Attractors

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Period ending 2026-09-21

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Attractors

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Dense Associative Memory

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Hopfield Networks

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119 papers

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Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning
Jun 8, 2026Chen-Rui Fan, Bo Lu, Xing-Yu Wu +2Hopfield Networks Phase Space
Discovering and decoding latent mean-field structure with variational autoencoders
Jun 7, 2026Marco Biroli, Max Welling, Vincenzo VitelliVariational Autoencoder Mean-Field Limit
Between Amnesia and Chaos: A Memory Stability Expressivity Trilemma for Trainable Dissipative Oscillator Networks
Jun 7, 2026Caleb MunigetyOscillatory Dynamics Reservoir Computing
Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series
Jun 5, 2026S. V. Manivelan, Andrei Velichko, I. ManimehanChaos Transients
Front-to-Attractors: Modifying the Front-to-Front Heuristic in Bidirectional Search
Jun 5, 2026Alvin Zou, Muhammad Suhail Saleem, Maxim LikhachevHeuristic Search Heuristics
From Prediction to Self: Developmental Conditions for Agency in Minimal Neural Systems
Jun 4, 2026Evan YeNext Activity Prediction Self-Organization
When Do Attention Circuits Form? Developmental Trajectories of Capability and Attention-Sink Emergence Across Three 1B-ClassArchitectures
Jun 1, 2026Yongzhong XuModel Activations Attractors
Continual Learning in Modern Hopfield Networks with an Application to Diffusion Models
May 27, 2026Ken Takeda, Masafumi Oizumi, Ryo KarakidaCatastrophic Forgetting Hopfield Networks
Balancing Fidelity and Diversity in Diffusion Models via Symmetric Attention Decomposition: Hopfield Perspective
May 26, 2026Hyunmin Cho, Woo Kyoung Han, Kyong Hwan JinSoftmax Attention Hopfield Networks
ARBITER: Reasoning Trajectory Basins and Majority Vote Failures in Test-Time Sampling
May 25, 2026Meng Cai, Lars Kulik, Farhana ChoudhuryArbitration Interaction Trajectories
Beyond Fixed Points: Superpolynomial Capacity of Asymmetric Hopfield Networks
May 23, 2026Aakash Kumar, Anatoly Khina, Frederik Mallmann-Trenn +1Hopfield Networks Attractors
Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning
May 20, 2026Benhao Huang, Zhengyang Geng, Zico KolterTest-Time Scaling Recursive Reasoner
Open-source LLMs administer maximum electric shocks in a Milgram-like obedience experiment
May 20, 2026Roland Pihlakas, Jan Llenzl DagohoyConformity Large Language
Large-Step Training Dynamics of a Two-Factor Linear Transformer Model
May 20, 2026Krishnakumar BalasubramanianTransformer Architectures Gradient Descent
The New Associationism: Lessons from Deep Learning
May 19, 2026Daniel RothschildArtificial Intelligence Systems Dense Associative Memory
Agentic Chunking and Bayesian De-chunking of AI Generated Fuzzy Cognitive Maps: A Model of the Thucydides Trap
May 18, 2026Akash Kumar Panda, Olaoluwa Adigun, Bart KoskoCognitive Map Reasoning Graphs
Learning in Position-Aware Multinomial Logit Bandits: From Multiplicative to General Position Effects
May 17, 2026Xi Chen, Shibo Dai, Jiameng Lyu +1Generalized Linear Bandit Semiparametric Framework
Dynamics of collective creativity in AI art competitions
May 16, 2026Mason Youngblood, Jeff Nusz, Joel SimonCreativity Human-Ai Collaboration
Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM
May 15, 2026Hiroyuki Chuma, Kanji Otsuka, Yoichi SatoDense Associative Memory Human Visual Cortex
Solve the Loop: Attractor Models for Language and Reasoning
May 12, 2026Jacob Fein-Ashley, Paria RashidinejadLarge Language Model Pretraining Attractors
Emergence of Frontier Superposition: Möbius attractor and Cascade Supervision
May 12, 2026Hongyu Gu, Jingwen FuSingle Forward Pass Gradient Concentration
Variational Linear Attention: Stable Associative Memory for Long-Context Transformers
May 11, 2026Vishal Pandey, Gopal SinghQuadratic Attention Dense Associative Memory
Attractor-Vascular Coupling Theory: Formal Grounding and Empirical Validation for AAMI-Standard Cuffless Blood Pressure Estimation from Smartphone Photoplethysmography
May 11, 2026Timothy Oladunni, Farouk Ganiyu AdewumiCuffless Blood Pressure Estimation Remote Photoplethysmography
Factual recall in linear associative memories: sharp asymptotics and mechanistic insights
May 11, 2026Alessio Giorlandino, Sebastian Goldt, Antoine MaillardDense Associative Memory Factual Recall
Joint sparse coding and temporal dynamics support context reconfiguration
May 11, 2026Qianqian Shi, Yue Che, Faqiang Liu +6Catastrophic Forgetting Dense Associative Memory
Hyperparameter Transfer for Dense Associative Memories
May 11, 2026Roi Holtzman, Dmitry Krotov, Boris HaninDense Associative Memory Hyperparameter Optimization
The Wittgensteinian Representation Hypothesis: Is Language the Attractor of Multimodal Convergence?
May 10, 2026Zhaoyang Zhang, Run Shao, Dongyue Wu +4Multi-Modal Representation Learning Convergence
Context-Gated Associative Retrieval: From Theory to Transformers
