Related papers: On the estimation of the Mori-Zwanzig memory integ…

Methods for the reduction of the complexity of computational problems are presented, as well as their connections to renormalization, scaling, and irreversible statistical mechanics. Several statistically stationary cases are analyzed; for…

In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed…

An enriched approximation space is the span of a conventional basis with a few extra functions included, for example to capture known features of the solution to a computational problem. Adding functions to a basis makes it overcomplete…

We develop an efficient algorithm to determine the memory-depth of finite state machines and apply the algorithm to a collection of iterated prisoner's dilemma strategies. The calculation agrees with the memory-depth of other…

The ability of discrete-time nonlinear recurrent neural networks to store time-varying small input signals is investigated by mean-field theory. The combination of a small input strength and mean-field assumptions makes it possible to…

We consider a reinforcement learning setting introduced in (Maillard et al., NIPS 2011) where the learner does not have explicit access to the states of the underlying Markov decision process (MDP). Instead, she has access to several models…

Large Language Models (LLMs) are often evaluated against ideals of perfect Bayesian inference, yet growing evidence suggests that their in-context reasoning exhibits systematic forgetting of past information. Rather than viewing this…

We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described by a computably enumerable set, such as lower semicomputable…

Making neural networks remember over the long term has been a longstanding issue. Although several external memory techniques have been introduced, most focus on retaining recent information in the short term. Regardless of its importance,…

Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…

This paper aims to establish an entropy-regularized value-based reinforcement learning method that can ensure the monotonic improvement of policies at each policy update. Unlike previously proposed lower-bounds on policy improvement in…

We analyse the convergence of an approximate, fully inexact, ADMM algorithm under additive, deterministic and probabilistic error models. We consider the generalized ADMM scheme that is derived from generalized Lagrangian penalty with…

Partially observable Markov decision processes (POMDPs) are standard models for dynamic systems with probabilistic and nondeterministic behaviour in uncertain environments. We prove that in POMDPs with long-run average objective, the…

This work proposes a machine-learning framework for modeling the error incurred by approximate solutions to parameterized dynamical systems. In particular, we extend the machine-learning error models (MLEM) framework proposed in Ref. 15 to…

This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…

This paper investigates the continuous-time limit of score-driven models with long memory. By extending score-driven models to incorporate infinite-lag structures with coefficients exhibiting heavy-tailed decay, we establish their weak…

Mutual information (MI) is a fundamental measure of statistical dependence between two variables, yet accurate estimation from finite data remains notoriously difficult. No estimator is universally reliable, and common approaches fail in…

This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read…

Machines that can replicate human intelligence with type 2 reasoning capabilities should be able to reason at multiple levels of spatio-temporal abstractions and scales using internal world models. Devising formalisms to develop such…

We extend the framework of quantum pushforward designs to the approximate setting, where averaging is achieved only up to finite precision. Using Schatten $p$-norms and Lipschitz continuity arguments, we derive bounds on the approximation…