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In neuroscience, classical Hopfield networks are the standard biologically plausible model of long-term memory, relying on Hebbian plasticity for storage and attractor dynamics for recall. In contrast, memory-augmented neural networks in…

Neurons and Cognition · Quantitative Biology 2021-10-28 Danil Tyulmankov , Ching Fang , Annapurna Vadaparty , Guangyu Robert Yang

The recently introduced continuous Hopfield network (see Ramsauer et al.) exhibits large memorization capabilities, which manifest as attractive fixed points of its update rule -- a differentiable function consisting of two linear mappings…

Dynamical Systems · Mathematics 2026-04-06 Hans-Peter Beise

Many observables of brain dynamics appear to be optimized for computation. Which connectivity structures underlie this fine-tuning? We propose that many of these structures are naturally encoded in the space that more directly relates to…

Disordered Systems and Neural Networks · Physics 2023-09-18 Lorenzo Tiberi , David Dahmen , Moritz Helias

Efficient continual learning in humans is enabled by a rich set of neurophysiological mechanisms and interactions between multiple memory systems. The brain efficiently encodes information in non-overlapping sparse codes, which facilitates…

Neural and Evolutionary Computing · Computer Science 2023-01-13 Fahad Sarfraz , Elahe Arani , Bahram Zonooz

Humans are adept at uncovering abstract associations in the world around them, yet the underlying mechanisms remain poorly understood. Intuitively, learning the higher-order structure of statistical relationships should involve complex…

Neurons and Cognition · Quantitative Biology 2020-03-26 Christopher W. Lynn , Ari E. Kahn , Nathaniel Nyema , Danielle S. Bassett

We introduce a novel approach to endowing neural networks with emergent, long-term, large-scale memory. Distinct from strategies that connect neural networks to external memory banks via intricately crafted controllers and hand-designed…

Machine Learning · Computer Science 2020-08-18 Tri Huynh , Michael Maire , Matthew R. Walter

Learning requires the traversal of inherently distinct cognitive states to produce behavioral adaptation. Yet, tools to explicitly measure these states with non-invasive imaging -- and to assess their dynamics during learning -- remain…

Metastable brain dynamics are characterized by abrupt, jump-like modulations so that the neural activity in single trials appears to unfold as a sequence of discrete, quasi-stationary states. Evidence that cortical neural activity unfolds…

Neurons and Cognition · Quantitative Biology 2019-06-20 Giancarlo La Camera , Alfredo Fontanini , Luca Mazzucato

The human brain exhibits large-scale spontaneous fluctuations that account for most of its total energy metabolism. Independent of any overt function, this immense ongoing activity likely creates or maintains a potential functional brain…

Neurons and Cognition · Quantitative Biology 2021-02-23 Ze Wang

We study how the connectivity within a recurrent neural network determines and is determined by the multistable solutions of network activity. To gain analytic tractability we let neural activation be a non-smooth Heaviside step function.…

Neural and Evolutionary Computing · Computer Science 2023-03-09 Magnus Tournoy , Brent Doiron

We consider the task of constructing a data structure for associating a static set of keys with values, while allowing arbitrary output values for queries involving keys outside the set. Compared to hash tables, these so-called static…

Data Structures and Algorithms · Computer Science 2026-05-20 Stefan Hermann , Hans-Peter Lehmann , Giorgio Vinciguerra , Stefan Walzer

The idea that memory behavior relies on a gradually-changing internal state has a long history in mathematical psychology. This chapter traces this line of thought from statistical learning theory in the 1950s, through distributed memory…

Neurons and Cognition · Quantitative Biology 2022-01-07 Marc W. Howard

Memory encoding by cyclic shear is a reliable process to store information in jammed solids, yet its underlying mechanism and its connection to the amorphous structure are not fully understood. When a jammed sphere packing is repeatedly…

Soft Condensed Matter · Physics 2021-10-27 Francesco Arceri , Eric I. Corwin , Varda F. Hagh

The demand for high-density data storage with ultrafast accessibility motivates the search for new memory implementations. Ideally such storage devices should be robust to input error and to unreliability of individual elements; furthermore…

Disordered Systems and Neural Networks · Physics 2007-05-23 P. Chandra , L. B. Ioffe

Word embeddings are powerful representations that form the foundation of many natural language processing architectures, both in English and in other languages. To gain further insight into word embeddings, we explore their stability (e.g.,…

Computation and Language · Computer Science 2021-09-13 Laura Burdick , Jonathan K. Kummerfeld , Rada Mihalcea

We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of $0$s and $1$s with about $\log N$ $1$s, only. We compare different synaptic weights, architectures and retrieval…

Probability · Mathematics 2016-06-27 Vincent Gripon , Judith Heusel , Matthias Löwe , Franck Vermet

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…

Systems and Control · Electrical Eng. & Systems 2021-12-08 Fangda Gu , He Yin , Laurent El Ghaoui , Murat Arcak , Peter Seiler , Ming Jin

This study explores the learnability of memory-less and memory-augmented RNNs, which are theoretically equivalent to Pushdown Automata. Empirical results show that these models often fail to generalize on longer sequences, relying more on…

Computation and Language · Computer Science 2024-10-07 Shrabon Das , Ankur Mali

Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…

Biological Physics · Physics 2021-06-07 Oskar H Schnaack , Luca Peliti , Armita Nourmohammad

Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic…

Dynamical Systems · Mathematics 2016-03-23 Pascal Chossat , Martin Krupa
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