[FEAT] Alpha differentiability in semirelaxed_gromov_wasserstein2 (#483)

* alpha differentiable

* autopep and update gradient test

* debug test gradient

---------

Co-authored-by: Rémi Flamary <remi.flamary@gmail.com>

Author: smazelet

RELEASES.md

@@ -3,6 +3,7 @@
 ## 0.9.1dev
 
 #### New features
+- Make alpha parameter in semi-relaxed Fused Gromov Wasserstein differentiable (PR #483)
 - Make alpha parameter in Fused Gromov Wasserstein differentiable (PR #463)
 - Added the sparsity-constrained OT solver to `ot.smooth` and added ` projection_sparse_simplex` to `ot.utils` (PR #459)
 - Add tests on GPU for master branch and approved PR (PR #473)

ot/gromov/_semirelaxed.py

@@ -467,8 +467,15 @@ def semirelaxed_fused_gromov_wasserstein2(M, C1, C2, p, loss_fun='square_loss',
     if loss_fun == 'square_loss':
         gC1 = 2 * C1 * nx.outer(p, p) - 2 * nx.dot(T, nx.dot(C2, T.T))
         gC2 = 2 * C2 * nx.outer(q, q) - 2 * nx.dot(T.T, nx.dot(C1, T))
-        srfgw_dist = nx.set_gradients(srfgw_dist, (C1, C2, M),
-                                      (alpha * gC1, alpha * gC2, (1 - alpha) * T))
+        if isinstance(alpha, int) or isinstance(alpha, float):
+            srfgw_dist = nx.set_gradients(srfgw_dist, (C1, C2, M),
+                                          (alpha * gC1, alpha * gC2, (1 - alpha) * T))
+        else:
+            lin_term = nx.sum(T * M)
+            srgw_term = (srfgw_dist - (1 - alpha) * lin_term) / alpha
+            srfgw_dist = nx.set_gradients(srfgw_dist, (C1, C2, M, alpha),
+                                          (alpha * gC1, alpha * gC2, (1 - alpha) * T,
+                                           srgw_term - lin_term))
 
     if log:
         return srfgw_dist, log_fgw

test/test_gromov.py

@@ -1752,6 +1752,23 @@ def test_semirelaxed_fgw2_gradients():
             assert C12.shape == C12.grad.shape
             assert M1.shape == M1.grad.shape
 
+            # full gradients with alpha
+            p1 = torch.tensor(p, requires_grad=False, device=device)
+            C11 = torch.tensor(C1, requires_grad=True, device=device)
+            C12 = torch.tensor(C2, requires_grad=True, device=device)
+            M1 = torch.tensor(M, requires_grad=True, device=device)
+            alpha = torch.tensor(0.5, requires_grad=True, device=device)
+
+            val = ot.gromov.semirelaxed_fused_gromov_wasserstein2(M1, C11, C12, p1, alpha=alpha)
+
+            val.backward()
+
+            assert val.device == p1.device
+            assert p1.grad is None
+            assert C11.shape == C11.grad.shape
+            assert C12.shape == C12.grad.shape
+            assert alpha.shape == alpha.grad.shape
+
 
 def test_srfgw_helper_backend(nx):
     n_samples = 20  # nb samples