Tsallis statistics generalizes Boltzmann-Gibbs statistical mechanics through a single real parameter $q$ that controls the weight assigned to rare and frequent events. Originally proposed to describe physical systems with long-range correlations, multifractal geometry, and heavy-tailed fluctuations, the framework has become a recurring ingredient in modern artificial intelligence (AI): it underlies sparse attention mechanisms (\textsc{sparsemax} and $α$-\textsc{entmax}), maximum-entropy reinforcement learning with controllable exploration, robust and heavy-tailed probabilistic models, and a family of generalized loss functions and regularizers.
arXiv:2604. 10727v2 Announce Type: replace-cross Abstract: Classical information-theoretic learning bounds typically rely on KL mutual information and moment-generating-function (MGF) arguments, which are well matched to bounded or sub-Gaussian losses but can be ineffective when losses or rewards are heavy-tailed.
The paper introduces the concept of behavior-consistent deep reinforcement learning, aiming to produce high-performing policies that remain distributionally similar across different training runs. It shows that maximum-entropy RL can control behavioral divergence by anchoring runs to a common prior, and proves that for Boltzmann policies, a temperature proportional to Q‑function disagreement limits pairwise KL divergence. Building on this, the authors propose Q‑value Expectile Disagreement (QED), a state‑dependent temperature schedule that uses double‑critic disagreement to approximate cross‑run disagreement, and demonstrate that QED reduces across‑run divergence by two orders of magnitude on 18 continuous‑control tasks without sacrificing performance.
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
arXiv:2607. 17316v1 Announce Type: new Abstract: The softmax policy $\pi(a \mid s) \propto \exp(\beta Q(s,a))$ is the default model of stochastic choice in reinforcement learning (RL).
arXiv:2601. 08136v2 Announce Type: replace Abstract: Diffusion and flow policies are gaining prominence in online reinforcement learning (RL) due to their expressive power, yet training them efficiently remains a critical challenge.
The paper proposes using the $q$Gaussian distribution, derived from Tsallis entropy maximization, to address the shortcomings of Gaussian assumptions in sparse learning with correlated and heterogeneous data. It introduces a new framework that adapts numerical equilibrium methods to composite optimization problems, applying it to the Hager‑Zhang conjugate gradient algorithm to create a stable, efficient sparse learning algorithm. The work offers both theoretical insights into alternative statistical distributions and practical tools for data analysis in fields like biostatistics.
arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
The paper investigates regression with bounded responses, comparing two learning frameworks: model selection aggregation, which requires improper algorithms to achieve minimax excess risk, and universal learning, where empirical risk minimization suffices for exponential learning rates. For finite hypothesis classes, the authors show that the $Q$-aggregation estimator simultaneously attains minimax optimal tails and exponential universal rates, while other common estimators fail to do so. For countably infinite classes, they prove an inherent trade‑off between exponential universal and minimax uniform rates, resolved by combining optimal algorithms from each framework via $Q$-aggregation.
arXiv:2606. 30512v1 Announce Type: cross Abstract: Why overparameterised deep networks generalise so remarkably well remains one of the most stubborn open questions in machine learning theory.
arXiv:2609.36945v1 Announce Type: new Abstract: We study the learning dynamics of fine-tuning a policy model on self-generated and reward-weighted data, with particular focus on a generalized version...
arXiv:2605. 26078v3 Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions.
arXiv:2609.07998v1 Announce Type: new Abstract: We study the control of Markov decision processes in which the quality of a policy is evaluated by a dynamic, time-consistent Markov risk measure rathe...