --git a/tutorials/move/04_methods_estimate_manifold_geometry.ipynb b/tutorials/move/04_methods_estimate_manifold_geometry.ipynb new file mode 100644 index 0000000..88a2ee8 --- /dev/null +++ b/tutorials/move/04_methods_estimate_manifold_geometry.ipynb @@ -0,0 +1,29839 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Classify Neural Manifold Topology" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Set-up + Imports" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Working directory: /home/facosta/neurometry/neurometry\n", + "Directory added to path: /home/facosta/neurometry\n", + "Directory added to path: /home/facosta/neurometry/neurometry\n", + "The autoreload extension is already loaded. To reload it, use:\n", + " %reload_ext autoreload\n", + "The jupyter_black extension is already loaded. To reload it, use:\n", + " %reload_ext jupyter_black\n" + ] + } + ], + "source": [ + "import setup\n", + "\n", + "setup.main()\n", + "%load_ext autoreload\n", + "%autoreload 2\n", + "%load_ext jupyter_black\n", + "\n", + "import os\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import torch\n", + "\n", + "os.environ[\"GEOMSTATS_BACKEND\"] = \"pytorch\"\n", + "import geomstats.backend as gs\n", + "import neurometry.datasets.synthetic as synthetic" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "import neurometry.datasets.synthetic as synthetic\n", + "\n", + "circle_task_points = synthetic.hypersphere(1, 1000)\n", + "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=10,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(10),\n", + " poisson_multiplier=100,\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "mode": "markers", + "type": "scatter3d", + "x": [ + 105.07, + 87.07, + 135.56, + 118.98, + 59.74, + 81.32, + 88.39, + 72.11, + 99.35, + 97.53, + 58.82, + 73.92, + 97.42, + 65.33, + 138.28, + 135.76, + 65.29, + 127.94, + 126.26, + 77.24, + 111.99, + 67.29, + 129.11, + 71.1, + 79.17, + 60.87, + 76.29, + 108.64, + 69.65, + 91.95, + 63.12, + 128.04, + 126.88, + 61.39, + 59.96, + 67.89, + 138.66, + 64.03, + 90.05, + 137.79, + 61.59, + 124.4, + 62.03, + 97.08, + 61.29, + 127.47, + 67.16, + 120.3, + 60.93, + 108.51, + 58.42, + 95.01, + 71.52, + 91.2, + 116.26, + 131.63, + 111.28, + 61.04, + 72.71, + 74.52, + 114.69, + 139.55, + 91.32, + 64.52, + 58.68, + 75.28, + 80.44, + 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synthetic\n", + "\n", + "circle_task_points = synthetic.hypersphere(1, 1000)\n", + "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=10,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(10),\n", + " poisson_multiplier=100,\n", + ")\n", + "\n", + "num_shuffles = 100\n", + "\n", + "circle_noisy_diagrams = compute_diagrams_shuffle(\n", + " circle_noisy_points, num_shuffles=num_shuffles, homology_dimensions=[0, 1, 2]\n", + ")\n", + "\n", + "\n", + "from gtda.diagrams import PersistenceEntropy\n", + "\n", + "circle_PE = PersistenceEntropy()\n", + "\n", + "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)\n", + "\n", + "# manifold_diagrams = compute_diagrams_shuffle(manifold_points, num_shuffles=num_shuffles)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "X = noisy_points\n", + "\n", + "\n", + "def _shuffle_entries(data, rng):\n", + " return np.array([rng.permutation(row) for row in data])\n", + "\n", + "\n", + "seed = 0\n", + "rng = np.random.default_rng(seed)\n", + "shuffled_Xs = [_shuffle_entries(X, rng) for _ in range(num_shuffles)]" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "size": 3 + }, + "mode": "markers", + "type": "scatter3d", + "x": [ + 196, + 154, + 173, + 98, + 165, + 183, + 86, + 186, + 114, + 25, + 15, + 201, + 24, + 96, + 34, + 29, + 33, + 30, + 203, + 163, + 43, + 17, + 97, + 103, + 150, + 87, + 78, + 142, + 23, + 185, + 86, + 8, + 22, + 172, + 19, + 137, + 100, + 23, + 24, + 162, + 118, + 16, + 21, + 111, + 35, + 34, + 166, + 12, + 200, + 173, + 178, + 146, + 160, + 186, + 128, + 17, + 175, + 155, + 24, + 185, + 62, + 164, + 41, + 25, + 85, + 137, + 18, + 