Amortized Optimal Transport from Sliced Potentials

The core insight here is not just speed: by learning to predict transport plans from sliced Kantorovich potentials rather than solving each problem from scratch, these methods separate the expensive optimization phase from deployment, which matters most in settings where you need OT repeatedly across many similar distributions.

This paper sits in a broader cluster of inference-efficiency work appearing in the archive this week. The K-Token Merging paper (from arXiv cs.CL, same date) attacks a structurally similar problem: expensive computation at inference time that can be partially precomputed or compressed. Both approaches trade some upfront training cost for faster repeated use. The connection is not tight at the algorithmic level, but the engineering motivation is shared. More broadly, the amortization framing here also echoes the efficiency-versus-retraining tension visible in the ORCA interpretability paper, which explicitly flags that avoiding retraining is a design goal worth advertising.

The practical test is whether RA-OT or OA-OT holds up on distribution pairs that are genuinely out-of-distribution relative to the training set used to learn the potentials. If follow-up benchmarks show degradation under distribution shift, the amortization gains come with a hidden fragility cost that limits real-world applicability.