Related papers: Spherical perceptron as a storage memory with limi…
Perceptrons with graded input-output relations and a limited output precision are studied within the Gardner-Derrida canonical ensemble approach. Soft non- negative error measures are introduced allowing for extended retrieval properties.…
A perceptron with N random weights can store of the order of N patterns by removing a fraction of the weights without changing their strengths. The critical storage capacity as a function of the concentration of the remaining bonds for…
We prove rigorously the well-known result of Gardner about the typical fractional volume of interactions between N spins which solve the problem of storing a given set of random patterns. The Gardner formula for this volume in the limit N,p…
Forecasting complex, chaotic signals is a central challenge across science and technology, with implications ranging from secure communications to climate modeling. Here we demonstrate that magnons - the collective spin excitations in…
Liquids equilibrated below an onset density share similar inherent states, while above that density their inherent states markedly differ. Although this phenomenon was first reported in simulations over 20 years ago, the physical origin of…
Invariant object recognition is one of the most fundamental cognitive tasks performed by the brain. In the neural state space, different objects with stimulus variabilities are represented as different manifolds. In this geometrical…
An overview is given about the statistical physics of neural networks generating and analysing time series. Storage capacity, bit and sequence generation, prediction error, antipredictable sequences, interacting perceptrons and the…
Convolutional neural networks (CNNs) have been widely used in various vision tasks, e.g. image classification, semantic segmentation, etc. Unfortunately, standard 2D CNNs are not well suited for spherical signals such as panorama images or…
Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of…
With the growing interest in quantum machine learning, the perceptron -- a fundamental building block in traditional machine learning -- has emerged as a valuable model for exploring quantum advantages. Two quantum perceptron algorithms…
Quantum machine learning represents a promising avenue for data processing, also for purposes of sequential temporal data analysis, as recently proposed in quantum reservoir computing (QRC). The possibility to operate on several platforms…
The encoder and decoder for lossy data compression of binary memoryless sources are developed on the basis of a specific-type nonmonotonic perceptron. Statistical mechanical analysis indicates that the potential ability of the…
In this paper we investigate the Erd\"os/Falconer distance conjecture for a natural class of sets statistically, though not necessarily arithmetically, similar to a lattice. We prove a good upper bound for spherical means that have been…
Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly…
Reservoir Computing is a type of recursive neural network commonly used for recognizing and predicting spatio-temporal events relying on a complex hierarchy of nested feedback loops to generate a memory functionality. The Reservoir…
In reservoir computing, an input sequence is processed by a recurrent neural network, the reservoir, which transforms it into a spatial pattern that a shallow readout network can then exploit for tasks such as memorization and time-series…
We consider an ensemble of $K$ single-layer perceptrons exposed to random inputs and investigate the conditions under which the couplings of these perceptrons can be chosen such that prescribed correlations between the outputs occur. A…
This paper studies numerically how the signal detector arrangement influences the performance of reservoir computing using spin waves excited in a ferrimagnetic garnet film. This investigation is essentially important since the input…
We study the storage capacity of quantum neural networks (QNNs) described as completely positive trace preserving (CPTP) maps, which act on an $N$-dimensional Hilbert space. We demonstrate that QNNs can store up to $N$ linearly independent…
Deep neural networks (DNNs) have been widely deployed across diverse domains such as computer vision and natural language processing. However, the impressive accomplishments of DNNs have been realized alongside extensive computational…