177, + 87, + 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 3d plot with plotly\n", + "fig = go.Figure()\n", + "\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=features[1:, 0],\n", + " y=features[1:, 1],\n", + " z=features[1:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3, color=\"blue\"),\n", + " )\n", + ")\n", + "\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=[features[0, 0]],\n", + " y=[features[0, 1]],\n", + " z=[features[0, 2]],\n", + " mode=\"markers\",\n", + " marker=dict(size=3, color=\"red\"),\n", + " )\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from neurometry.estimators.topology.plotting import plot_all_barcodes_with_null\n", + "\n", + "plot_all_barcodes_with_null(\n", + " noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n", + ");" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "def _get_lifespan_from_diagram(diagram):\n", + " birth = diagram[:, 0]\n", + " death = diagram[:, 1]\n", + " if np.isfinite(death).any():\n", + " inf_value = 3 * np.max(death[death != np.inf])\n", + " else:\n", + " inf_value = 1000\n", + " death[death == np.inf] = inf_value\n", + " lifespan = death - birth\n", + " indices = np.argsort(-lifespan)[:20]\n", + "\n", + " return lifespan[indices]" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "def estimate_betti_numbers(points, num_shuffles, homology_dimensions=(0, 1, 2)):\n", + " all_diagrams = compute_diagrams_shuffle(\n", + " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", + " )\n", + " diagram = all_diagrams[0]\n", + " shuffled_diagrams = all_diagrams[1:]\n", + "\n", + " betti_numbers = {dim: None for dim in homology_dimensions}\n", + "\n", + " for dim in homology_dimensions:\n", + " filtered_diagram = diagram[diagram[:, 2] == dim]\n", + " lifespan = _get_lifespan_from_diagram(filtered_diagram)\n", + " filtered_shuffled_diagrams = np.array(\n", + " [\n", + " shuffled_diagrams[i, shuffled_diagrams[i, :, 2] == 1]\n", + " for i in range(shuffled_diagrams.shape[0])\n", + " ]\n", + " )\n", + " betti_number = []\n", + " for diag in filtered_shuffled_diagrams:\n", + " shuffled_lifespan = _get_lifespan_from_diagram(diag)\n", + " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", + " betti_number.append(sum(significant_features))\n", + " betti_numbers[dim] = (np.mean(betti_number), np.std(betti_number))\n", + "\n", + " return betti_numbers" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{0: (1.28, 2.209434316742636), 1: (1.0, 0.0), 2: (0.0, 0.0)}\n" + ] + } + ], + "source": [ + "betti_numbers = estimate_betti_numbers(\n", + " manifold_points, num_shuffles=100, homology_dimensions=(0, 1, 2)\n", + ")\n", + "print(betti_numbers)" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "homology_dimensions = (0, 1)\n", + "points = manifold_points\n", + "num_shuffles = 100\n", + "\n", + "all_diagrams = compute_diagrams_shuffle(\n", + " points, num_shuffles=num_shuffles, homology_dimensions=homology_dimensions\n", + ")\n", + "\n", + "plot_all_barcodes_with_null(all_diagrams, \"manifold\")\n", + "\n", + "\n", + "diagram = all_diagrams[0]\n", + "lifespan = _get_lifespan_from_diagram(diagram)\n", + "shuffled_diagrams = all_diagrams[1:]\n", + "\n", + "betti_numbers = {dim: None for dim in homology_dimensions}\n", + "\n", + "for dim in homology_dimensions:\n", + " betti_number = []\n", + " for shuffled_diagram in shuffled_diagrams:\n", + " shuffled_lifespan = _get_lifespan_from_diagram(shuffled_diagram)\n", + " significant_features = (lifespan > shuffled_lifespan).astype(int)\n", + " betti_number.append(sum(significant_features))\n", + " betti_numbers[dim] = np.mean(betti_number)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [], + "source": [ + "def get_betti_numbers(diagrams):\n", + " original_diagram = diagrams[0]\n", + " shuffled_diagrams = diagrams[1:]\n", + "\n", + " dims = np.unique(original_diagram[:, 2]).astype(int)\n", + "\n", + " betti_numbers = {dim: None for dim in dims}\n", + " for i, dim in enumerate(dims):\n", + " diagram_dim = original_diagram[original_diagram[:, 2] == dim]\n", + " null_diagram_dim = shuffled_diagrams[:, :, 2] == dim\n", + " null_diagram = shuffled_diagrams[null_diagram_dim]\n", + "\n", + " null_lifespans_dim = _get_lifespan_from_diagram(null_diagram)\n", + " lifespans_dim = _get_lifespan_from_diagram(diagram_dim)\n", + "\n", + " comparison = (lifespans_dim > null_lifespans_dim).astype(int)\n", + "\n", + " betti_numbers[dim] = sum(comparison)\n", + "\n", + " return betti_numbers" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "betti = get_betti_numbers(noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 0, 1: 5, 2: 2}" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "betti" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Classify circle, sphere, torus point clouds" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [], + "source": [ + "import neurometry.datasets.synthetic as synthetic\n", + "from neurometry.estimators.topology.persistent_homology import compute_diagrams_shuffle\n", + "from gtda.diagrams import PersistenceEntropy\n", + "\n", + "num_points = 1000\n", + "encoding_dim = 10\n", + "poisson_multiplier = 100\n", + "homology_dimensions = [0, 1, 2]\n", + "num_shuffles = 100" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "circle_task_points = synthetic.hypersphere(1, num_points)\n", + "circle_noisy_points, circle_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "\n", + "circle_noisy_diagrams = compute_diagrams_shuffle(\n", + " circle_noisy_points,\n", + " num_shuffles=num_shuffles,\n", + " homology_dimensions=homology_dimensions,\n", + ")\n", + "\n", + "circle_PE = PersistenceEntropy()\n", + "\n", + "circle_features = circle_PE.fit_transform(circle_noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "sphere_task_points = synthetic.hypersphere(2, num_points)\n", + "sphere_noisy_points, sphere_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=sphere_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "sphere_noisy_diagrams = compute_diagrams_shuffle(\n", + " sphere_noisy_points,\n", + " num_shuffles=num_shuffles,\n", + " homology_dimensions=homology_dimensions,\n", + ")\n", + "\n", + "sphere_PE = PersistenceEntropy()\n", + "sphere_features = sphere_PE.fit_transform(sphere_noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 71, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "noise level: 0.71%\n" + ] + } + ], + "source": [ + "torus_task_points = synthetic.hypertorus(2, num_points)\n", + "torus_noisy_points, torus_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=torus_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "torus_noisy_diagrams = compute_diagrams_shuffle(\n", + " torus_noisy_points,\n", + " num_shuffles=num_shuffles,\n", + " homology_dimensions=homology_dimensions,\n", + ")\n", + "\n", + "torus_PE = PersistenceEntropy()\n", + "\n", + "torus_features = torus_PE.fit_transform(torus_noisy_diagrams)" + ] + }, + { + "cell_type": "code", + "execution_count": 72, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "marker": { + "color": "lightpink", + "size": 3 + }, + "mode": "markers", + "name": "Shuffled Circle", + "type": "scatter3d", + "x": [ + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + -1, + 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TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)
In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.
" + ], + "text/plain": [ + "TopologicalClassifier(num_samples=10, poisson_multiplier=100, reduce_dim=True)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "num_points = 500\n", + "encoding_dim = 10\n", + "poisson_multiplier = 100\n", + "\n", + "\n", + "test_task_points = synthetic.hypertorus(2, 400)\n", + "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=test_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=poisson_multiplier,\n", + ")\n", + "\n", + "from neurometry.estimators.topology.persistent_homology import TopologicalClassifier\n", + "\n", + "num_samples = 10\n", + "\n", + "TC = TopologicalClassifier(\n", + " num_samples=num_samples, poisson_multiplier=poisson_multiplier, reduce_dim=True\n", + ")\n", + "TC.fit(test_noisy_points)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([2.])" