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This paper enhances the classic Smagorinsky model by introducing an innovative, adaptive dissipation term that adjusts dynamically with distance from boundary regions. This modification addresses a known limitation of the standard model…
The sequential nature of autoregressive next-token prediction imposes a fundamental speed limit on large language models. While continuous flow models offer a path to parallel generation, they traditionally demand expensive iterative…
Disentangled representation learning offers useful properties such as dimension reduction and interpretability, which are essential to modern deep learning approaches. Although deep learning techniques have been widely applied to…
We consider the problem of decentralized nonconvex optimization over a compact submanifold, where each local agent's objective function defined by the local dataset is smooth. Leveraging the powerful tool of proximal smoothness, we…
We show that the sensor self-localization problem can be cast as a static parameter estimation problem for Hidden Markov Models and we implement fully decentralized versions of the Recursive Maximum Likelihood and on-line…
This paper presents novel Gaussian process decentralized data fusion algorithms exploiting the notion of agent-centric support sets for distributed cooperative perception of large-scale environmental phenomena. To overcome the limitations…
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. The state variable satisfies a discrete diffusion law on a weighted, oriented graph, where conductances are scaled by…
This paper establishes central limit theorems for Polyak-Ruppert averaged Q-learning under asynchronous updates. We prove a non-asymptotic central limit theorem, where the convergence rate in Wasserstein distance explicitly reflects the…
Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or…
Modeling stochastic dynamics from discrete observations is a key interdisciplinary challenge. Existing methods often fail to estimate the continuous evolution of probability densities from trajectories or face the curse of dimensionality.…
This paper studies the theoretical underpinnings of machine learning of ergodic It\^o diffusions. The objective is to understand the convergence properties of the invariant statistics when the underlying system of stochastic differential…
Recent breakthroughs in self-supervised learning show that such algorithms learn visual representations that can be transferred better to unseen tasks than joint-training methods relying on task-specific supervision. In this paper, we found…
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exhibits fundamental limitations. KL-based analyses diverge…
We consider the "all-for-one" decentralized learning problem for generalized linear models. The features of each sample are partitioned among several collaborating agents in a connected network, but only one agent observes the response…
In the paradigm of decentralized learning, a group of agents collaborate to learn a global model using a distributed dataset without a central server; nevertheless, it is severely challenged by the heterogeneity of the data distribution…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of…
Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns…
In this paper, we study the generalization properties of online learning based stochastic methods for supervised learning problems where the loss function is dependent on more than one training sample (e.g., metric learning, ranking). We…
For stochastic approximation algorithms with discontinuous dynamics, it is shown that under suitable distributional assumptions, the interpolated iterates track a Fillipov solution of the limiting differential inclusion. In addition, we…