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Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problem

NeurIPS 2026 · Learning theory and algorithms › Optimal transport · approach: Sinkhorn and entropic OT algorithms

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Benchmarks existing continuous Gromov-Wasserstein OT solvers under correlated vs. uncorrelated data setups and proposes NeuralGW, a discrete-free minimax neural solver for inner-product GWOT that handles uncorrelated data better.

Problem

Continuous Gromov-Wasserstein OT solvers are evaluated mostly on correlated (paired) data, and it is unclear whether they work when source and target samples are independent; existing continuous methods also depend on discrete GW techniques that scale poorly.

Approach

Defines (un)correlatedness of training data via a permutation-based construction and shows existing solvers degrade when uncorrelated; proposes NeuralGW, a min-max-min neural formulation of inner-product GW with a learnable Frobenius-norm matrix P, trained by SGD on random samples without any discrete OT or pairing.

Key results

• NeuralGW is the only solver that remains usable across all correlatedness levels, including uncorrelated alpha=0, on Twitter-GloVe with 380K training samples per the paper's large-scale experiments.
• Baseline solvers StructuredGW, AlignGW and FlowGW perform well for totally correlated data (alpha=1) but their performance drops significantly as alpha decreases.
• With only 6K training samples, NeuralGW fails to model inner structure (Top-1 near 0.000), and the paper attributes this to the data requirements of adversarial training.

Surprising findings

• RegGW, CycleGW and FlowGW fail for any alpha <= 1 when trained on randomly batched large data, because random permutation yields batches with near-zero correlation.
• Existing word-embedding alignment results on MUSE reportedly rely on CSLS, which may inflate apparent performance.

Limitations

• NeuralGW training is adversarial and unstable, with high variance across initializations.
• NeuralGW is not guaranteed to converge to an optimal GW solution and requires large datasets.
• All continuous solvers, including NeuralGW, fail for low-to-high dimensional mappings.

Experimental setup

Datasets: Twitter GloVe embeddings MUSE bilingual vocabularies with BPEmb embeddings

Benchmarks: Twitter-GloVe MUSE-BPEmb

Metrics: Top-k accuracy cosine similarity FOSCTTM MMD Sinkhorn divergence BW2^2-UVP distortion

Baselines: StructuredGW AlignGW FlowGW RegGW CycleGW

Builds on: Gromov-Wasserstein distance entropic maps Monge Gap Sinkhorn divergence Conditional Flow Matching

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