Related papers: A multifractal phase-space analysis of perceptrons…
For four decades statistical physics has been providing a framework to analyse neural networks. A long-standing question remained on its capacity to tackle deep learning models capturing rich feature learning effects, thus going beyond the…
We analysed the generalisation performance of a binary perceptron with quantum fluctuations using the replica method. An exponential number of local minima dominate the energy landscape of the binary perceptron. Local search algorithms…
The problem of the transformation of microscopic information to the macroscopic level is an intriguing challenge in computational neuroscience, but also of general mathematical importance. Here, a phenomenological mathematical model is…
Perceptual multistability, observed across species and sensory modalities, offers valuable insights into numerous cognitive functions and dysfunctions. For instance, differences in temporal dynamics and information integration during…
The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the…
Statistical-physics calculations in machine learning and theoretical neuroscience often involve lengthy derivations that obscure physical interpretation. Here, we give concise, non-replica derivations of several key results and highlight…
The Boltzmann-Gibbs probability distributions generated by logarithmically correlated random potentials provide a simple yet nontrivial example of disorder-induced multifractal measures. We introduce and discuss two analytically tractable…
We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well…
The binary perceptron is the simplest artificial neural network formed by $N$ input units and one output unit, with the neural states and the synaptic weights all restricted to $\pm 1$ values. The task in the teacher--student scenario is to…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
A computer model of the feed-forward neural network with the hidden layer is developed to reconstruct physical field investigated by the fiber-optic measuring system. The Gaussian distributions of some physical quantity are selected as…
We propose to formulate multi-label learning as a estimation of class distribution in a non-linear embedding space, where for each label, its positive data embeddings and negative data embeddings distribute compactly to form a positive…
The emission rate of minority atmospheric gases is inferred by a new approach based on neural networks. The neural network applied is the multi-layer perceptron with backpropagation algorithm for learning. The identification of these…
Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input…
In federated learning problems, data is scattered across different servers and exchanging or pooling it is often impractical or prohibited. We develop a Bayesian nonparametric framework for federated learning with neural networks. Each data…
There is increasing interest in learning how human brain networks vary as a function of a continuous trait, but flexible and efficient procedures to accomplish this goal are limited. We develop a Bayesian semiparametric model, which…
We study the effects of the finite number of experimental data on the computation of a generalized fluctuation-dissipation relation around a nonequilibrium steady state of a Brownian particle in a toroidal optical trap. We show that the…
We study the spectral properties of a stochastic process obtained by multiplicative inversion of a non-zero-mean Gaussian process. We show that its autocorrelation and power spectrum exist for most regular processes, and we find a…
Feature learning in the presence of a mixed type of variables, numerical and categorical types, is an important issue for related modeling problems. For simple neighborhood queries under mixed data space, standard practice is to consider…
The weight space of the Ising perceptron in which a set of random patterns is stored is examined using the generating function of the partition function $\phi(n)=(1/N)\log [Z^n]$ as the dimension of the weight vector $N$ tends to infinity,…