May 8, 2026Moulik Choraria, Argyrios Gerogiannis, Vidhata Jayaraman +2Dense Associative Memory In-Context Learning
Broken-symmetry shape discrimination on a driven Duffing ring
May 8, 2026Kaspar Anton SchindlerSymmetry Quantum Topological Phases
Bifurcation Models: Learning Set-Valued Solution Maps with Weight-Tied Dynamics
May 8, 2026Caleb Jore, Jialin LiuBifurcation Attractors
Efficient event-driven retrieval in high-capacity kernel Hopfield networks
May 7, 2026Akira TamamoriHopfield Networks Neuromorphic Hardware
Attractor Geometry of Transformer Memory: From Conflict Arbitration to Confident Hallucination
May 7, 2026Qiyao Liang, Risto Miikkulainen, Ila FieteLarge Language Model Hallucination Hidden States
Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval
May 6, 2026Nicholas Barnfield, Juno Kim, Eshaan Nichani +2Dense Associative Memory Decision Thresholds
FAAST: Forward-Only Associative Learning via Closed-Form Fast Weights for Test-Time Supervised Adaptation
May 6, 2026Guangsheng Bao, Hongbo Zhang, Han Cui +4Parameter-Efficient Adaptation Unseen-Task Adaptation
Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs
May 5, 2026Karsten BohlenOrdinary Differential Equations Attractors
A Structural Threshold in Decision Capacity Governs Collapse in Self-Play Reinforcement Learning
May 4, 2026Arahan KujurSelf-Play Attractors
Hall-Like Transversal Stress and Sandpile Criticality on Real Production Networks
May 2, 2026Diego VallarinoHopfield Networks
Benchmarking local Hebbian learning rules for memory storage and prototype extraction
May 1, 2026Anders Lansner, Andreas Knoblauch, Naresh B Ravichandran +1Dense Associative Memory Prototype
Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks
May 1, 2026Akira TamamoriHopfield Networks Attractors
Attractor FCM
Apr 30, 2026Alexis KafantarisAttractors Gradient Descent
Causal Learning with Neural Assemblies
Apr 29, 2026Evangelia Kopadi, Dimitris KallesStructural Causal Model Synaptic Plasticity
Option-Order Randomisation Reveals a Distributional Position Attractor in Prompted Sandbagging
Apr 29, 2026Jon-Paul CacioliMmlu-Pro Distractor
Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics
Apr 28, 2026Arnau Vivet, Alex ArenasHopfield Networks Attractors
Biased Dreams: Limitations to Epistemic Uncertainty Quantification in Latent Space Models
Apr 28, 2026Julia Berger, Bernd Frauenknecht, Sebastian Trimpe +1Latent Dynamics Entropy Regularized Reinforcement Learning
Latent-Hysteresis Graph ODEs: Modeling Coupled Topology-Feature Evolution via Continuous Phase Transitions
Apr 27, 2026Qinhan Hou, Jing TangNeural Ordinary Differential Equations Ordinary Differential Equations
Learning Hippo: Multi-attractor Dynamics and Stability Effects in a Biologically Detailed CA3 Extension of Hopfield Networks
Apr 22, 2026Daniele Corradetti, Renato CorradettiHopfield Networks Dense Associative Memory
Quantization robustness from dense representations of sparse functions in high-capacity kernel associative memory
Apr 22, 2026Akira TamamoriHopfield Networks Quantization
Where to Bind Matters: Hebbian Fast Weights in Vision Transformers for Few-Shot Character Recognition
Apr 22, 2026Gavin Money, Sindhuja Penchala, Jiacheng Li +1Vision Transformer Plasticity
ATLAS: Constitution-Conditioned Latent Geometry and Redistribution Across Language Models and Neural Perturbation Data
Apr 19, 2026Gareth Seneque, Lap-Hang Ho, Nafise Erfanian Saeedi +2Atlas Representational Geometry
Impact of leaky dynamics on predictive path integration accuracy in recurrent neural networks
Apr 17, 2026Yanlin Zhang, Yan Zhang, Muhua Zheng +1Recurrent Neural Networks Synaptic Plasticity
SRMU: Relevance-Gated Updates for Streaming Hyperdimensional Memories
Apr 16, 2026Shay Snyder, Andrew Capodieci, David Gorsich +1Dense Associative Memory Non-Stationarity
Hallucination as Trajectory Commitment: Causal Evidence for Asymmetric Attractor Dynamics in Transformer Generation
Apr 16, 2026G. Aytug AkarlarHallucinations Autoregressive Language Models
From Dispersion to Attraction: Spectral Dynamics of Hallucination Across Whisper Model Scales
Mar 31, 2026Ivan Viakhirev, Kirill Borodin, Grach MkrtchianLlm-Based Automatic Speech Recognition Large Language Model Hallucination
Attractor-Keyed Memory
Mar 17, 2026Natalia G. BerloffDense Associative Memory Signatures
Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits
Dec 16, 2025Michael Murray, Tenzin Chan, Kedar Karhadker +1Hopfield Networks Symmetry
Formalized Hopfield Networks and Boltzmann Machines
Dec 8, 2025Matteo Cipollina, Michail Karatarakis, Freek WiedijkHopfield Networks Stochastic Systems
Distributed Dynamic Associative Memory via Online Convex Optimization
Nov 28, 2025Bowen Wang, Matteo Zecchin, Osvaldo SimeoneDense Associative Memory Learning-Augmented Algorithms
Redundancy Maximization as a Principle of Associative Memory Learning in Hopfield Networks
Nov 4, 2025Mark Blümel, Andreas C. Schneider, Valentin Neuhaus +5Hopfield Networks Dense Associative Memory
Eyes-on-Me: Scalable RAG Poisoning through Transferable Attention-Steering Attractors
Oct 1, 2025Yen-Shan Chen, Sian-Yao Huang, Cheng-Lin Yang +1Retrieval-Augmented Generation Systems Data Poisoning