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "TC.predict(test_noisy_points)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "from sklearn.ensemble import RandomForestClassifier\n", + "from sklearn.model_selection import train_test_split\n", + "from sklearn.base import BaseEstimator, ClassifierMixin\n", + "\n", + "\n", + "class TopologicalClassifier(ClassifierMixin, BaseEstimator):\n", + " def __init__(\n", + " self,\n", + " num_samples,\n", + " poisson_multiplier,\n", + " homology_dimensions=[0, 1, 2],\n", + " reduce_dim=False,\n", + " ):\n", + " self.num_samples = num_samples\n", + " self.poisson_multiplier = poisson_multiplier\n", + " self.homology_dimensions = homology_dimensions\n", + " self.reduce_dim = reduce_dim\n", + " self.classifier = RandomForestClassifier()\n", + "\n", + " def _generate_ref_data(self, input_data):\n", + " num_points = input_data.shape[0]\n", + " encoding_dim = input_data.shape[1]\n", + " circle_task_points = synthetic.hypersphere(1, num_points)\n", + " circle_point_clouds = []\n", + " for i in range(self.num_samples):\n", + " circle_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=circle_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " circle_point_clouds.append(circle_noisy_points)\n", + "\n", + " sphere_task_points = synthetic.hypersphere(2, num_points)\n", + " sphere_point_clouds = []\n", + " for i in range(num_samples):\n", + " sphere_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=sphere_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " sphere_point_clouds.append(sphere_noisy_points)\n", + "\n", + " torus_task_points = synthetic.hypertorus(2, num_points)\n", + " torus_point_clouds = []\n", + " for i in range(num_samples):\n", + " torus_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=torus_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " torus_point_clouds.append(torus_noisy_points)\n", + "\n", + " klein_bottle_task_points = synthetic.klein_bottle(num_points)\n", + " klein_bottle_point_clouds = []\n", + " for i in range(num_samples):\n", + " klein_bottle_noisy_points, _ = synthetic.synthetic_neural_manifold(\n", + " points=klein_bottle_task_points,\n", + " encoding_dim=encoding_dim,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(encoding_dim),\n", + " poisson_multiplier=self.poisson_multiplier,\n", + " )\n", + " klein_bottle_point_clouds.append(klein_bottle_noisy_points)\n", + "\n", + " circle_labels = np.zeros(num_samples)\n", + " sphere_labels = np.ones(num_samples)\n", + " torus_labels = 2 * np.ones(num_samples)\n", + " klein_bottle_labels = 3 * np.ones(num_samples)\n", + " ref_labels = np.concatenate(\n", + " [\n", + " circle_labels,\n", + " sphere_labels,\n", + " torus_labels,\n", + " klein_bottle_labels,\n", + " ]\n", + " )\n", + "\n", + " ref_point_clouds = [\n", + " *circle_point_clouds,\n", + " *sphere_point_clouds,\n", + " *torus_point_clouds,\n", + " *klein_bottle_point_clouds,\n", + " ]\n", + "\n", + " return ref_point_clouds, ref_labels\n", + "\n", + " def _compute_topo_features(self, diagrams):\n", + " PE = PersistenceEntropy()\n", + " features = PE.fit_transform(diagrams)\n", + " return features\n", + "\n", + " def fit(self, X, y=None):\n", + " ref_point_clouds, ref_labels = self._generate_ref_data(X)\n", + " if 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Example color mapping\n", + "color_map = {0: \"darkblue\", 1: \"deeppink\", 2: \"limegreen\", 3: \"orange\"}\n", + "colors = [color_map[label] for label in labels]\n", + "\n", + "names = {0: \"Circle\", 1: \"Sphere\", 2: \"Torus\", 3: \"Klein Bottle\"}\n", + "\n", + "# Create a figure\n", + "fig = go.Figure()\n", + "\n", + "# Add the trace with colored markers based on labels\n", + "fig.add_trace(\n", + " go.Scatter3d(\n", + " x=features[:, 0],\n", + " y=features[:, 