Related papers: Machine Learning H-theorem
A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the…
We consider a Brownian particle in harmonic confinement of stiffness $k$, in one dimension in the underdamped regime. The whole setup is immersed in a heat bath at temperature $T$. The center of harmonic trap is dragged under any arbitrary…
We treat a quantum mechanical system with certain general properties which are expected to be common in macroscopic quantum systems. Starting from a PURE initial state (which may not describe an equilibrium) in which energy is mildly…
Classic supervised learning involves algorithms trained on $n$ labeled examples to produce a hypothesis $h \in \mathcal{H}$ aimed at performing well on unseen examples. Meta-learning extends this by training across $n$ tasks, with $m$…
The second-largest order statistic is of special importance in reliability theory since it represents the time to failure of a $2$-out-of-$n$ system. Consider two $2$-out-of-$n$ systems with heterogeneous random lifetimes. The lifetimes are…
The use of machine learning methods for predictive purposes has increased dramatically over the past two decades, but uncertainty quantification for predictive comparisons remains elusive. This paper addresses this gap by extending the…
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models…
Master equation could be applied to model various kinds of biochemical systems. A general theory for its time-dependent nonequilibrium thermodynamics is rigorously derived. We not only introduce a concept of general internal energy, but…
Sparse deep learning has become a popular technique for improving the performance of deep neural networks in areas such as uncertainty quantification, variable selection, and large-scale network compression. However, most existing research…
Although statistical learning theory provides a robust framework to understand supervised learning, many theoretical aspects of deep learning remain unclear, in particular how different architectures may lead to inductive bias when trained…
Repeated application of machine-learning, eigen-centric methods to an evolving dataset reveals that eigenvectors calculated by well-established computer implementations are not stable along an evolving sequence. This is because the sign of…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
Thermodynamic inference from coarse observations remains a key challenge. Memory, in particular correlations between consecutively observed mesostates, blur signatures of irreversibility and must be accounted for in defining physical…
We investigate the use of models from the theory of regularity structures as features in machine learning tasks. A model is a polynomial function of a space-time signal designed to well-approximate solutions to partial differential…
Machine learning plays a role in many deployed decision systems, often in ways that are difficult or impossible to understand by human stakeholders. Explaining, in a human-understandable way, the relationship between the input and output of…
We test Boltzmann's H-theorem for several models of particle random walk. We study the influence of interaction between the particle and reservoir/detectors on entropy and find entropy increasing in time for some models and behaving…
This paper sheds new light on several interrelated topics of second-order variational analysis, both in finite and infinite-dimensional settings. We establish new relationships between second-order growth conditions on functions, the basic…
The presence of label noise often misleads the training of deep neural networks. Departing from the recent literature which largely assumes the label noise rate is only determined by the true label class, the errors in human-annotated…
As an intrinsic and fundamental property of big data, data heterogeneity exists in a variety of real-world applications, such as precision medicine, autonomous driving, financial applications, etc. For machine learning algorithms, the…
We describe recent progress towards deriving the Fundamental Laws of thermodynamics (the 0th, 1st and 2nd Law) from nonequilibrium quantum statistical mechanics in simple, yet physically relevant models. Along the way, we clarify some basic…