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.

On the Recall Scaling Laws in Mamba: A Theoretical and Mechanistic Study via Hashing
Sep 7, 2026Yuval Koren, Assaf Ben-Kish, Raja Giryes +2Mechanistic Interpretability Scaling Laws
Blavatnik School of Computer Science and AI, Tel Aviv University
Memory as an Energy Landscape---Hopfield
Sep 2, 2026Nima DehghaniHopfield Networks Associative Memory
McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA · The NSF AI Institute for Artificial Intelligence and Fundamental Interactions (IAIFI), Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing
Sep 1, 2026Ling-Wei Kong, Ying-Cheng LaiDynamical Systems Reservoir Computing
Department of Computational Biology, Cornell University, Ithaca, NY 14850, USA · School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA · Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
SSAKG 2.0: An Open-Source Package for Structural Associative Sequence Memory and Context-Based Retrieval
Sep 1, 2026Przemysław Stokłosa, Janusz A. Starzyk, Paweł RaifGraph-Based Retrieval Knowledge Graphs
Institute of Management and Information Technology Bielsko-Biała, Poland · University of Information Technology and Management Rzeszów, Poland · Silesian University of Technology Gliwice, Poland
Kathleen Remembers: Length-Invariant One-Shot Recall Without Attention
Aug 31, 2026George FountzoulasMemory-Augmented Neural Networks Persistent Memory for Language Models
Department of Computer Engineering & Informatics Frederick University, Nicosia, Cyprus
Rate-Coding Bundle Memory: A Unified Model of Memory and Control for Symbolic Computation in the Brain
Aug 29, 2026Teun van Gils, Rowan P. Sommers, Markus Ostarek +1Computational Cognitive Modeling Neurosymbolic Learning
Neurobiology of Language Department, Max Planck Institute for Psycholinguistics · Donders Institute for Brain, Cognition and Behaviour, Radboud University
RippleMem: From Isolated Retrieval to Associative Recollection for Long-Term Agent Memory
Aug 13, 2026Jingbo Ji, Lingyi Li, Xilong Cheng +4Agent Memory Persistent Memory for Language Models
Communication University of China, Beijing, China. · Zhilian Yinghe Technology Co., Ltd., Beijing, China · State Key Laboratory of Media Convergence and Communication, Beijing, China
Consolidator: Learning Persistent Routed Memory Across Context Boundaries
Aug 12, 2026Sungwoo Goo, Hwi-yeol Yun, Sangkeun JungMemory-Augmented Neural Networks Persistent Memory for Language Models
College of Pharmacy, Chungnam National University · Department of Computer Science & Engineering, Chungnam National University
High-Capacity Generalized Hopfield Networks
Aug 8, 2026Victor GalitskiHopfield Networks Associative Memory
Joint Quantum Institute, Department of Physics, University of Maryland, College Park, MD 20742, USA
DART: Decoded Attention over Recurrent States for Efficient Long-Context Sequence Modeling
Aug 3, 2026Yixiao Qian, Song Chen, Pengkai Wang +3Memory-Augmented Language Models KV Caching
College of Control Science and Engineering, Zhejiang University · Department of Mathematics, National University of Singapore · Hong Kong Polytechnic University +1
Memoir: Should a Model Write to Its Memory While It Thinks?
Jul 22, 2026Jaber Jaber, Osama JaberMemory-Augmented Neural Networks Recurrent Neural Networks
RightNow AI
Associative Emotional Learning in Convolutional Neural Networks
Jul 21, 2026Seowung Leem, Andreas Keil, Mingzhou Ding +1Convolutional Neural Networks Associative Memory
J. Crayton Pruitt Family Dept. of Biomedical Engineering, University of Florida, Gainesville, FL 32611, USA · Center for the Study of Emotion and Attention, University of Florida, Gainesville, Florida, USA · Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611, USA +3
Free energy landscape of Dense Associative Memory
Jul 21, 2026Sumedha, Abhishek SinghFree Energy Calculation Neural Network Memorization
School of Physical Sciences, National Institute of Science Education and Research, Bhubaneswar, P.O. Jatni, 752050, India · 2Homi Bhabha National Institute, Training School Complex, Anushakti Nagar 400094, India
Kernelized Linear Attention: Breaking the Capacity Wall with Symmetric Cones
Jul 19, 2026Ayoub Ghriss, Sourav ChakrabortyEfficient Attention Linear Attention
Department of Computer Science, University of Colorado Boulder
MLPs are Hebbians: Constructing Efficient Fact-Storing MLPs for Transformers
Jul 10, 2026Roberto Garcia, Jerry Liu, Ronny Junkins +3Transformer Memorization in Language Models
Institute for Computational & Mathematical Engineering, Stanford University · Department of Computer Science, Stanford University · Department of Computer Science and Engineering, University at Buffalo
Remembering Distinct Items, Not Tokens: A Learnable Dirichlet-Process Cache Between State-Space Models and Attention
Jul 10, 2026Siddharth Pal, Viktoria RojkovaMemory-Augmented Neural Networks KV Caching
The Orthogonalized Read Is a Removable Training Scaffold for Recurrent Memory
Jul 2, 2026Keston Aquino-MichaelsLong Short-Term Memory Networks Associative Memory
No Way Labs
Self-Organized Learning in Oscillatory Neural Networks with Memristive Signed Couplings
Jul 1, 2026Riley Acker, Aman Desai, Garrett Kenyon +1Oscillatory Neural Networks Neuromorphic Computing
1Computing and Artificial Intelligence (CAI) Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA · Center for Nonlinear Studies (CNLS), Los Alamos National Laboratory, Los Alamos, NM 87545, USA · 3Theoretical Division , Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Creating Intelligence: A Computational Foundation for AGI
Jun 30, 2026Peter OvermannComputational Cognitive Modeling Hyperdimensional Computing
Explaining Machine Learning and Memorization with Statistical Mechanics
Jun 30, 2026Robin TheriaultStatistical Physics of Learning Neural Network Memorization
Faculty of Science
Supervised Hebbian learning in Deep Counterstream Associative Networks
Jun 28, 2026Andreas KnoblauchHebbian Learning Associative Memory
Albstadt-Sigmaringen University, KEIM Institute, Poststrasse 6, 72458 Albstadt-Ebingen, Germany
Parallel Manifold Steering: Efficient Adaptation of Large Associative Memories via Residual Energy Shaping
Jun 23, 2026Kanishk AwadhiyaMemory-Augmented Neural Networks Transformer Attention
Independent Researcher
Towards Version-aware Operations and Transaction Memories for Multi-layer MeMo
Jun 23, 2026Peiran LiKnowledge Editing Continual Learning for LLMs
Freie Universität Berlin, Kaiserswerther Str. 16-18, 14195 Berlin, Germany
T-Mem: Memory That Anticipates, Not Archives
Jun 13, 2026Weidong Guo, Dakai Wang, Zixuan Wang +2Persistent Memory for Language Models LLM Memory
1Tencent · 2The Hong Kong University of Science and Technology (Guangzhou)
Controlled Dynamics Attractor Transformer
Jun 13, 2026Cheng Zhang, Minnan Luo, Zesheng Yang +3Energy-Based Models Continuous Attractor Neural Networks
School of Computer Science and Technology, MOEK-LINNS Lab, Xi’an Jiaotong University, Xi’an, Shaanxi, China · Department of Computer Science and Technology, Tsinghua University, Beijing, China
Robust Auto-associative Memory via Convolutional Restricted Hopfield Networks
Jun 11, 2026Ci Lin, Tet Yeap, Iluju KiringaAdversarial Robustness Hopfield Networks
Electrical Engineering and Computer Science University of Ottawa
Recursive Binding on a Budget: Subspace Carving in Order-p Tensor Memories
Jun 9, 2026Travis Pence, Daisuke Yamada, Vikas SinghMemory-Efficient Inference Vector Symbolic Architectures
Department of Computer Science, University of Wisconsin-Madison, United States · Department of Biostatistics and Med. Info., University of Wisconsin-Madison, United States
Parallel Causal Associative Fields: Gated Sparse Memory for Long-Context Language Modeling
Jun 9, 2026Muhammad AhmedMemory-Augmented Language Models Long-Context Language Model Inference
Independent Researcher
Hyperbolic Neural Population Geometry Benefits Computation
Jun 8, 2026Dennis Wu, Yi-Chun Hung, Braden Yuille +2Neural Representation Geometry Neural Processes
Department of Computer Science, Northwestern University · Center for Foundation Models and Generative AI, Northwestern University · Integrated Science Program, Northwestern University +3
An RRAM-based Hardware Implementation of a Radial Basis Function Neuron for Edge Classifiers
Jun 2, 2026Georgios Papandroulidakis, Shady Agwa, Themis ProdromakisCompute-in-Memory Edge ML
Centre for Electronics Frontiers, Institute of Micro and Nano Systems, School of Engineering, The University of Edinburgh, EH9 3BF, UK.