1],\n", + " z=features[:, 2],\n", + " mode=\"markers\",\n", + " marker=dict(size=3, color=colors),\n", + " showlegend=False,\n", + " )\n", + ")\n", + "\n", + "# Manually add the legend entries\n", + "for label, color in color_map.items():\n", + " fig.add_trace(\n", + " go.Scatter3d(\n", + " x=[None],\n", + " y=[None],\n", + " z=[None],\n", + " mode=\"markers\",\n", + " marker=dict(size=3, color=color),\n", + " showlegend=True,\n", + " name=f\"{names[label]}\",\n", + " )\n", + " )\n", + "\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 110, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8" + ] + }, + "execution_count": 110, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.ensemble import RandomForestClassifier\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "X_train, X_valid, y_train, y_valid = train_test_split(features, labels)\n", + "model = RandomForestClassifier()\n", + "model.fit(X_train, y_train)\n", + "model.score(X_valid, y_valid)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "ename": "AssertionError", + "evalue": "scales must have same shape as tensor", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAssertionError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[9], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m test_task_points \u001b[38;5;241m=\u001b[39m synthetic\u001b[38;5;241m.\u001b[39mhypertorus(\u001b[38;5;241m2\u001b[39m, \u001b[38;5;241m400\u001b[39m)\n\u001b[0;32m----> 2\u001b[0m test_noisy_points, test_manifold_points \u001b[38;5;241m=\u001b[39m \u001b[43msynthetic\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msynthetic_neural_manifold\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 3\u001b[0m \u001b[43m \u001b[49m\u001b[43mpoints\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtest_task_points\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 4\u001b[0m \u001b[43m \u001b[49m\u001b[43mencoding_dim\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m5\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 5\u001b[0m \u001b[43m \u001b[49m\u001b[43mnonlinearity\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43msigmoid\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 6\u001b[0m \u001b[43m \u001b[49m\u001b[43mscales\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mgs\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mones\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m10\u001b[39;49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m 7\u001b[0m \u001b[43m \u001b[49m\u001b[43mpoisson_multiplier\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m 8\u001b[0m \u001b[43m)\u001b[49m\n\u001b[1;32m 10\u001b[0m TC\u001b[38;5;241m.\u001b[39mfit(test_noisy_points)\n", + "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:42\u001b[0m, in \u001b[0;36msynthetic_neural_manifold\u001b[0;34m(points, encoding_dim, nonlinearity, poisson_multiplier, ref_frequency, **kwargs)\u001b[0m\n\u001b[1;32m 40\u001b[0m encoding_matrix \u001b[38;5;241m=\u001b[39m random_encoding_matrix(manifold_extrinsic_dim, encoding_dim)\n\u001b[1;32m 41\u001b[0m encoded_points \u001b[38;5;241m=\u001b[39m encode_points(points, encoding_matrix)\n\u001b[0;32m---> 42\u001b[0m manifold_points \u001b[38;5;241m=\u001b[39m ref_frequency \u001b[38;5;241m*\u001b[39m \u001b[43mapply_nonlinearity\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m 43\u001b[0m \u001b[43m \u001b[49m\u001b[43mencoded_points\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mnonlinearity\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\n\u001b[1;32m 44\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 45\u001b[0m \u001b[38;5;28;01mtry\u001b[39;00m:\n\u001b[1;32m 46\u001b[0m noisy_points \u001b[38;5;241m=\u001b[39m poisson_spikes(manifold_points, poisson_multiplier)\n", + "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:218\u001b[0m, in \u001b[0;36mapply_nonlinearity\u001b[0;34m(encoded_points, nonlinearity, **kwargs)\u001b[0m\n\u001b[1;32m 216\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m