Xinran Liu

Navid NaderiAlizadeh, Darian Salehi, Xinran Liu et al.

Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions has proven challenging, often necessitating a large number of slices to achieve desirable performance and thereby increasing computational complexity. We introduce a constrained learning approach to optimize the slicing directions for SW distances. Specifically, we constrain the 1D transport plans to approximate the optimal plan in the original space, ensuring meaningful slicing directions. By leveraging continuous relaxations of these transport plans, we enable a gradient-based primal-dual approach to train the slicer parameters, alongside the remaining model parameters. We demonstrate how this constrained slicing approach can be applied to pool high-dimensional embeddings into fixed-length permutation-invariant representations. Numerical results on foundation models trained on images, point clouds, and protein sequences showcase the efficacy of the proposed constrained learning approach in learning more informative slicing directions. Our implementation code can be found at https://github.com/Stranja572/constrainedswe.

Xinran Liu, Yikun Bai, Rocío Díaz Martín et al.

Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein distances, have recently been developed to address this need. These methods reduce the computational burden of optimal transport by slicing hyperspheres into one-dimensional projections, i.e., lines or circles. Concurrently, linear optimal transport has been proposed to embed distributions into \( L^2 \) spaces, where the \( L^2 \) distance approximates the optimal transport distance, thereby simplifying comparisons across multiple distributions. In this work, we introduce the Linear Spherical Sliced Optimal Transport (LSSOT) framework, which utilizes slicing to embed spherical distributions into \( L^2 \) spaces while preserving their intrinsic geometry, offering a computationally efficient metric for spherical probability measures. We establish the metricity of LSSOT and demonstrate its superior computational efficiency in applications such as cortical surface registration, 3D point cloud interpolation via gradient flow, and shape embedding. Our results demonstrate the significant computational benefits and high accuracy of LSSOT in these applications.

Saptarshi Nath, Christos Peridis, Eseoghene Benjamin et al.

Agentic AI aims to create systems that set their own goals, adapt proactively to change, and refine behavior through continuous experience. Recent advances suggest that, when facing multiple and unforeseen tasks, agents could benefit from sharing machine-learned knowledge and reusing policies that have already been fully or partially learned by other agents. However, how to query, select, and retrieve policies from a pool of agents, and how to integrate such policies remains a largely unexplored area. This study explores how an agent decides what knowledge to select, from whom, and when and how to integrate it in its own policy in order to accelerate its own learning. The proposed algorithm, \emph{Modular Sharing and Composition in Collective Learning} (MOSAIC), improves learning in agentic collectives by combining (1) knowledge selection using performance signals and cosine similarity on Wasserstein task embeddings, (2) modular and transferable neural representations via masks, and (3) policy integration, composition and fine-tuning. MOSAIC outperforms isolated learners and global sharing approaches in both learning speed and overall performance, and in some cases solves tasks that isolated agents cannot. The results also demonstrate that selective, goal-driven reuse leads to less susceptibility to task interference. We also observe the emergence of self-organization, where agents solving simpler tasks accelerate the learning of harder ones through shared knowledge.