Associative Memory

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Associative memory asks how a system can store information so that a cue brings back a related pattern, fact, or sequence, a problem central to neural memory and efficient AI. Classical Hopfield networks, dense and kernel associative memories, and Hebbian learning use attractor dynamics or similarity-based retrieval; newer recurrent and linear-attention models add sparse key-value stores, while agent systems use linked episodic memories. Theory examines capacity, retrieval basins, stability, and interference, while experiments test noisy pattern completion, long-range recall, language-model memory, and hardware implementations. A persistent tension is that more storage does not guarantee reliable, selective recall: finite state and overlapping representations can cause interference, forgetting, and false associations, even as explicit retrieval improves access at added cost.

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120 papers16 papers in the last four weeks, down 16% on the four weeks before. 0.1% of all new papers.

Sample-efficient learning with Dense Associative Memories
Oct 19, 2026Andrew Lucas, Dmitry KrotovAssociative Memory Data-Efficient Learning
Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA · Dynamical Mind, Cambridge, MA 02141, USA
Kronecker Delta Rule for Long Context Linear Attention
Oct 19, 2026Anamaria-Roberta Hartl, Levente Zólyomi, Michael List +3Delta-Rule Linear Attention Attention Mechanisms
Institute for Machine Learning, Johannes Kepler University, Linz · NXAI GmbH, Linz
Phase Kernel Lifts Capacity of Dense Associative Memory
Oct 15, 2026Yifei Zhao, Ying TangHopfield Networks Associative Memory
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China · School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China · Key Laboratory of Quantum Physics and Photonic Quantum Information, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China +1
MemCode: Discrete Semantic Representations for Long-Term Agent Memory
Oct 14, 2026Xin Li, Liang Hu, Duoqian Miao +2LLM Agent Memory Memory Management for LLM Agents
Tongji University · WorldMind
Depth Memory
Oct 13, 2026David González-Martínez, Philipp Nazari, T. Konstantin Rusch +1Memory-Augmented Language Models Associative Memory
ELLIS Institute Tübingen · Max Planck Institute for Intelligent Systems, Tübingen · Tübingen AI Center +2
AMemOps: Evaluating Memory Updates in Long Audio Streams
Oct 13, 2026Peiwei Chang, Li Zhang, Mark D. Plumbley +2Audio Understanding Associative Memory
Centre for Vision, Speech and Signal Processing, University of Surrey, UK · Department of Computer Science, Royal Holloway, University of London, UK · Department of Informatics, King’s College London, UK
Where Polanyi Meets Galois: Tacit Knowing as an Algebro-Deterministic Operation, Toward Re-rooting AI-Generated Science
Oct 12, 2026Hiroyuki Chuma, Kanji Otsuka, Yoichi Sato +1Associative Memory Hyperdimensional Computing
Professor Emeritus, Hitotsubashi University · Professor Emeritus, Meisei University · Shuhari System
DeltaNet-PC: Test-Time Memory Without Backpropagation Through Time
Oct 10, 2026Todd Morrill, Richard ZemelNeural Network Memorization Predictive Coding
Computer Science, Columbia University New York, NY, USA
Double-Take: Improving Capacity, Binding, and Selectivity In Long-Context Within Bidirectional Memory
Oct 9, 2026Vakul Raghavan, Utkarsh Grover, Mingyang Mao +2Long-Context Modeling Memory-Augmented Neural Networks
Department of Mathematics and Computer Science, Rutgers University, Newark, NJ, USA · Embodied Robotics and Automation Lab, University of South Florida, Tampa, FL, USA
BRACE: Differential Privacy for Dense Associative Memory with LSR Energy
Oct 8, 2026Chang Qu, Zhaoyang ShiAssociative Memory Differential Privacy
Department of Mathematics and Statistics, University of Ottawa · Center for Applied Mathematics, Fudan University
A Geometry-Based Capacity Theory for Finite-Feature Associative Memory
Oct 6, 2026Jianhai Zhang, Donghao Zhang, Pattarawut Charatpangoon +4Associative Memory Information Retrieval
Department of Biomedical Engineering, Schulich School of Engineering, University of Calgary, and the Ron and Rene Ward Centre for Healthy Brain Aging Research, Hotchkiss Brain Institute, University of Calgary
Madeleine: Learning Involuntary Recall for Conversational Memory from Simulated Lives
Oct 1, 2026Zhiyun ShiMemory-Augmented Language Models Persistent Memory for Language Models
Nanyang Technological University, Singapore
Finite-Horizon Fisher Memory in Two-Sided Power-Bounded Recurrent Systems
Sep 30, 2026Jeonghoon LeeRecurrent Neural Networks Linear RNNs
Attractor Dynamics Inc.
Beyond Diagonal State Space Models: Exact Non-Abelian Group Tracking, Solvability Barriers, and Geometric Physical Manifolds
Sep 29, 2026Zeyu JiaState Space Models Sequence Modeling
School of Biomedical Engineering and Technology, Tianjin Medical University, Medical School, Tianjin University · School of Biomedical Engineering and Technology, Tianjin Medical University · Medical School, Tianjin University
CyFA: Linear Sequence Modeling with Relative-Time-Partitioned Memory
Sep 28, 2026Yixiao Chen, Shuojin Yang, Shi-Min HuLinear RNNs Linear Attention
Tsinghua University
Intrinsic Associative Memory on Riemannian Manifolds: Curvature, Capacity, and Emergent Modes
Sep 28, 2026Krishnakumar Balasubramanian, Zhaoyang ShiAssociative Memory
Department of Statistics, University of California, Davis. · Center for Applied Mathematics, Fudan University.
SchemaMem: Schema-Indexed Recurrent Memory for Delayed State Retrieval
Sep 27, 2026Sungwoo Goo, Hwi-yeol Yun, Sangkeun JungMemory-Augmented Neural Networks Persistent Memory for Language Models
College of Pharmacy, Chungnam National University Daejeon, Republic of Korea · Department of Computer Science & Engineering, Chungnam National University Daejeon, Republic of Korea
How Linear Attention Remembers
Sep 27, 2026Kichang Lee, JaeYeon Park, Songkuk Kim +1Linear Attention Memorization in Language Models
KAIST · Yonsei University · Dankook University
DRAM: Delta-rule Recurrent Associative Memory for Robot Manipulation Policies
Sep 26, 2026Xinyu Zhao, Yixiang Shan, Tao Yang +5Long-Horizon Robotic Manipulation Delta-Rule Linear Attention
Simplexity Robotics
Graph Memory: Spectral Associative Memory via Dirichlet Energy
Sep 26, 2026Zhaoyang ShiAssociative Memory Graph-Based Retrieval
Center for Applied Mathematics, Fudan University Shanghai, China
Boolean threshold functions, neuron capacity, and memory retrieval
Sep 24, 2026Xinyuan XieBoolean Function Learning Neural Network Memorization
Constant-Memory Recall: Learned Associations in a Fixed Matrix State
Sep 23, 2026Samuel LarsonAssociative Memory Memory-Efficient Inference
Pebble ML
Latest Exact Match Attention
Sep 22, 2026Moritz BrösamleTransformer Expressivity Memory-Augmented Language Models
Department of Mathematics, University of Tübingen, Germany
Bias-Induced Crossover in Absolute Capacity of Dense Associative Memory
Sep 15, 2026Yuto Sakurai, Takeaki Shimokawa, Kazunori Iwata +1Hopfield Networks Associative Memory
Graduate School of Information Sciences, Hiroshima City University, 3-4-1 Ohtsuka-higashi, Asaminami-ku, Hiroshima 731-3194, Japan · RIKEN Center for Advanced Intelligence Project and The University of Tokyo
Information Geometric Self-Organization at the Edge of Stability in High-Capacity Kernel Associative Memories
Sep 15, 2026Akira TamamoriInformation Geometry Edge of Stability
Faculty of Information Science, Aichi Institute of Technology, Aichi, 470-0392, Japan
Anatomy of Associative Recall in Fixed-State Recurrences: A Matched-State Decomposition, an Interference Wall, and a Curriculum That Breaks It
Sep 14, 2026Julian Boesch, Andrew WeeRecurrent Neural Networks Curriculum Learning
1Purdue University · 2Obit Research
When the Gradient Sees Rank: Provable Necessity, Causal Recruitment, and Composition in Trained Matrix Memories
Sep 12, 2026Samuel LarsonAssociative Memory Memory-Augmented Neural Networks
Pebble ML
RunningTensor: Generalizing Linear Attention to Higher-Order Recurrent States
Sep 11, 2026Luca Herranz-Celotti, Vincent GuigueRecurrent Neural Networks Linear Attention
ISIR Sorbonne, France
Hierarchical Prototype Emergence in Modern Hopfield Models
Sep 10, 2026Aditya Cowsik, Adithya SriramNeural Network Generalization Hopfield Networks
Department of Physics, Stanford University, Stanford, CA 94305, USA
Phases in a class of associative memories via hidden neurons
Sep 10, 2026Toshihiro Ota, Masato TakiPhase Transitions Hopfield Networks
CyberAgent AI Lab, Shibuya, Tokyo 150–0002, Japan · RIKEN iTHEMS, Wako, Saitama 351–0198, Japan · Graduate School of Artificial Intelligence and Science, Rikkyo University, Toshima, Tokyo 171–8501, Japan

