[linjiaye929]

Types of changes

• Bug fix

Motivation and context

TensorFlowBackend.set_gradients currently discards the upstream cotangent. Multiplying a loss by zero, a negative coefficient, or a positive coefficient therefore leaves its supplied gradients unchanged. For example, for x=[1,2] and a supplied gradient 2*x, multiplying the returned scalar by 7 gives [2,4] instead of [14,28].

Apply the upstream cotangent to each supplied gradient with tf.nest.map_structure. The forward value, public API, and other backends are unchanged.

Related: #923 explicitly documents this independent TensorFlow backend issue as outside its scope. This PR does not modify dmmot or the JAX work in #917.

Validation and limits

• Added 11 regression cases: eager and tf.function multi-input chain-rule checks for coefficients 0, 1, -2 and 7, plus emd2 cost-gradient checks for coefficients 0, -2 and 7.
• Eight direct checks loading the exact current-source backend.py pass. On the unpatched source, the six non-unit-coefficient cases fail and both unit-coefficient controls pass.
• The exact 11 added pytest cases pass using the released POT 0.9.7.post1 wheel with only TensorflowBackend.set_gradients replaced by this exact current-source method. The three emd2 scaling cases fail using the wheel's original method and pass with the replacement.
• Environment: Linux CPU, Python 3.12.14, TensorFlow CPU 2.21.0, NumPy 2.5.4, SciPy 1.18.1.
• pre-commit run --all-files passes all six configured hooks; git diff --check passes.

This is not a full current-source test-suite pass. Building master was blocked when the compiler was killed while compiling the unrelated BSP/Eigen extension, including lower-optimization attempts. Temporary build-option changes were restored and are not part of this PR. The wheel-backed integration checks use released native extensions, not current master native code. The full compatibility matrix, GPU behavior, and remote CI have not been verified.

Keeping this PR as a Draft while that validation remains outstanding.

PR checklist

• I have read the CONTRIBUTING document.
• The documentation is up-to-date with the changes I made (check build artifacts).
• All tests passed, and additional code has been covered with new tests.
• I have added a release note to RELEASES.md.

The unchecked test box is intentional: targeted checks passed as described above, but the full source suite did not run. No documentation API change is needed; documentation artifacts were not built.

AI assistance

Prepared with AI assistance. The defect, minimal change, and regression checks were independently reviewed by a second assistant; this is not a claim of human or maintainer review.