We propose a new regularized optimal transport (OT) formulation, termed sliced-regularized optimal transport (SROT). Unlike entropic OT (EOT), which regularizes the transport plan toward an independent coupling, SROT regularizes it toward a smoothened sliced OT (SOT) plan. To the best of our knowledge, SROT is the first approach to leverage a version of SOT plan as a reference to improve classical OT. We provide a formal definition of SROT, derive its dual formulation, and provide a post-Bayesian interpretation of SROT. We then develop a Sinkhorn-style algorithm for efficient computation, retaining the same scalability advantages as EOT. By incorporating a scalable SOT plan as a prior, SROT yields more accurate approximations of the exact OT plan than EOT under the same level of regularization. Moreover, the resulting transport plan improves upon the reference SOT plan itself. We further introduce the corresponding OT divergence induced by SROT, named SROT divergence, and analyze its topological and computational properties. Finally, we validate our approach through experiments on synthetic datasets and color transfer tasks, demonstrating that SROT is better than both EOT and SOT in approximating exact OT. Additional experiments on gradient flows further highlight the advantages of SROT divergence.

Actor-critic methods have achieved significant success in many challenging applications. However, its finite-time convergence is still poorly understood in the most practical single-timescale form. Existing works on analyzing single-timescale actor-critic have been limited to i.i.d.

Assuc k isthe Assumption (trained. Standardtraining (70 epochs) takes 35 minutes. Trainingwithdata by Gaussiannoise (30 epochs) takes 15 minutes.

Attackskm Success Untar 10 5 50 1 Targeted 10 5 50 1 Case Study:Westart stochasticdefense 2 [ 90,90] degrees (chosen tion.

In this work, we propose a new approach to R-D estimation from the perspective of optimal transport.

In this work, we propose a new approach to R-D estimation from the perspective of optimal transport.

Defending against adversarial examples remains an open problem. A common belief is that randomness at inference increases the cost of finding adversarial inputs. An example of such a defense is to apply a random transformation to inputs prior to feeding them to the model.

As multi-modal large language models (MLLMs) are increasingly applied to complex reasoning tasks, the diversity and quality of reasoning paths become crucial factors affecting their performance. Although current methods aim to enhance reasoning quality through path expansion, they often neglect the diversity of reasoning paths and effective information sharing, leading to local optima and inefficiency. To address these challenges, we propose Evolution of Thought (EoT), a multi-objective framework designed to improve reasoning by fostering both high-quality and diverse reasoning paths. Specifically, we introduce the Non-dominated Sorting Genetic Algorithm II for multi-objective optimization, utilizing crossover and mutation operators to promote greater diversity in reasoning solutions. Additionally, we propose a Condensation-Aggregation mechanism to cluster and eliminate redundant paths, facilitate improved information sharing among parent nodes, and ultimately enhance both the efficiency and quality of the reasoning process. Validation experiments on various vision-language and language reasoning tasks demonstrate that EoT achieves superior reasoning performance and efficiency compared to other competitive baselines. Our study provides a novel perspective on the design of heuristic reasoning frameworks for MLLMs.