Mean-Field Limit

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Period ending 2026-09-21

2 new papers

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Period ending 2026-09-14

4 new papers

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Period ending 2026-09-07

1 new paper

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58 papers

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Learning-Induced Dynamical Transition in Recurrent Neural Networks
Sep 16, 2026Varun VaidyaLearning Dynamics Recurrent Neural Networks
Attention Mean Fields Predict Average Representation Dynamics and Reveal Context-Specific Computation
Sep 14, 2026Micah Adler, John W. Byers, Mark CrovellaGraph Language Models Mean-Field Limit
Logit Refiner: Improving Visual Autoregressive Models via Intra-Scale Dependency Modeling
Sep 12, 2026Meimingwei Li, Stefan Andreas Baumann, Felix Krause +1Visual Autoregressive Models Text-To-Image
Critical initialization destabilizes higher input derivatives in wide scalar-input networks
Sep 10, 2026Prashant Singh, Pranav SinghTwo-Layer Neural Networks Mean-Field Limit
Graph neural networks and the energetic cavity method for combinatorial optimization
Sep 7, 2026Joe Bacchus George, George T. CantwellGraph Neural Networks Two-Dimensional Ising Model
Estimating Population-Risk Curves Along Nonconvex Gradient Flows from the Training Sample
Aug 31, 2026Mingzhi SongFinite-Sample Wasserstein Gradient Flows
A Mean-Field Framework for Inference-Time Distributional Control of Diffusion Models
Aug 9, 2026Samuel Howard, Nikolas NüskenInference-Time Control Distributional Learning
Particle-based Generalised Stochastic Optimisation
Aug 3, 2026Jiechen Jackie Zhang, O. Deniz AkyildizStochastic Optimization Langevin Dynamics
Multi-Agent Privacy Game in Federated Learning: A Unified Mean-Field View
Jul 25, 2026Kun Zhao, Xu ChenFederated Learning AI Privacy Risks and Protection
Actor-Critic Learning for Extended Mean Field Control with Deterministic Policies
Jul 13, 2026Ziheng Cheng, Xin Guo, Huyên Pham +1Model-Free Reinforcement Learning Stochastic Optimal Control
A Formalization of the Mean-Field Derivation of the Vlasov Equation: AI-Assisted Lean Formalization as a Strategy Game
Jul 9, 2026Joseph K. MillerTheorem Formalization
Constrained Decoding for Diffusion Language Models via Efficient Inference over Finite Automata
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Width-Robust Learnability in Mean-Field Bayesian Neural Networks
Jul 7, 2026Dmitry Vaintrob, Kaarel HänniBayesian Neural Networks Two-Layer Neural Networks
Broken Ergodicity and the Violation of the Fluctuation-Dissipation Theorem Lead to Generalization Beyond Overfitting in Machine Learning
Jul 5, 2026Chan Li, Nigel GoldenfeldMean-Field Limit Two-Layer Neural Networks
Implicit Bias of SGD in Multivariate ReLU Networks: Effective Width Collapse
Jul 3, 2026Shuang Liang, Tom Jacobs, Guido MontúfarRectified Linear Unit Networks Stochastic Gradient Descent
Mean Field Reinforcement Learning
Jul 1, 2026René Carmona, Mathieu LaurièreMean-Field Limit Multi-Agent Reinforcement Learning
Predictable GRPO: A Closed-Form Model of Training Dynamics
Jun 29, 2026Rajat Ghosh, Datta Nimmaturi, Aryan Singhal +4Group Relative Policy Optimization Reward Modeling
Exit-and-Join Dynamics and Equilibrium in Continuum Cooperative Games
Jun 27, 2026Quanyan ZhuCoalition Formation Equilibrium
Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data
Jun 25, 2026Erhan Bayraktar, Martin Hernandez, Qinxin Yan +1Model-Free Reinforcement Learning Stochastic Optimal Control
Neural Parameter Calibration for Finite-State Mean Field Games
Jun 22, 2026Anna C. M. Thöni, Grégoire Lambrecht, Gökçe Dayanıklı +3Mean-Field Limit Zero--Sum Differential Game
Stationary Robust Mean-Field Games under Model Mismatches
Jun 21, 2026Yue WangMulti-Agent Reinforcement Learning Zero--Sum Differential Game
Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning
Jun 18, 2026Luciano Campi, Federico Cannerozzi, Ioannis TzouanasEquilibrium Mean-Field Limit
Attention as Frustrated Synchronization
Jun 17, 2026Joshua NunleyBest-Epoch Metrics Mean-Field Limit
Operator Calculus for Population-Based Optimization: A Mean-Field Convergence Theory
Jun 12, 2026Pekka Malo, Lauri Viitasaari, Patrik Nummi +3Mean-Field Limit Lyapunov Function
Convergence of Monte Carlo Optimistic Policy Iteration: Beyond Uniform State-Action Updates
Jun 9, 2026Octave Oliviers, Glenn VinnicombeOptimal Policies Monte Carlo
Discovering and decoding latent mean-field structure with variational autoencoders
Jun 7, 2026Marco Biroli, Max Welling, Vincenzo VitelliVariational Autoencoder Mean-Field Limit
Beyond Linear and Overcomplete Regimes: A Mean-Field Analysis of Bottleneck Autoencoders
Jun 5, 2026Santanu Das, Ramyak Bilas, Pascal Esser +1Masked Autoencoders Two-Layer Neural Networks
Quantifying Uncertainty In Wide Two-Layer Neural Networks: On The Law Of The Limiting Fluctuation Process
Jun 4, 2026Arnaud Descours, Arnaud Guillin, Geoffrey Lacour +3Two-Layer Neural Networks Central Limit Theorem
Gradient descent at the Edge of Stability: free energy model and kinetic description of the two-layer network
Jun 3, 2026Antonin Chodron de CourcelGradient Descent Two-Layer Neural Networks
Derivative Informed Learning of Exchange-Correlation Functionals
Jun 2, 2026Eike S. Eberhard, Luca A. Thiede, Abdul Aldossary +5Density Functional Theory Mean-Field Limit
Nonlocal Mean Field Schrödinger Bridge with Learned Interactions
Jun 2, 2026Daisuke Inoue, Dante Kalise, Mathieu LaurièreSchrödinger Bridges Mean-Field Limit
The Crowded Embedding Space: A Mean-Field Mechanism for Emergent Marginalization in Retrieval-Augmented Agents
Jun 1, 2026Shwan Ashrafi, Dan RothRelevance Minority
Recognize Your Orchestrator: An Entropy Dynamics Perspective for LLM Multi-Agent Systems
May 31, 2026Junze Zhu, Weihao Chen, Xuanwang Zhang +2Multi-Agent Systems Orchestration
Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
May 28, 2026Moyi Tian, Daniel A. Messenger, Vanja Dukic +2System Identification Stochastic Systems
Mean-Field Diffuser: Scaling Offline MARL to Thousands of Agents
May 28, 2026Wenhao Li, Xiangfeng Wang, Bo JinMulti-Agent Reinforcement Learning Offline Reinforcement Learning
Composing Non-Conjugate Factor Graphs with Closed-Form Variational Inference
May 28, 2026Mykola Lukashchuk, Kyrylo Yemets, Wouter M. Kouw +4Variational Inference Factor Graphs
Kernel-based potential mean-field games with unbiased random Fourier $U$ -statistics
May 28, 2026Yumiharu NakanoMaximum Mean Discrepancy Mean-Field Limit
A Minimal Bifurcation Model of Load Imbalance in a Softmax Mixture-of-Experts Router
May 27, 2026O. M. KiselevLoad Balancing Mixture-of-Experts Models
The incremental voter model: mean-field analysis and convergence to equilibrium
May 27, 2026Fei Cao, Xiaoqian GongMean-Field Limit Equilibrium
Thinned Mean Field Langevin Dynamics
May 27, 2026Zonghao Chen, Heishiro Kanagawa, François-Xavier Briol +2Mean-Field Limit Langevin Dynamics
Feature Learning in Wide Neural Networks under $μ$ P: Identifiability and Sparse-Dictionary Decomposition of the Mean-Field Limit
May 23, 2026Akmal XodarevTwo-Layer Neural Networks Feature Learning
Move on Muon : A Hamiltonian probability gradient flow perspective of Muon optimizer
May 22, 2026Aratrika Mustafi, Soumya Mukherjee, Bharath K. SriperumbudurMuon Optimizer Muon
Convergence of Consensus-Based Particle Methods for Nonconvex Bi-Level Optimization
May 19, 2026Yutong Chao, Xudong Sun, Konstantin Riedl +2Bilevel Optimization Mean-Field Limit
From Mean-Field Limits to Semiclassical Concentration: Global Convergence of the Canonical Evolutionary Strategy