relu(encoded_points, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[1;32m 217\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m nonlinearity \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124msigmoid\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[0;32m--> 218\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mscaled_sigmoid\u001b[49m\u001b[43m(\u001b[49m\u001b[43mencoded_points\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43mkwargs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m 219\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m nonlinearity \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mtanh\u001b[39m\u001b[38;5;124m\"\u001b[39m:\n\u001b[1;32m 220\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m scaled_tanh(encoded_points, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n", + "File \u001b[0;32m~/neurometry/neurometry/datasets/synthetic.py:231\u001b[0m, in \u001b[0;36mscaled_sigmoid\u001b[0;34m(tensor, scales)\u001b[0m\n\u001b[1;32m 230\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mscaled_sigmoid\u001b[39m(tensor, scales):\n\u001b[0;32m--> 231\u001b[0m \u001b[38;5;28;01massert\u001b[39;00m tensor\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m==\u001b[39m scales\u001b[38;5;241m.\u001b[39mshape[\u001b[38;5;241m0\u001b[39m], \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mscales must have same shape as tensor\u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[1;32m 232\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;241m1\u001b[39m \u001b[38;5;241m/\u001b[39m (\u001b[38;5;241m1\u001b[39m \u001b[38;5;241m+\u001b[39m gs\u001b[38;5;241m.\u001b[39mexp(\u001b[38;5;241m-\u001b[39mscales \u001b[38;5;241m*\u001b[39m tensor))\n", + "\u001b[0;31mAssertionError\u001b[0m: scales must have same shape as tensor" + ] + } + ], + "source": [ + "test_task_points = synthetic.hypertorus(2, 400)\n", + "test_noisy_points, test_manifold_points = synthetic.synthetic_neural_manifold(\n", + " points=test_task_points,\n", + " encoding_dim=5,\n", + " nonlinearity=\"sigmoid\",\n", + " scales=gs.ones(10),\n", + " poisson_multiplier=100,\n", + ")\n", + "\n", + "TC.fit(test_noisy_points)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### NOTE: Try different coefficients to distinguish between torus and klein bottle?" + ] + }, + { + "cell_type": "code", + "execution_count": 105, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{0: (19.814, 0.7066852198822331), 1: (13.214, 2.555817677378416)}\n" + ] + } + ], + "source": [ + "betti_numbers = estimate_betti_numbers(\n", + " manifold_points, num_shuffles=500, homology_dimensions=(0, 1)\n", + ")\n", + "print(betti_numbers)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "num_shuffles = 10\n", + "\n", + "noisy_diagrams = compute_diagrams_shuffle(\n", + " noisy_points, num_shuffles=num_shuffles, homology_dimensions=(0, 1, 2)\n", + ")\n", + "\n", + "manifold_diagrams = compute_diagrams_shuffle(\n", + " manifold_points, num_shuffles=num_shuffles, homology_dimensions=(0, 1, 2)\n", + ")\n", + "\n", + "plot_all_barcodes_with_null(\n", + " noisy_diagrams, \"noisy\", diagrams_2=manifold_diagrams, dataset_name_2=\"manifold\"\n", + ");" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "{0: 0, 1: 5, 2: 2}\n" + ] + } + ], + "source": [ + "betti = get_betti_numbers(noisy_diagrams)\n", + "print(betti)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### TODO: FIX get_betti_numbers FUNCTION!!!!\n", + "\n", + "Also: how to deal with betti 0 ? There should be a single \"significant\" feature?