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:2607. 24304v1 Announce Type: cross Abstract: We formulate a statistical physics framework to model a networked stochastic dynamical system exhibiting bistability, driven by additive noise and social conformity.
arXiv:2511. 02258v3 Announce Type: replace-cross Abstract: This paper studies the high-dimensional scaling limits of online stochastic gradient descent (SGD).
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:2605. 30432v2 Announce Type: replace-cross Abstract: Social systems consist of networks of individuals who influence one another through social interactions.
arXiv:2607. 22758v1 Announce Type: cross Abstract: The integration of iterative LLMs within multi-agent diagnostic frameworks requires a rigorous quantitative reevaluation of underlying communication topologies.
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.
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...
The paper presents a supervised, scale‑shared neural architecture that learns a coarse‑graining rule for two‑dimensional site percolation. By recursively applying this rule, the model generates a latent field from which the crossing probability is predicted and a fine‑graining decoder reconstructs the largest‑cluster mask. Trained only on small lattices, the network extrapolates to larger systems, accurately recovers the spanning cluster, and reproduces finite‑size scaling near the critical point, demonstrating that the latent representation captures critical fluctuations and scale‑dependent flows consistent with renormalization‑group theory.
The paper demonstrates that long‑time stochastic dynamics can be predicted using generative diffusion models trained only on configuration pairs separated by a short, fixed time lag, without requiring the underlying equations of motion. Applied to two‑dimensional Model B and driven colloids in a periodic optical potential, the learned transition kernels accurately reproduce dynamic critical scaling, self‑similar coarsening, and experimental observables such as particle current and mean passage time, even on larger lattices and unseen initial conditions. This shows that short‑time observations contain sufficient information to forecast emergent non‑equilibrium behavior over extended periods.
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.
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.
arXiv:2602. 14885v2 Announce Type: replace-cross Abstract: Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that restricts network dynamics to gradient-like flows.