Hopfield Networks

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3 papers in the last four weeks, down 40% on the four weeks before. 0.0% of all new papers.

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Training-Free Generation of Protein Sequences from Small Family Alignments via Stochastic Attention
Mar 16, 2026Jeffrey D. VarnerHopfield Networks Molecular Generation
R.F. Smith School of Chemical and Biomolecular Engineering · Cornell University, Ithaca, NY 14850
Stochastic Attention via Langevin Dynamics on the Modern Hopfield Energy
Mar 6, 2026Abdulrahman Alswaidan, Jeffrey D. VarnerHopfield Networks Energy-Based Models
R.F. Smith School of Chemical and Biomolecular Engineering Cornell University, Ithaca, NY 14850
Graph Hopfield Networks: Energy-Based Node Classification with Associative Memory
Mar 3, 2026Abinav Rao, Alex Wa, Rishi AthavaleNode Classification Hopfield Networks
A Dynamical Theory of Sequential Retrieval in Input-Driven Hopfield Networks
Mar 3, 2026Simone Betteti, Giacomo Baggio, Sandro ZampieriHopfield Networks Associative Memory
The Italian Institute of Artificial Intelligence for Industry · Department of Information Engineering, Università degli Studi di Padova
Implicit Bias and Invariance: How Hopfield Networks Efficiently Learn Graph Orbits
Dec 16, 2025Michael Murray, Tenzin Chan, Kedar Karhadker +1Sample Complexity Neural Network Memorization
Mathematical Sciences, University of Bath · Department of Mathematics, UCLA · Algebraic
Formalized Hopfield Networks and Boltzmann Machines
Dec 8, 2025Matteo Cipollina, Michail Karatarakis, Freek WiedijkNeural Network Verification Hopfield Networks
Axiomatic AI, Barcelona, Spain · Radboud University, Nijmegen, The Netherlands
Redundancy Maximization as a Principle of Associative Memory Learning in Hopfield Networks
Nov 4, 2025Mark Blümel, Andreas C. Schneider, Valentin Neuhaus +5Neural Network Memorization Hopfield Networks
Complex Systems Theory, Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany · Faculty of Physics, Institute for the Dynamics of Complex Systems, University of Göttingen · Göttingen Campus Institute for Dynamics of Biological Networks, University of Göttingen, Göttingen, Germany +1
Dynamical stability for dense patterns in attractor neural networks
Jul 14, 2025Uri Cohen, Máté LengyelDynamical Systems Neural Processes
Computational and Biological Learning Lab, Department of Engineering, University of Cambridge, Cambridge, UK · Center for Cognitive Computation, Department of Cognitive Science, Central European University, Budapest, Hungary

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Training-Free Generation of Protein Sequences from Small Family Alignments via Stochastic Attention

Jeffrey D. Varner

R.F. Smith School of Chemical and Biomolecular Engineering · Cornell University, Ithaca, NY 14850

Hopfield Networks Molecular Generation Sequence Modeling

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Generating novel protein sequences that respect a family's statistical constraints typically requires training deep generative models on thousands to millions of examples. Yet most protein families are small: the median Pfam seed alignment contains only 22 sequences, a regime where learned models overfit or collapse. We propose stochastic attention (SA), a training-free sampler that treats the modern Hopfield energy over stored sequences as a Boltzmann distribution and draws samples via Langevin dynamics. The score function is the residual of a single softmax attention operation, eliminating the need for a trained score network, pretraining data, or graphics processing units (GPUs). Across eight Pfam families spanning 37 to 420 sequences and 23 to 262 residues, SA generates sequences with low composition divergence, novelty, and structural plausibility supported by ESMFold and AlphaFold2. Compared with profile hidden Markov models (HMMs), EvoDiff, and the multiple sequence alignment (MSA) Transformer, SA is the only tested method to simultaneously achieve low composition divergence, genuine novelty, and sequence identity within each family's nearest-neighbor identity range; the others drift outside this range or produce near-copies. The critical inverse temperature is predicted from principal component analysis (PCA) dimensionality alone, enabling fully automatic operation from a seed alignment. In two domains with deep mutational scanning data, SA-generated substitutions are enriched for experimentally tolerated mutations beyond a position-matched null, and an independent language model (ESM2-650M) scores them within the natural range. Stochastic attention thus opens training-free sequence generation to the long tail of protein families too small for deep learning.