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Efficient Transferable Optimal Transport via Min-Sliced Transport Plans

NeurIPS 2026 · Learning theory and algorithms › Optimal transport · approach: Transport map estimation · 0 citations (OpenAlex)

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Studies transferability of learned slicers in min-sliced transport plans (min-STP): proves slicer stability under distribution perturbations, derives minibatch statistical rates, and shows amortized slicers work for point-cloud alignment, flow generation, and image translation.

Problem

Learned 1D slicers for sliced transport plans are optimized per distribution pair; it is unclear whether they transfer to new, shifted pairs, and full-batch OT-style computation is costly at scale.

Approach

Smooth the min-STP objective with Laplace perturbations of the slicer (via LapSum differentiable sorting), prove continuity of the smoothed objective so that optimal slicers vary little when source/target distributions are close (Berge's maximum theorem), and train slicers on minibatch estimators with finite-sample bounds.

Key results

• Amortized min-STP achieves test Pearson correlation with exact OT of 0.902 on ModelNet10 category pairs, close to per-pair min-STP (0.947) and above Wasserstein Wormhole (0.770) and random-slicer STP (0.719).
• In the gradual-drift experiment, pretrained slicer initialization starts at a substantially lower STP objective than random initialization in every step and sits closer to the OT reference.
• Min-STP-based flow achieves a favorable trade-off of low OT compute time per epoch and low W2 on ShapeNet-Chairs versus baselines, per the reported plot.

Limitations

• Transferability theorem is qualitative (Berge's theorem) and the quantitative epsilon-tau relation is only sketched for finite supports with high probability.
• Theory assumes compact space, Lipschitz bounded slicer class, and discrete measures with countable support.
• Gains over baselines reported on limited settings (2D toy, ModelNet10, one ShapeNet class, FFHQ latents).

Experimental setup

Datasets: ModelNet10 ShapeNet FFHQ

Benchmarks: ModelNet10 ShapeNet-Chairs FFHQ adult-to-child translation

Metrics: Pearson correlation with exact OT W2 distance OT compute time per epoch objective value vs OT lower bound

Baselines: STP with random slicer Wasserstein Wormhole Sinkhorn Expected Transport Plan (EST) ProgOT LOT DGSWP OT-MF

Builds on: LapSum DGSWP (differentiable generalized sliced Wasserstein plan) min-SWGG Projected Wasserstein OT-MF

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