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Sample-efficient learning with Dense Associative Memories

Andrew Lucas, Dmitry Krotov

Department of Physics and Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA · Dynamical Mind, Cambridge, MA 02141, USA

Associative Memory Data-Efficient Learning Statistical Physics of Learning Representation Learning

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We analytically study the evolution of the energy function of Dense Associative Memories (DenseAMs) as they train on randomly sampled codewords of random expander low-density parity-check codes (a.k.a. solutions of random XORSAT problems). We identify two distinct regimes and a transition between them, reminiscent of grokking in neural networks. A regime of small training set size is where the model memorizes a few training examples but cannot discover the underlying rules of the entire codeword dictionary generative process. The opposite regime, corresponding to a larger training set size, is where the model has uncovered the sparse constraints that generated the entire data set after seeing only polynomially many patterns. We also design a novel class of DenseAMs with a thresholding learning rule, and show that any amount of thresholding enables the model to perform simplified sparse Hamiltonian learning, which exponentially reduces the number of training examples needed to learn the true underlying data set. In this regime, the model learns how to discover

\exp[\mathrm{O}(n)]

solutions from only

\mathrm{O}(\log n)

training samples, which is asymptotically optimal for any learning algorithm. When training on codewords of certain random codes, the model can even learn the underlying code when a small O(1) fraction of bits are latent variables. These latent variables are not shown to the model during learning, but will be discovered by sparsifying observed higher-order correlations. For certain random codes, we show that a simple and conservative algorithm learns a minimal latent representation for the data set. This provides a transparent, physics-motivated, and analytically tractable toy model for how deep latent representations emerge in an associative memory training.