Related papers: Analyzing Training Using Phase Transitions in Entr…

We provide a mutual information lower bound that can be used to analyze the effect of training in models with unknown parameters. For large-scale systems, we show that this bound can be calculated using the difference between two…

In a physical system, changing parameters such as temperature can induce a phase transition: an abrupt change from one state of matter to another. Analogous phenomena have recently been observed in large language models. Typically, the task…

The microscopic model in which nodes interacting with each other are statistical systems is introduced. The nodes conditions are connected with a string of distinct microscopic configurations and depend on external parameters (pressure and…

The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…

Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…

We study the evolution of artificial learning systems by means of selection. Genetic programming is used to generate a sequence of populations of algorithms which can be used by neural networks for supervised learning of a rule that…

Machine learning theory has mostly focused on generalization to samples from the same distribution as the training data. Whereas a better understanding of generalization beyond the training distribution where the observed distribution…

In this Letter, we present a new strategy for applying the learning machine to study phase transitions. We train the learning machine with samples only obtained at a non-critical parameter point, aiming to establish intrinsic correlations…

Entropy and order parameter are two key concepts in phase transition theory. This paper proposes an unified method to both find order parameter and estimate entropy automatically with unsupervised learning. The contributions of this paper…

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…

An ensemble of trajectories with dynamical activity and first-passage time (FPT) is considered in the context of the thermodynamics of trajectories. The relationship between the average FPT and the total change in entropy is determined,…

This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…

Thermodynamic phase transitions, a central concept in physics and chemistry, are typically controlled by an interplay of enthalpic and entropic contributions. In most cases, the estimation of the enthalpy in simulations is straightforward…

For sensory networks, we determine the rate with which they acquire information about the changing external conditions. Comparing this rate with the thermodynamic entropy production that quantifies the cost of maintaining the network, we…

We discuss an aspect of neural networks for the purpose of phase transition detection. To this end, we first train the neural network by feeding Ising/Potts configurations with labels of temperature so that it can predict the temperature of…

The time until the failure of some node of the system or until the end of some stage of the operation of the tribological system is associated with the change in entropy in the system that occurs during this time. Methods of the…

We consider a set of fully connected spins models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence,…

Machine learning is the dominant approach to artificial intelligence, through which computers learn from data and experience. In the framework of supervised learning, a necessity for a computer to learn from data accurately and efficiently…

One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by…

Measurement-induced entanglement phase transitions, caused by the competition between entangling unitary dynamics and disentangling projective measurements, have been studied in various random circuit models in recent years. In this paper,…