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We examine the large-network, low-loading behaviour of an attractor neural network, the so-called bistable gradient network (BGN). We use analytical and numerical methods to characterize the attractor states of the network and their basins…

The phenomenon of grokking in over-parameterized neural networks has garnered significant interest. It involves the neural network initially memorizing the training set with zero training error and near-random test error. Subsequent…

We study zero-temperature Glauber dynamics for Ising-like spin variable models in quenched random networks with random zero-magnetization initial conditions. In particular, we focus on the absorbing states of finite systems. While it has…

Neural networks have been successfully used for classification tasks in a rapidly growing number of practical applications. Despite their popularity and widespread use, there are still many aspects of training and classification that are…

Attentional Neural Network is a new framework that integrates top-down cognitive bias and bottom-up feature extraction in one coherent architecture. The top-down influence is especially effective when dealing with high noise or difficult…

It is well known that a sparsely coded network in which the activity level is extremely low has intriguing equilibrium properties. In the present work, we study the dynamical properties of a neural network designed to store sparsely coded…

We study the stable phases of an attractor neural network model, with binary units, for hippocampal place cells encoding 1D or 2D spatial maps or environments. Using statistical mechanics tools we show that, below critical values for the…

We define a neural network as a septuple consisting of (1) a state vector, (2) an input projection, (3) an output projection, (4) a weight matrix, (5) a bias vector, (6) an activation map and (7) a loss function. We argue that the loss…

A suitable similarity index for comparing learnt neural networks plays an important role in understanding the behaviour of the highly-nonlinear functions, and can provide insights on further theoretical analysis and empirical studies. We…

This document gives a specification for the model used in [1]. It presents a simple way of optimizing mutual information between some input and the attractors of a (noisy) network, using a genetic algorithm. The nodes of this network are…

We consider a class of adaptive network models where links can only be created or deleted between nodes in different states. These models provide an approximate description of a set of systems where nodes represent agents moving in physical…

Fixed point networks are dynamic networks that encode stimuli via distinct output patterns. Although such networks are omnipresent in neural systems, their structures are typically unknown or poorly characterized. It is therefore valuable…

Simultaneously recorded neurons exhibit correlations whose underlying causes are not known. Here, we use a population of threshold neurons receiving correlated inputs to model neural population recordings. We show analytically that small…

In principle, zero-shot learning makes it possible to train a recognition model simply by specifying the category's attributes. For example, with classifiers for generic attributes like \emph{striped} and \emph{four-legged}, one can…

A rank-dependent deactivation mechanism is introduced to network evolution. The growth dynamics of the network is based on a finite memory of individuals, which is implemented by deactivating one site at each time step. The model shows…

Object recognition has become a crucial part of machine learning and computer vision recently. The current approach to object recognition involves Deep Learning and uses Convolutional Neural Networks to learn the pixel patterns of the…

Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…

Triplet networks are widely used models that are characterized by good performance in classification and retrieval tasks. In this work we propose to train a triplet network by putting it as the discriminator in Generative Adversarial Nets…

We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution,…

In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…