We prove that the Kim--Milman flow map enjoys favorable stability properties with respect to variations in the target measure, provided that one of the target measures is sufficiently regular. Our results include stability in relative entropy, and more notably, Lipschitz stability in the $2$-Wasserstein distance up to a logarithmic factor. We complement our results with a general existence theorem for these maps for any target measure with finite second moment.

Cross-modal representation learning aims to extract semantically aligned representations from heterogeneous modalities such as images and text. Existing multimodal VAE-based models often suffer from limited capability to align heterogeneous modalities or lack sufficient structural constraints to clearly separate the modality-specific and shared factors. In this work, we propose a novel framework, termed Disentangled Cross-Modal Representation Learning with Enhanced Mutual Supervision (DCMEM). Specifically, our model disentangles the common and distinct information across modalities and regularizes the shared representation learned from each modality in a mutually supervised manner. Moreover, we incorporate the information bottleneck principle into our model to ensure that the shared and modality-specific factors encode exclusive yet complementary information. Notably, our model is designed to be trainable on both complete and partial multimodal datasets with a valid Evidence Lower Bound. Extensive experimental results demonstrate significant improvements of our model over existing methods on various tasks including cross-modal generation, clustering and classification.

Decentralized learning is a learning process in which data is distributed across computational agents or collected by individual agents, and model parameters are computed as the consensus of the agents. It has gained a lot of interest for applications where agents can collaboratively learn a predictive model without sharing their own data, but sharing only their local models with their immediate neighbors to generate a global model [He et al., 2018, Hendrikx et al., 2019, Arjevani et al., 2020]. We assume there are N agents who are connected over an undirected communication network G = (V,E) where V = {1,...,N} represents the agents and E V V denotes the set of edges; i.e., if agent i and j are connected then (i,j) E implies (j,i) E. Suppose we have a collection of n independent and identically distributed (i.i.d.) data pairs zi = (ai,yi), where ai Rp is the feature vector and yi the label or response of the i-th observation. Let Z = [z1,z2,,zn] Rnp be sampled from the distribution p(Z|x) where the parameter x Rd has a common prior. The goal is to sample from the posterior distribution p(x|Z) p(Z|x)p(x) by distributing Z among N agents such that Zi = {zi1,zi2,,zini} is the subset of data exclusive to agent i.

Neural Information Processing Systems http://nips.cc/

How can the stochastic properties of input data and labels be appropriately captured to handle severe perturbations? To answer this question, we represent both input data and target labels as probability measures (i.e., probability densities), denoted asµn and ˆνn, respectively, in the Wasserstein space and solve a distance-based classification problem (i.e.,

We propose Terminal Velocity Matching (TVM), a generalization of flow matching that enables high-fidelity one- and few-step generative modeling. TVM models the transition between any two diffusion timesteps and regularizes its behavior at its terminal time rather than at the initial time. We prove that TVM provides an upper bound on the $2$-Wasserstein distance between data and model distributions when the model is Lipschitz continuous. However, since Diffusion Transformers lack this property, we introduce minimal architectural changes that achieve stable, single-stage training. To make TVM efficient in practice, we develop a fused attention kernel that supports backward passes on Jacobian-Vector Products, which scale well with transformer architectures. On ImageNet-256x256, TVM achieves 3.29 FID with a single function evaluation (NFE) and 1.99 FID with 4 NFEs. It similarly achieves 4.32 1-NFE FID and 2.94 4-NFE FID on ImageNet-512x512, representing state-of-the-art performance for one/few-step models from scratch.

Neural Information Processing Systems http://nips.cc/