arXiv subjects

Uri Cohen

Publications and source records attributed to Uri Cohen.

5 recordsLinked to original sources

arXiv2025

Dynamical stability for dense patterns in attractor neural networks

Recurrent neural networks are canonical models of biological memory. In these models, memories are represented by distributed patterns of neural activity that are stored in the recurrent connections between neurons, such that they become attractors of the network's dynamics. During memory recall, network dynamics thus converge toward one of these memory patterns when started from a noisy or partial cue. Therefore, memory performance critically hinges on the dynamical stability of the stored patterns. However, previous theoretical approaches only studied dynamical stability under highly restrictive conditions that do not readily apply to biological neural circuits. Here, we develop a theory of the local stability of discrete fixed points in a broad class of networks with graded neural activities and in the presence of noise. Using methods from random matrix theory, we analyze the bulk and outliers of the eigenvalue spectra of the Jacobians that characterize network dynamics around fixed points. We show that either all fixed points are stable or all of them are unstable, depending on whether their number is below a ``critical load for stability'', which is distinct from the classical critical capacity that measures the maximal number of achievable fixed points regardless of their stability. We further analyze the dependence of this critical load for stability on experimentally measurable quantities characterizing the statistics of memory patterns and the activation functions of neurons. Our analysis highlights the computational benefits of sparse-like patterns and threshold-linear activation functions and offers testable predictions for neural circuits supporting memory.

cond-mat.dis-nn↗

arXiv2025

Eigenvalue spectrum support of paired random matrices with pseudo-inverse

The Moore-Penrose pseudo-inverse $X^\dagger$, defined for rectangular matrices, naturally emerges in many areas of mathematics and science. For a pair of rectangular matrices $X, Y$ where the corresponding entries are jointly Gaussian and i.i.d., we analyse the support of the eigenvalue spectrum of $XY^\dagger$.

math.SP↗

arXiv2025

Neural mechanisms of predictive processing: a collaborative community experiment through the OpenScope program

This review synthesizes advances in predictive processing within the sensory cortex. Predictive processing theorizes that the brain continuously predicts sensory inputs, refining neuronal responses by highlighting prediction errors. We identify key computational primitives, such as stimulus adaptation, dendritic computation, excitatory/inhibitory balance and hierarchical processing, as central to this framework. Our review highlights convergences, such as top-down inputs and inhibitory interneurons shaping mismatch signals, and divergences, including species-specific hierarchies and modality-dependent layer roles. To address these conflicts, we propose experiments in mice and primates using in-vivo two-photon imaging and electrophysiological recordings to test whether temporal, motor, and omission mismatch stimuli engage shared or distinct mechanisms. The resulting dataset, collected and shared via the OpenScope program, will enable model validation and community analysis, fostering iterative refinement and refutability to decode the neural circuits of predictive processing.

q-bio.NC↗

arXiv2022

Soft-margin classification of object manifolds

A neural population responding to multiple appearances of a single object defines a manifold in the neural response space. The ability to classify such manifolds is of interest, as object recognition and other computational tasks require a response that is insensitive to variability within a manifold. Linear classification of object manifolds was previously studied for max-margin classifiers. Soft-margin classifiers are a larger class of algorithms and provide an additional regularization parameter used in applications to optimize performance outside the training set by balancing between making fewer training errors and learning more robust classifiers. Here we develop a mean-field theory describing the behavior of soft-margin classifiers applied to object manifolds. Analyzing manifolds with increasing complexity, from points through spheres to general manifolds, a mean-field theory describes the expected value of the linear classifier's norm, as well as the distribution of fields and slack variables. By analyzing the robustness of the learned classification to noise, we can predict the probability of classification errors and their dependence on regularization, demonstrating a finite optimal choice. The theory describes a previously unknown phase transition, corresponding to the disappearance of a non-trivial solution, thus providing a soft version of the well-known classification capacity of max-margin classifiers.

cond-mat.dis-nn↗

arXiv2017

Learning Data Manifolds with a Cutting Plane Method

We consider the problem of classifying data manifolds where each manifold represents invariances that are parameterized by continuous degrees of freedom. Conventional data augmentation methods rely upon sampling large numbers of training examples from these manifolds; instead, we propose an iterative algorithm called M_{CP} based upon a cutting-plane approach that efficiently solves a quadratic semi-infinite programming problem to find the maximum margin solution. We provide a proof of convergence as well as a polynomial bound on the number of iterations required for a desired tolerance in the objective function. The efficiency and performance of M_{CP} are demonstrated in high-dimensional simulations and on image manifolds generated from the ImageNet dataset. Our results indicate that M_{CP} is able to rapidly learn good classifiers and shows superior generalization performance compared with conventional maximum margin methods using data augmentation methods.

cs.LG↗