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On the Recall Scaling Laws in Mamba: A Theoretical and Mechanistic Study via Hashing

Yuval Koren, Assaf Ben-Kish, Raja Giryes, Lior Wolf+1

Blavatnik School of Computer Science and AI, Tel Aviv University

Mechanistic Interpretability Scaling Laws Associative Memory State Space Models

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Associative Recall (AR) is the cognitive ability to learn and retrieve links between items in memory. In NLP, AR is used as a benchmark for evaluating the in-context memory capacity of architectures such as Mamba, and has been found to strongly correlate with language modeling performance. This paper explores AR from the perspective of mechanistic interpretability, aiming to reverse-engineer the exact internal algorithm used by Mamba to perform recall. Our key insight is that Mamba performs recall by implicitly learning linear hash functions, and we identify the low-level circuit that enables this behavior. Building on these findings and inspired by theoretical tools in similarity-preserving hashing, such as the Johnson-Lindenstrauss lemma, we develop a theoretical framework for analyzing AR, which we term Recall Scaling Laws. Given the vocabulary size and the number of facts in context, this framework allows us to (1) predict the embedding and state dimensions required for Mamba to achieve perfect recall, (2) predict recall success probability given the model dimensions, and (3) analyze multi-layer models and multi-head SSM patterns. Empirical results show that our theoretical findings are accurate and predictive, offering insights into how AR capacity scales with vocabulary, state, embedding size, and architecture.