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if [ -d "CAP_project/CompilerForCAP" ]; then make -C "CAP_project/CompilerForCAP" doc; fi
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if [ -d "CAP_project/MonoidalCategories" ]; then make -C "CAP_project/MonoidalCategories" doc; fi
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if [ -d "CAP_project/CartesianCategories" ]; then make -C "CAP_project/CartesianCategories" doc; fi
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if [ -d "CAP_project/AdditiveClosuresForCAP" ]; then make -C "CAP_project/AdditiveClosuresForCAP" doc; fi
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if [ -d "CAP_project/FreydCategoriesForCAP" ]; then make -C "CAP_project/FreydCategoriesForCAP" doc; fi
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if [ -d "HigherHomologicalAlgebra/ToolsForHigherHomologicalAlgebra" ]; then make -C "HigherHomologicalAlgebra/ToolsForHigherHomologicalAlgebra" doc; fi
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if [ -d "homalg_project/homalg" ]; then make -C "homalg_project/homalg" doc; fi
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if [ -d "homalg_project/Modules" ]; then make -C "homalg_project/Modules" doc; fi
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if [ -d "CategoricalTowers/ToolsForCategoricalTowers" ]; then make -C "CategoricalTowers/ToolsForCategoricalTowers" doc; fi
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if [ -d "CategoricalTowers/Toposes" ]; then make -C "CategoricalTowers/Toposes" doc; fi
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- name: Test GradientDescentForCAP
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- name: Test GradientBasedLearningForCAP
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run: |
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make -C GradientDescentForCAP --trace -j $(nproc) --output-sync ci-test
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make -C GradientBasedLearningForCAP --trace -j $(nproc) --output-sync ci-test
This package provides tools for exploring categorical machine learning using the CAP (Categories, Algorithms, Programming) system.
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It implements automatic differentiation using the lens pattern and provides constructs for building and training neural networks.
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@Section Overview
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The package implements the following main concepts:
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* **Examples**: Examples for creating and training neural networks.
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* **Expressions**: A symbolic expression system for representing mathematical formulas.
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* **Skeletal Category of Smooth Maps**: A category where objects are Euclidean spaces $\mathbb{R}^n$ and morphisms are smooth maps with their Jacobian matrices.
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* **Category of Parametrised Morphisms**: A category that represents morphisms with learnable parameters, used to model neural network layers.
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* **Neural Networks**: High-level operations for constructing and training neural networks.
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* **Category of Lenses**: A category that models bidirectional data flow, essential for backpropagation in neural networks.
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* **Fitting Parameters**: Explain how to learn the parameters in order to minimize a parametrised morphism.
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* **CAP Operation**: The new categorical operations needed in this package.
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* **Tools**: Few GAP operations and helper functions.
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@Chapter Examples for neural networks
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@Section Binary-class neural network with binary cross-entropy loss function
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@Section Multi-class neural network with cross-entropy loss function
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@Section Neural network with quadratic loss function
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@Chapter Expressions
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@Section Constructors
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@Section Attributes
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@Section Operations
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@Section Global Functions
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@Section Examples
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@Section GAP Categories
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@Chapter Skeletal Category of Smooth Maps
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@Section Constructors
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@Section Attributes
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@Section Operations
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@Section Available Smooth Maps
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@Section Supported CAP Operations
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@Section Examples
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@Section GAP Categories
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@Chapter Category of Parametrised Morphisms
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@Section Definition
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@Section Constructors
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@Section Attributes
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@Section Operations
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@Section Available Parametrised Morphisms
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@Section Supported CAP Operations
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@Section Examples
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@Section GAP Categories
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@Chapter Neural Networks
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@Section Definition
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@Section Operations
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@Section Examples
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@Chapter Category of Lenses
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@Section Definition
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@Section Constructors
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@Section Attributes
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@Section Operations
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@Section Available Lenses
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@Section Optimizers
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@Section Supported CAP Operations
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@Section Examples
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@Section GAP Categories
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@Chapter Fitting Parameters
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@Section Introduction
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@Section Notes on Batching
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@Section Operations
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@Section Examples
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@Chapter CAP Operations for GradientBasedLearningForCAP
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