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Sequential learning paradigms pose challenges for gradient-based deep learning due to difficulties incorporating new data and retaining prior knowledge. While Gaussian processes elegantly tackle these problems, they struggle with…

In recent years, deep neural network exhibits its powerful superiority on information discrimination in many computer vision applications. However, the capacity of deep neural network architecture is still a mystery to the researchers.…

Network binarization is a promising hardware-aware direction for creating efficient deep models. Despite its memory and computational advantages, reducing the accuracy gap between binary models and their real-valued counterparts remains an…

The classical perceptron is a simple neural network that performs a binary classification by a linear mapping between static inputs and outputs and application of a threshold. For small inputs, neural networks in a stationary state also…

One of the key issues in the analysis of machine learning models is to identify the appropriate function space and norm for the model. This is the set of functions endowed with a quantity which can control the approximation and estimation…

We analyze the problem of storing random pattern-label associations using two classes of continuous non-convex weights models, namely the perceptron with negative margin and an infinite-width two-layer neural network with non-overlapping…

In this paper, we introduce a model of a distributed storage system that is locally recoverable from any single server failure. Unlike the usual local recovery model of codes for distributed storage, this model accounts for the fact that…

We examine numerically the storage capacity and the behaviour near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the Bistable Gradient Network (BGN). For strong coupling, we…

Deep learning has become a powerful and popular tool for a variety of machine learning tasks. However, it is challenging to understand the mechanism of deep learning from a theoretical perspective. In this work, we propose a random active…

Deploying deep learning models, comprising of non-linear combination of millions, even billions, of parameters is challenging given the memory, power and compute constraints of the real world. This situation has led to research into model…

The total memory capacity (MC) of linear recurrent neural networks (RNNs) has been proven to be equal to the rank of the corresponding Kalman controllability matrix, and it is almost surely maximal for connectivity and input weight matrices…

This work suggests using sampling theory to analyze the function space represented by neural networks. First, it shows, under the assumption of a finite input domain, which is the common case in training neural networks, that the function…

Learning in networks of binary synapses is known to be an NP-complete problem. A combined stochastic local search strategy in the synaptic weight space is constructed to further improve the learning performance of a single random walker. We…

Binary neural networks, i.e., neural networks whose parameters and activations are constrained to only two possible values, offer a compelling avenue for the deployment of deep learning models on energy- and memory-limited devices. However,…

Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we…

Large language models demonstrate remarkable ability in factual recall, yet the fundamental limits of storing and retrieving input--output associations with neural networks remain unclear. We study these limits in a minimal setting: a…

We study the trade-offs between storage/bandwidth and prediction accuracy of neural networks that are stored in noisy media. Conventionally, it is assumed that all parameters (e.g., weight and biases) of a trained neural network are stored…

For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…

Neural networks are capable of superposition -- representing more features than there are dimensions. Recent work considers the analogous concept for computation instead of storage, proposing theoretical constructions. But there has been…

Self-sustained, elevated neuronal activity persisting on time scales of ten seconds or longer is thought to be vital for aspects of working memory, including brain representations of real space. Continuous-attractor neural networks, one of…