arXiv:2605. 19178v2 Announce Type: replace-cross Abstract: The great success of neural networks primarily arises from the presence of the large number of weight parameters combined with nonlinearities in the input-output relationship of single neurons.
arXiv:2607. 23349v1 Announce Type: new Abstract: We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions.
arXiv:2606. 31110v1 Announce Type: new Abstract: Artificial neural networks (NNs) and machine learning (ML) algorithms are poorly understood from a theoretical perspective, which makes it difficult to fully realize their potential and overcome their weaknesses.
arXiv:2608. 06823v1 Announce Type: cross Abstract: In this paper, we extend a weak adversary neural network pushforward method for solving time dependent Boltzmann equation and a weak formulation of the collision operator is proposed where an invertible neural pushforward mapping is used to generating samples given by the distribution governed by the Boltzmann equation.
arXiv:2501. 02436v5 Announce Type: replace Abstract: Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning.
arXiv:2607. 08406v1 Announce Type: new Abstract: Backpropagation (BP) dominates deep learning training, but its reliance on gradients brings inherent troubles -- vanishing and exploding gradients.
arXiv:2511. 07308v3 Announce Type: replace Abstract: Understanding the training dynamics of deep neural networks remains a major open problem, with physics-inspired approaches offering promising insights.
arXiv:2509. 04899v4 Announce Type: replace-cross Abstract: Restricted Boltzmann machines (RBMs) are energy-based models originating from statistical physics, in which hidden units mediate the probability distribution of high-dimensional visible configurations.
arXiv:2608. 17450v1 Announce Type: cross Abstract: Learning restricted Boltzmann machines (RBMs) is computationally challenging because it requires expectations whose exact evaluation is generally intractable.
arXiv:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
Backpropagation (BP) dominates deep learning training, but its reliance on gradients brings inherent troubles -- vanishing and exploding gradients. The pursuit of gradient-free methods has long been a goal in the field of artificial intelligence.
arXiv:2607. 08091v1 Announce Type: cross Abstract: The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases.
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.