Related papers: Negative spherical perceptron
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…
Bayesian inference is an effective approach for solving statistical learning problems, especially with uncertainty and incompleteness. However, Bayesian inference is a computing-intensive task whose efficiency is physically limited by the…
Quantum measurements affect the state of the observed systems via back-action. While projective measurements extract maximal classical information, they drastically alter the system's configuration. In contrast, indirect measurements…
Let $R$ be a root system of type BC in $\mathfrak a=\mathbb R^r$ of general positive multiplicity. We introduce certain canonical weight function on $\mathbb R^r$ which in the case of symmetric domains corresponds to the integral kernel of…
We introduce a statistical physics inspired supervised machine learning algorithm for classification and regression problems. The method is based on the invariances or stability of predicted results when known data is represented as…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Quantum kernel methods are a proposal for achieving quantum computational advantage in machine learning. They are based on a hybrid classical-quantum computation where a function called the quantum kernel is estimated by a quantum device…
Statistical mechanics is used to study unrealizable generalization in two large feed-forward neural networks with binary weights and output, a perceptron and a tree committee machine. The student is trained by a teacher being larger, i.e.…
We study the capacity of \emph{sign} perceptrons neural networks (SPNN) and particularly focus on 1-hidden layer \emph{treelike committee machine} (TCM) architectures. Similarly to what happens in the case of a single perceptron neuron, it…
The goal of Ordinal Regression is to find a rule that ranks items from a given set. Several learning algorithms to solve this prediction problem build an ensemble of binary classifiers. Ranking by Projecting uses interdependent binary…
Determining the statistics of work done on a quantum system while strongly coupled to a reservoir is a formidable task, requiring the calculation of the full eigenspectrum of the combined system and reservoir. Here we show that this issue…
We introduce into the classical perceptron algorithm with margin a mechanism that shrinks the current weight vector as a first step of the update. If the shrinking factor is constant the resulting algorithm may be regarded as a…
Reservoir computing is a neuromorphic architecture that potentially offers viable solutions to the growing energy costs of machine learning. In software-based machine learning, neural network properties and performance can be readily…
Indentation tests are largely exploited in experiments to characterize the mechanical and fracture properties of the materials from the resulting crack patterns. This work proposes an efficient theoretical and computational framework, whose…
Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials.…
Physical reservoir computing is a framework for brain-inspired information processing that utilizes nonlinear and high-dimensional dynamics in non-von-Neumann systems. In recent years, spintronic devices have been proposed for use as…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
Spatiotemporal information processing is fundamental to brain functions. The present study investigates a canonic neural network model for spatiotemporal pattern recognition. Specifically, the model consists of two modules, a reservoir…
Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…
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.…