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Many measurements in computer vision and machine learning manifest as non-Euclidean data samples. Several researchers recently extended a number of deep neural network architectures for manifold valued data samples. Researchers have…

Machine Learning · Statistics 2020-04-07 Rudrasis Chakraborty

Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…

Disordered Systems and Neural Networks · Physics 2007-05-23 Markus Brede , John Finnigan

We formulate the Fast-Weights Homeostatic Reentry Network (FHRN) as a continuous-time neural-ODE system, revealing its role as a norm-regulated reentrant dynamical process. Starting from the discrete reentry rule $x_t = x_t^{(\mathrm{ex})}…

Dynamical Systems · Mathematics 2025-12-08 Byung Gyu Chae

In this work, we show that Latent Flow-Matching (LFM) models are robust to different types of perturbations, including data reduction and model capacity shrinkage. We characterize this stability by their tendency to generate similar outputs…

Machine Learning · Computer Science 2026-05-12 Rania Briq , Michael Kamp , Ohad Fried , Sarel Cohen , Stefan Kesselheim

Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…

Disordered Systems and Neural Networks · Physics 2018-08-23 Shun-ichi Amari , Ryo Karakida , Masafumi Oizumi

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large…

Working memory (WM) allows information to be stored and manipulated over short time scales. Performance on WM tasks is thought to be supported by the frontoparietal system (FPS), the default mode system (DMS), and interactions between them.…

Neurons and Cognition · Quantitative Biology 2020-09-09 Andrew C. Murphy , Maxwell A. Bertolero , Lia Papadopoulos , David M. Lydon-Staley , Danielle S. Bassett

Recurrent neural networks (RNNs) provide a theoretical framework for understanding computation in biological neural circuits, yet classical results, such as Hopfield's model of associative memory, rely on symmetric connectivity that…

Disordered Systems and Neural Networks · Physics 2026-02-17 Ramón Nartallo-Kaluarachchi , Renaud Lambiotte , Alain Goriely

Training neural networks to perform different tasks is relevant across various disciplines. In particular, Recurrent Neural Networks (RNNs) are of great interest in Computational Neuroscience. Open-source frameworks dedicated to Machine…

Machine Learning · Computer Science 2023-08-01 Cecilia Jarne

Asymmetry in the synaptic interactions between neurons plays a crucial role in determining the memory storage and retrieval properties of recurrent neural networks. In this work, we analyze the problem of storing random memories in a…

Disordered Systems and Neural Networks · Physics 2022-10-11 Fabián Aguirre-López , Mauro Pastore , Silvio Franz

Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of…

Neurons and Cognition · Quantitative Biology 2015-07-29 Marcus K. Benna , Stefano Fusi

Continuous attractors offer a unique class of solutions for storing continuous-valued variables in recurrent system states for indefinitely long time intervals. Unfortunately, continuous attractors suffer from severe structural instability…

Neurons and Cognition · Quantitative Biology 2025-03-25 Ábel Ságodi , Guillermo Martín-Sánchez , Piotr Sokół , Il Memming Park

Deep neural networks have achieved remarkable performance in various applications but are extremely vulnerable to adversarial perturbation. The most representative and promising methods that can enhance model robustness, such as adversarial…

Computer Vision and Pattern Recognition · Computer Science 2022-08-30 Faqiang Liu , Rong Zhao

Neuromorphic computing is a brainlike information processing paradigm that requires adaptive learning mechanisms. A spiking neuro-evolutionary system is used for this purpose; plastic resistive memories are implemented as synapses in…

Neural and Evolutionary Computing · Computer Science 2015-05-19 Gerard David Howard , Larry Bull , Ben de Lacy Costello , Andrew Adamatzky , Ella Gale

Conditional Neural Fields (CNFs) are increasingly being leveraged as continuous signal representations, by associating each data-sample with a latent variable that conditions a shared backbone Neural Field (NeF) to reconstruct the sample.…

A persistent paradox in continual learning (CL) is that neural networks often retain linearly separable representations of past tasks even when their output predictions fail. We formalize this distinction as the gap between deep…

Machine Learning · Computer Science 2026-03-20 Giulia Lanzillotta , Damiano Meier , Thomas Hofmann

Active systems across scales, ranging from molecular machines to human crowds, are usually modeled as assemblies of self-propelled particles driven by internally generated forces. However, these models often assume memoryless dynamics and…

Statistical Mechanics · Physics 2025-12-10 Marc Besse , Raphaël Voituriez

Plastic self-adaptation, nonlinear recurrent dynamics and multi-scale memory are desired features in hardware implementations of neural networks, because they enable them to learn, adapt and process information similarly to the way…

The ability to learn new concepts continually is necessary in this ever-changing world. However, deep neural networks suffer from catastrophic forgetting when learning new categories. Many works have been proposed to alleviate this…

Computer Vision and Pattern Recognition · Computer Science 2022-07-21 Fu-Yun Wang , Da-Wei Zhou , Han-Jia Ye , De-Chuan Zhan

Learning with physical systems is an emerging paradigm that seeks to harness the intrinsic nonlinear dynamics of physical substrates for learning. The impetus for a paradigm shift in how hardware is used for computational intelligence stems…

Disordered Systems and Neural Networks · Physics 2026-04-28 Francesco Caravelli , Gianluca Milano , Adam Z. Stieg , Carlo Ricciardi , Simon Anthony Brown , Zdenka Kuncic