Related papers: Continuous Limits of Coupled Flows in Representati…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
In continual learning scenarios, catastrophic forgetting of previously learned tasks is a critical issue, making it essential to effectively measure such forgetting. Recently, there has been growing interest in focusing on representation…
Representation learning is a widely adopted framework for learning in data-scarce environments to obtain a feature extractor or representation from various different yet related tasks. Despite extensive research on representation learning,…
Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals…
Biased attributes, spuriously correlated with target labels in a dataset, can problematically lead to neural networks that learn improper shortcuts for classifications and limit their capabilities for out-of-distribution (OOD)…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
We consider the problem of average consensus in a distributed system comprising a set of nodes that can exchange information among themselves. We focus on a class of algorithms for solving such a problem whereby each node maintains a state…
Multimodal learning has been lacking principled ways of combining information from different modalities and learning a low-dimensional manifold of meaningful representations. We study multimodal learning and sensor fusion from a latent…
We study the local convergence of diffusive mean-field systems, including Wasserstein gradient flows, min-max dynamics, and multi-species games. We establish exponential local convergence in $\chi^2$-divergence with sharp rates, under two…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
In this paper, a distributed stochastic approximation algorithm is studied. Applications of such algorithms include decentralized estimation, optimization, control or computing. The algorithm consists in two steps: a local step, where each…
In this study we consider limit theorems for microscopic stochastic models of neural fields. We show that the Wilson-Cowan equation can be obtained as the limit in probability on compacts for a sequence of microscopic models when the number…
Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…
We study the consensus decentralized optimization problem where the objective function is the average of $n$ agents private non-convex cost functions; moreover, the agents can only communicate to their neighbors on a given network topology.…
A key challenge in decentralized optimization is determining the optimal convergence rate and designing algorithms to achieve it. While this problem has been extensively addressed for doubly-stochastic and column-stochastic mixing matrices,…
Parallel stochastic gradient methods are gaining prominence in solving large-scale machine learning problems that involve data distributed across multiple nodes. However, obtaining unbiased stochastic gradients, which have been the focus of…
Estimation of interface curvature in surface-tension dominated flows is a remaining challenge in Volume of Fluid (VOF) methods. Data-driven methods are recently emerging as a promising alternative in this domain. They outperform…
We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…
For a nondegenerate analytic system with a conserved quantity, a classic result by Lyapunov guarantees the existence of an analytic manifold of periodic orbits tangent to any two-dimensional, elliptic eigenspace of a fixed point satisfying…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…