Jun 8, 2026 · cs.LGJ/K move · Enter open · S save

Hybridizing Equilibrium Propagation with Ising Machines for Efficient Energy-Based Learning

Chen-Rui Fan, Bo Lu, Xing-Yu Wu, Tie-Jun Wang+1

School of Artificial Intelligence, Beijing Normal University, Beijing 100875, China · Laboratory for Advanced Computing and Intelligence Engineering, Information Engineering University, Zhengzhou 450001, China · School of Physical Science and Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China

The rapid evolution of artificial intelligence has led to substantial advances in deep neural networks. Nonetheless, conventional GPU-based training remains highly energy-demanding, motivating the exploration of physical dynamics and compatible energy-based learning schemes, such as equilibrium propagation (EP). EP-based training, however, frequently suffers from convergence to local minima due to phase-space contraction. Here we introduce an Ising-dynamics-inspired equilibrium-propagation framework in which dissipative Hopfield relaxation is replaced by an extended phase-space dynamics with conjugate variables. The resulting training paradigm keeps the local two-phase learning rule of EP while changing the physical route by which neural states reach equilibrium. We show that this dynamics lowers effective energy barriers, accelerates convergence, improves noise robustness, and trains deep convolutional Hopfield networks on MNIST, FashionMNIST, and CIFAR-10 with performance comparable to backpropagation.

Hopfield Networks Phase Space

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