May 19, 2026Matías Neto, Nicolás Garay, Luis Martí +1Evolutionary Search Convergence Analysis
Training Infinitely Deep and Wide Transformers
May 17, 2026Raphaël Barboni, Maarten V. de Hoop, Takashi Furuya +1Transformer Architectures Mean-Field Limit
Saturating Scaling Laws for Equational Discovery: A Phenomenology of Growth Dynamics in Three Toy Substrates with Two Real-World Replications
May 14, 2026Fabio RovaiPower-Law Distribution Scaling Laws
Kinetic theory for Transformers and the lost-in-the-middle phenomenon
May 9, 2026Mitia Duerinckx, Borjan Geshkovski, Stefano RossiMean-Field Limit Causal Attention
Spherical Boltzmann machines: a solvable theory of learning and generation in energy-based models
May 9, 2026Thomas Tulinski, Simona Cocco, Rémi Monasson +1Boltzmann Distributions Statistical Mechanics
Spectral Dynamics in Deep Networks: Feature Learning, Outlier Escape, and Learning Rate Transfer
May 8, 2026Clarissa Lauditi, Cengiz Pehlevan, Blake BordelonDeep Network Neural Network
Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers
May 8, 2026Noboru Isobe, Daisuke Inoue, Masaaki ImaizumiTransformer Architectures Mean-Field Limit
MEMOA: Massive Mixtures of Online Agents via Mean-Field Decentralized Nash Equilibria
May 6, 2026Xuwei Yang, David B. Emerson, Fatemeh Tavakoli +1Federated Reinforcement Learning Multi-Agent Reinforcement Learning
Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations
Apr 30, 2026Zhenjie Ren, Xiaoli Wei, Xiang Yu +1Stochastic Optimal Control Q-Learning
Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Apr 21, 2026Simmaco Di Lillo, Leonardo Maini, Domenico MarinucciCentral Limit Theorem Asymptotics
Local exponential stability of mean-field Langevin descent-ascent and associated particle system
Feb 2, 2026Geuntaek Seo, Minseop Shin, Pierre Monmarché +1Mean-Field Limit Nash Equilibrium
Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization
Nov 26, 2025William De Deyn, Michael Herty, Giovanni SamaeyNeural Network Optimization Two-Layer Neural Networks
Consensus-based optimization for closed-box adversarial attacks and a connection to evolution strategies
Jun 30, 2025Tim Roith, Leon Bungert, Philipp WackerEvolutionary Search Evolution
A Functional-Space Mean-Field Theory of Partially-Trained Three-Layer Neural Networks
Oct 28, 2022Zhengdao Chen, Eric Vanden-Eijnden, Joan BrunaTwo-Layer Neural Networks Mean-Field Limit
On Universality of Non-Separable Approximate Message Passing Algorithms
Date pendingMax Lovig, Tianhao Wang, Zhou FanApproximation Message Passing Neural Networks

Sep 16, 2026 · cs.LGJ/K move · Enter open · S save

Learning-Induced Dynamical Transition in Recurrent Neural Networks

Varun Vaidya

Department of Physics, University of South Dakota, Vermillion 57069, USA

Learning in recurrent neural networks can fundamentally reshape their underlying dynamics, transforming initially chaotic activity into stable task-dependent behavior. We develop a non-equilibrium dynamical mean-field theory(DMFT) to describe this transition during learning. We show that a slow feedback-driven learning process generates an evolving effective feedback strength that drives the network through a transition from chaotic to stable dynamics defined by a bifurcation of the DMFT solution. By deriving the two-time correlation function throughout learning, we identify a critical feedback strength and a corresponding learning rate dependent critical time separating these regimes. The transition arises from the progressive deformation of an effective dynamical landscape by the growing learned feedback structure. Starting from the untrained state, the theory predicts the time evolution of the network output during training and shows quantitative agreement with numerical simulations.

Learning Dynamics Recurrent Neural Networks Mean-Field Limit Transitions

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