fix the sign of gradient for kl gromov

RELEASES.md

@@ -10,6 +10,7 @@
 - Fix gpu compatibility of sr(F)GW solvers when `G0 is not None`(PR #596)
 - Fix doc and example for lowrank sinkhorn (PR #601)
 - Fix issue with empty weights for `ot.emd2` (PR #606, Issue #534)
+- Fix a sign error regarding the gradient of `ot.gromov._gw.fused_gromov_wasserstein2` and `ot.gromov._gw.gromov_wasserstein2` for the kl loss (PR #610)
 
 ## 0.9.2
 *December 2023*

ot/gromov/_gw.py

@@ -315,7 +315,7 @@ def gromov_wasserstein2(C1, C2, p=None, q=None, loss_fun='square_loss', symmetri
         gC2 = 2 * C2 * nx.outer(q, q) - 2 * nx.dot(T.T, nx.dot(C1, T))
     elif loss_fun == 'kl_loss':
         gC1 = nx.log(C1 + 1e-15) * nx.outer(p, p) - nx.dot(T, nx.dot(nx.log(C2 + 1e-15), T.T))
-        gC2 = nx.dot(T.T, nx.dot(C1, T)) / (C2 + 1e-15) + nx.outer(q, q)
+        gC2 = - nx.dot(T.T, nx.dot(C1, T)) / (C2 + 1e-15) + nx.outer(q, q)
 
     gw = nx.set_gradients(gw, (p, q, C1, C2),
                           (log_gw['u'] - nx.mean(log_gw['u']),
@@ -627,7 +627,7 @@ def fused_gromov_wasserstein2(M, C1, C2, p=None, q=None, loss_fun='square_loss',
         gC2 = 2 * C2 * nx.outer(q, q) - 2 * nx.dot(T.T, nx.dot(C1, T))
     elif loss_fun == 'kl_loss':
         gC1 = nx.log(C1 + 1e-15) * nx.outer(p, p) - nx.dot(T, nx.dot(nx.log(C2 + 1e-15), T.T))
-        gC2 = nx.dot(T.T, nx.dot(C1, T)) / (C2 + 1e-15) + nx.outer(q, q)
+        gC2 = - nx.dot(T.T, nx.dot(C1, T)) / (C2 + 1e-15) + nx.outer(q, q)
     if isinstance(alpha, int) or isinstance(alpha, float):
         fgw_dist = nx.set_gradients(fgw_dist, (p, q, C1, C2, M),
                                     (log_fgw['u'] - nx.mean(log_fgw['u']),