Related papers: Universal Approximation of Mean-Field Models via T…

A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential…

Transformer models have shown great success in natural language processing; however, their potential remains mostly unexplored for dynamical systems. In this work, we investigate the optimal output estimation problem using transformers,…

The transformer architecture has demonstrated remarkable capabilities in modern artificial intelligence, among which the capability of implicitly learning an internal model during inference time is widely believed to play a key role in the…

Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…

We develop a scalable algorithm for mean field control problems with kernel interactions by combining particle system simulations with random Fourier feature approximations. The method replaces the quadratic-cost kernel evaluations by…

We consider a system consisting of $n$ particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle ``jumps forward'' at some time points, with the instantaneous rate…

Currently, this paper is under review in IEEE. Transformers have intrigued the vision research community with their state-of-the-art performance in natural language processing. With their superior performance, transformers have found their…

We propose a general deep architecture for learning functions on multiple permutation-invariant sets. We also show how to generalize this architecture to sets of elements of any dimension by dimension equivariance. We demonstrate that our…

The filtering distribution captures the statistics of the state of a dynamical system from partial and noisy observations. Classical particle filters provably approximate this distribution in quite general settings; however they behave…

Equilibrium properties of long-range interacting systems on lattices are investigated. There was a conjecture by Cannas et. al. that the mean-field theory is exact for spin systems with non-additive long-range interactions. This is called…

In this talk I review some recent developments which shed light on the main connections between structural glasses and mean-field spin glass models with a discontinuous transition. I also discuss the role of quantum fluctuations on the…

We consider particle systems with mean-field interactions whose distribution is invariant by translations. Under the assumption that the system seen from its centre of mass be reversible with respect to a Gibbs measure, we establish large…

We study a two-level system coupled to two quantized electromagnetic modes within the Jaynes-Cummings framework. While the single-mode model is exactly solvable due to its conserved excitation number, yielding finite-dimensional invariant…

We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the TAP approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings…

Mean-Field is an efficient way to approximate a posterior distribution in complex graphical models and constitutes the most popular class of Bayesian variational approximation methods. In most applications, the mean field distribution…

In recent years, reinforcement learning and its multi-agent analogue have achieved great success in solving various complex control problems. However, multi-agent reinforcement learning remains challenging both in its theoretical analysis…

We study the approximation of shift-invariant or equivariant functions by deep fully convolutional networks from the dynamical systems perspective. We prove that deep residual fully convolutional networks and their continuous-layer…

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…

A dynamic mean field theory is developed for finite state and action Bayesian reinforcement learning in the large state space limit. In an analogy with statistical physics, the Bellman equation is studied as a disordered dynamical system;…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…