Related papers: Thermodynamic Response Functions in Singular Bayes…
Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…
Universality of classical thermodynamics rests on the central limit theorem, due to which, measurements of thermal fluctuations are unable to reveal detailed information regarding the microscopic structure of a macroscopic body. When small…
We present a simple theory that uses thermodynamic parameters to predict the probability that a protein retains the wildtype structure after one or more random amino acid substitutions. Our theory predicts that for large numbers of…
Grokking, the abrupt transition from memorization to generalisation after extended training, suggests the presence of competing solution basins with distinct statistical properties. We study this phenomenon through the lens of Singular…
Bayesian methods feature useful properties for solving inverse problems, such as tomographic reconstruction. The prior distribution introduces regularization, which helps solving the ill-posed problem and reduces overfitting. In practice,…
Sparse high-dimensional functions have arisen as a rich framework to study the behavior of gradient-descent methods using shallow neural networks, showcasing their ability to perform feature learning beyond linear models. Amongst those…
Microscopic heat engines operate in regimes where thermodynamic quantities fluctuate strongly, making stochastic effects an essential aspect of their performance. However, existing geometric formulations of finite-time thermodynamics…
Deep linear networks have been extensively studied, as they provide simplified models of deep learning. However, little is known in the case of finite-width architectures with multiple outputs and convolutional layers. In this manuscript,…
Thermodynamic uncertainty relations quantify how the signal-to-noise ratio of a given observable is constrained by dissipation. Fluctuation relations generalize the second law of thermodynamics to stochastic processes. We show that any…
The relationships between reversible Carnot cycles, the absence of perpetual motion machines and the existence of a non-decreasing, globally unique entropy function forms the starting point of many textbook presentations of the foundations…
Predicting the response of a system to perturbations is a key challenge in mathematical and natural sciences. Under suitable conditions on the nature of the system, of the perturbation, and of the observables of interest, response theories…
The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of…
Topological phase transitions in generic multiband systems are mediated by band-touching defects whose codimension -- the number of momentum directions along which the gap closes linearly -- varies across universality classes. Although…
The recently introduced concept of generalized thermodynamics is explored here in the context of 1d, 2d and 3d data analysis, performed on samples drawn from a 3d X-ray soil sample image. Different threshold levels are used to binarize the…
Mixtures of regression are a powerful class of models for regression learning with respect to a highly uncertain and heterogeneous response variable of interest. In addition to being a rich predictive model for the response given some…
We study the relaxation of a highly collisional, ultracold but nondegenerate gas of polar molecules. Confined within a harmonic trap, the gas is subject to fluid-gaseous coupled dynamics that lead to a breakdown of first-order…
We investigate a one-dimensional water-like lattice model with Van der Waals and hydrogen-bond interactions, allowing for particle number fluctuations through a chemical potential. The model, defined on a chain with periodic boundary…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
Neural models are usually adapted through changes in parameters shared among model components via fine-tuning, alignment-based training, and reinforcement learning. These changes have been found effective in short-term optimization.…
In many complex applications, data heterogeneity and homogeneity exist simultaneously. Ignoring either one will result in incorrect statistical inference. In addition, coping with complex data that are non-Euclidean becomes more common. To…