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While the difficulty of reinforcement learning problems is typically related to the complexity of their state spaces, Abstraction proposes that solutions often lie in simpler underlying latent spaces. Prior works have focused on learning…

Reinforcement learning (RL) is currently one of the most prominent methods for optimizing dynamical systems, with breakthrough results across various fields. The framework is based on the concept of a Markov decision process (MDP), leading…

Dissipative cognitive architectures maintain computation through continuous energy expenditure, where units that exhaust their energy are stochastically replaced with fresh random state. This creates a fundamental challenge: how can…

We apply functional acceleration to the Policy Mirror Descent (PMD) general family of algorithms, which cover a wide range of novel and fundamental methods in Reinforcement Learning (RL). Leveraging duality, we propose a momentum-based PMD…

This paper introduces an algorithm for discovering implicit and delayed causal relations between events observed by a robot at arbitrary times, with the objective of improving data-efficiency and interpretability of model-based…

A large class of linear memory differential equations in one dimension, where the evolution depends on the whole history, can be equivalently described as a projection of a Markov process living in a higher dimensional space. Starting with…

Accelerated gradient descent iterations are widely used in optimization. It is known that, in the continuous-time limit, these iterations converge to a second-order differential equation which we refer to as the accelerated gradient flow.…

Signatures, one of the key concepts of rough path theory, have recently gained prominence as a means to find appropriate feature sets in machine learning systems. In this paper, in order to compute signatures directly from discrete data…

As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the…

Episodic memory is a psychology term which refers to the ability to recall specific events from the past. We suggest one advantage of this particular type of memory is the ability to easily assign credit to a specific state when remembered…

Policy learning for partially observed control tasks requires policies that can remember salient information from past observations. In this paper, we present a method for learning policies with internal memory for high-dimensional,…

The parking-lot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a $2-$parameter…

Deep neural networks have shown superior performance in many regimes to remember familiar patterns with large amounts of data. However, the standard supervised deep learning paradigm is still limited when facing the need to learn new…

Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in velocity and potentials of acceleration; the equation system consists of a single vector equation and potentials updates. The…

Scaling laws describe how learning performance improves with data, compute, or training time, and have become a central theme in modern deep learning. We study this phenomenon in a canonical nonlinear model: phase retrieval with anisotropic…

In this article we present a novel discrete-time design approach which reduces the deteriorating effects of sampling on stability and performance in digitally controlled nonlinear mechanical systems. The method is motivated by recent…

Transformers have achieved remarkable success in sequence modeling and beyond but suffer from quadratic computational and memory complexities with respect to the length of the input sequence. Leveraging techniques include sparse and linear…

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

The relaxation of stochastic systems after sudden perturbations is constrained by speed limits and often reveals memory effects that hinder attempts to accelerate their dynamics. Here we demonstrate Kovacs-type nonmonotonic relaxation in…

First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…