Teacher Knows It Best: Spontaneous Symmetry Breaking and Tipping Points in Networked Langevin Dynamics AI Sycophancy

• URL: http://arxiv.org/abs/2607.24304v1
• Date: Mon, 27 Jul 2026 11:47:57 GMT
• Title: Teacher Knows It Best: Spontaneous Symmetry Breaking and Tipping Points in Networked Langevin Dynamics AI Sycophancy
• Abstract summary: We formulate a statistical physics framework to model a networked dynamical system exhibiting bistability, driven by additive noise and social conformity.<n>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.<n>We prove mathematically that under certain conditions, a highly concentrated, rapid intervention targeting massive hubs strictly outperforms a distributed, slow approach to rescue the network.
• Score: 5.868852957948178
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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. By partitioning the network into a majority of regular agents and a minority of "aware" nodes (Teachers) placed at topological hubs, we use a degree-weighted mean-field approximation to reduce high-dimensional coupled Langevin equations into a single macroscopic drift equation. We provide a closed-form analytical derivation for the deterministic critical tipping time through a saddle-node bifurcation. We validate this analytical boundary using finite-size scaling and demonstrate a universal data collapse across diverse network topologies. Finally, we optimize an intervention strategy under a strict budget constraint that balances the topological footprint against driving velocity. We prove mathematically that under certain conditions, a highly concentrated, rapid intervention targeting massive hubs strictly outperforms a distributed, slow approach to rescue the network.

Related papers

• Physics-Informed Coarsening for Multigrid Graph Neural Surrogates [0.769672852567215]
  We introduce a graph neural network for solid mechanics that couples an encoder-processor-decoder backbone with a physics-informed coarsening strategy.<n>Our results highlight the importance of physics-informed coarsening for scalable surrogate modeling in solid mechanics.
  arXiv  Detail & Related papers  (2026-05-29T08:47:04Z)
• Robust Multi-Agent Target Tracking in Intermittent Communication Environments via Analytical Belief Merging [2.3559161556025887]
  We formulate the decentralized belief merging problem as Forward and Reverse Kullback-Leibler (KL) divergence optimizations.<n>By deploying these derivations, we mathematically eliminate optimization artifacts, achieving perfect mathematical fidelity.<n>We propose a novel spatially-aware visit-weighted KL merging strategy that dynamically weighs agent beliefs based on their physical visitation history.
  arXiv  Detail & Related papers  (2026-04-08T20:27:48Z)
• Dynamics of Finite Width Kernel and Prediction Fluctuations in Mean Field Neural Networks [47.73646927060476]
  We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Our results are non-perturbative in the strength of feature learning.
  arXiv  Detail & Related papers  (2023-04-06T23:11:49Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Mean-field analysis for heavy ball methods: Dropout-stability, connectivity, and global convergence [17.63517562327928]
  This paper focuses on neural networks with two and three layers and provides a rigorous understanding of the properties of the solutions found by SHB. We show convergence to the global optimum and give a quantitative bound between the mean-field limit and the SHB dynamics of a finite-width network.
  arXiv  Detail & Related papers  (2022-10-13T08:08:25Z)
• Losing momentum in continuous-time stochastic optimisation [42.617042045455506]
  momentum-based optimisation algorithms have become particularly widespread. In this work, we analyse a continuous-time model for gradient descent with momentum. We also train a convolutional neural network in an image classification problem.
  arXiv  Detail & Related papers  (2022-09-08T10:46:05Z)
• Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks [72.09574528342732]
  Physics-informed neural network (PINN) algorithms have shown promising results in solving a wide range of problems involving partial differential equations (PDEs) They often fail to converge to desirable solutions when the target function contains high-frequency features, due to a phenomenon known as spectral bias. In the present work, we exploit neural tangent kernels (NTKs) to investigate the training dynamics of PINNs evolving under gradient descent with momentum (SGDM)
  arXiv  Detail & Related papers  (2022-06-29T19:03:10Z)
• LordNet: An Efficient Neural Network for Learning to Solve Parametric Partial Differential Equations without Simulated Data [47.49194807524502]
  We propose LordNet, a tunable and efficient neural network for modeling entanglements. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements can be well modeled by the LordNet.
  arXiv  Detail & Related papers  (2022-06-19T14:41:08Z)
• NN-EUCLID: deep-learning hyperelasticity without stress data [0.0]
  We propose a new approach for unsupervised learning of hyperelastic laws with physics-consistent deep neural networks. In contrast to supervised learning, which assumes the stress-strain, the approach only uses realistically measurable full-elastic field displacement and global force availability data.
  arXiv  Detail & Related papers  (2022-05-04T13:54:54Z)
• Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
  convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
  arXiv  Detail & Related papers  (2022-01-25T17:13:56Z)
• Revisit Geophysical Imaging in A New View of Physics-informed Generative Adversarial Learning [2.12121796606941]
  Full waveform inversion produces high-resolution subsurface models. FWI with least-squares function suffers from many drawbacks such as the local-minima problem. Recent works relying on partial differential equations and neural networks show promising performance for two-dimensional FWI. We propose an unsupervised learning paradigm that integrates wave equation with a discriminate network to accurately estimate the physically consistent models.
  arXiv  Detail & Related papers  (2021-09-23T15:54:40Z)
• Generalization bound of globally optimal non-convex neural network training: Transportation map estimation by infinite dimensional Langevin dynamics [50.83356836818667]
  We introduce a new theoretical framework to analyze deep learning optimization with connection to its generalization error. Existing frameworks such as mean field theory and neural tangent kernel theory for neural network optimization analysis typically require taking limit of infinite width of the network to show its global convergence.
  arXiv  Detail & Related papers  (2020-07-11T18:19:50Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.