We formulate a statistical physics framework to model a networked stochastic dynamical system exhibiting bistability, driven by additive noise and social conformity. We apply this model to understand and mitigate AI-induced delusional spiraling-a phenomenon where algorithmic sycophancy from Large Language Models continuously reinforces inaccurate beliefs within a socially interacting society.
arXiv:2511. 02258v3 Announce Type: replace-cross Abstract: This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD).
By Parsa Rangriz
arXiv:2511.12836v2 Announce Type: replace-cross
Abstract: Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGL...
By Waheed U. Bajwa, Mert Gurbuzbalaban, Mustafa Ali Kutbay, Lingjiong Zhu, Muhammad Zulqarnain
arXiv:2605. 30432v2 Announce Type: replace-cross Abstract: Social systems consist of networks of individuals who influence one another through social interactions.
By Moyi Tian, Daniel A. Messenger, Vanja Dukic, Nancy Rodr\'iguez, David M. Bortz
arXiv:2606. 03067v1 Announce Type: cross Abstract: A recurring data mining task in complex networks is to determine how individual nodes contribute to system behavior.
By Valentina Kuskova, Dmitry Zaytsev, Michael Coppedge
The paper introduces a supervised, scale‑shared neural architecture for two‑dimensional site percolation, implementing a neural renormalization group flow. The model recursively applies a learned coarse‑graining rule across scales, producing a latent field that predicts crossing probability and a fine‑graining decoder that reconstructs the largest‑cluster mask. Trained only on small lattices, it extrapolates to larger systems, accurately recovers the spanning cluster, and yields observables that follow expected finite‑size scaling near the critical point, highlighting the importance of critical fluctuations in the latent representation.
arXiv:2604. 23952v2 Announce Type: replace-cross Abstract: Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging.
By Ludovico T. Giorgini
arXiv:2610.01522v1 Announce Type: cross
Abstract: Many scientific and machine learning systems, from molecular dynamics to diffusion models and beyond, are governed by stochastic dynamics with low-di...
By Vladimir R. Kostic, Karim Lounici, H\'el\`ene Halconruy, Timoth\'ee Devergne, Michele Parrinello, Massimiliano Pontil
Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem.
The paper investigates gradient descent dynamics in the Edge of Stability regime, where a large learning rate causes persistent oscillations linked to improved generalization. It introduces a tractable continuous‑time mean–fluctuation model that couples the window‑averaged trajectory with its fluctuation covariance, derives this model rigorously from a sharp‑valley framework, and analyzes its stationary states and linear stability. The authors also extend the model to wide two‑layer networks, deriving a Wasserstein‑2 gradient flow for weights and fluctuations, proving well‑posedness, a mean‑field limit, and conditional convergence results, with numerical experiments illustrating the predictions and finite‑time limitations.
By Antonin Chodron de Courcel
arXiv:2607. 07232v1 Announce Type: cross Abstract: Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.
By Sergio Rozada, Yiming Qin, Manuel Madeira, Pascal Frossard, Alejandro Ribeiro
The paper studies finite‑horizon minimum‑energy steering of inertial swarms under stochastic disturbances, focusing on mean‑field models with Cucker–Smale alignment or Morse attraction–repulsion interactions. It formulates the problem as a Schr"odinger bridge, deriving nonlinear, time‑symmetric optimality systems and proposing nested fixed‑point schemes for numerical solution. Numerical experiments demonstrate that the optimal corrective drift can either exploit or counteract the natural interaction forces, depending on their alignment with the steering objective.
By Asmaa Eldesoukey, Md Zulfiqur Haider, Italo Napolitano, Yongxin Chen, Abhishek Halder