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "sphere_1_betti = {0: 1, 1: 1, 2: 0}\n", + "torus_2_betti = {0: 1, 1: 2, 2: 1}\n", + "sphere_2_betti = {0: 1, 1: 0, 2: 1}\n", + "\n", + "# if betti == sphere_1_betti:\n", + "# print(\"The manifold is a ring\") ----> use ring VAE\n", + "\n", + "\n", + "# elif betti == torus_2_betti:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "neurometry", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.3" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/tutorials/05_explore_diffeomorphisms_of_space.ipynb b/tutorials/move/05_explore_diffeomorphisms_of_space.ipynb similarity index 100% rename from tutorials/05_explore_diffeomorphisms_of_space.ipynb rename to tutorials/move/05_explore_diffeomorphisms_of_space.ipynb diff --git a/tutorials/06_application_synthetic_v1.ipynb b/tutorials/move/06_application_synthetic_v1.ipynb similarity index 100% rename from tutorials/06_application_synthetic_v1.ipynb rename to tutorials/move/06_application_synthetic_v1.ipynb diff --git a/tutorials/071_application_dual_agent_rnns.ipynb b/tutorials/move/071_application_dual_agent_rnns.ipynb similarity index 100% rename from tutorials/071_application_dual_agent_rnns.ipynb rename to tutorials/move/071_application_dual_agent_rnns.ipynb diff --git a/tutorials/07_application_rnns_grid_cells.ipynb b/tutorials/move/07_application_rnns_grid_cells.ipynb similarity index 100% rename from tutorials/07_application_rnns_grid_cells.ipynb rename to tutorials/move/07_application_rnns_grid_cells.ipynb diff --git a/tutorials/08_applications_synthetic_grid_cells.ipynb b/tutorials/move/08_applications_synthetic_grid_cells.ipynb similarity index 100% rename from tutorials/08_applications_synthetic_grid_cells.ipynb rename to tutorials/move/08_applications_synthetic_grid_cells.ipynb diff --git a/tutorials/10_methods_estimate_manifold_curvature.ipynb b/tutorials/move/10_methods_estimate_manifold_curvature.ipynb similarity index 100% rename from tutorials/10_methods_estimate_manifold_curvature.ipynb rename to tutorials/move/10_methods_estimate_manifold_curvature.ipynb diff --git a/tutorials/11_visualize_rnn.ipynb b/tutorials/move/11_visualize_rnn.ipynb similarity index 100% rename from tutorials/11_visualize_rnn.ipynb rename to tutorials/move/11_visualize_rnn.ipynb diff --git a/tutorials/plot_klein_bottle.py b/tutorials/move/plot_klein_bottle.py similarity index 100% rename from tutorials/plot_klein_bottle.py rename to tutorials/move/plot_klein_bottle.py diff --git a/tutorials/load_runs.py b/tutorials/old_curvature/load_runs.py similarity index 100% rename from tutorials/load_runs.py rename to tutorials/old_curvature/load_runs.py From 554d0f3c5affd73a3b7f9095a9309cae3f4787ca Mon Sep 17 00:00:00 2001 From: franciscoeacosta Date: Tue, 24 Jun 2025 11:02:03 -0700 Subject: [PATCH 5/6] notebook changes --- .../01_methods_create_synthetic_data.ipynb | 15956 ++++++++-------- 1 file changed, 7975 insertions(+), 7981 deletions(-) diff --git a/tutorials/01_methods_create_synthetic_data.ipynb b/tutorials/01_methods_create_synthetic_data.ipynb index 3df3e04..1ebba53 100644 --- a/tutorials/01_methods_create_synthetic_data.ipynb +++ b/tutorials/01_methods_create_synthetic_data.ipynb @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -27,12 +27,34 @@ "text": [ "Working directory: /home/facosta/neurometry/neurometry\n", "Directory added to path: /home/facosta/neurometry\n", - "Directory added to path: /home/facosta/neurometry/neurometry\n", - "The autoreload extension is already loaded. To reload it, use:\n", - " %reload_ext autoreload\n", - "The jupyter_black extension is already loaded. To reload it, use:\n", - " %reload_ext jupyter_black\n" + "Directory added to path: /home/facosta/neurometry/neurometry\n" ] + }, + { + "data": { + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" } ], "source": [ @@ -68,7 +90,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -96,7 +118,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 11, "metadata": {}, "outputs": [], "source": [ @@ -105,7 +127,8 @@ " points=task_points,\n", " encoding_dim=3,\n", " nonlinearity=\"sigmoid\",\n", - " scales=gs.array([5, 3, 1]),\n", + " scales=gs.array([1, 1, 1]),\n", + " fano_factor=0.0,\n", ")" ] }, @@ -118,45 +141,16 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "mean firing rate: 100.48 Hz\n" + "mean firing 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