Related papers: Machine Learning H-theorem
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
A heuristic generalization of the Boltzmann-Gibbs microcanonical entropy is proposed, able to describe meta-equilibrium features and evolution of macroscopic systems. Despite its simple-minded derivation, such a function of "collective…
Recent advances in machine learning make it possible to design efficient prediction algorithms for data sets with huge numbers of parameters. This paper describes a new technique for "hedging" the predictions output by many such algorithms,…
The basic equations of physics involve a time variable t and are invariant under the transformation $t goes to -t$. This invariance at first sight appears to impose time reversibility as a principle of physics, in conflict with…
The second law of thermodynamics constitutes a fundamental principle of physics, precluding the existence of perpetual motion machines and providing a natural definition of the arrow of time. Its scope extends across virtually all areas of…
There currently exist no quantitative methods to determine the appropriate conditions for solid-state synthesis. This not only hinders the experimental realization of novel materials but also complicates the interpretation and understanding…
In this thesis, we develop various techniques for working with sets in machine learning. Each input or output is not an image or a sequence, but a set: an unordered collection of multiple objects, each object described by a feature vector.…
Counting small patterns in a large dataset is a fundamental algorithmic task. The most common version of this task is subgraph/homomorphism counting, wherein we count the number of occurrences of a small pattern graph $H$ in an input graph…
Hierarchies are of fundamental interest in both stochastic optimal control and biological control due to their facilitation of a range of desirable computational traits in a control algorithm and the possibility that they may form a core…
The Hahn-Banach Theorem, a cornerstone of modern functional analysis, is a natural companion of the Second Law of Thermodynamics. From a Kelvin-Planck version of the Second Law, the Hahn-Banach Theorem delivers, immediately and…
The aim of this article is to analyze the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of…
The high-dimesionality, non-linearity and emergent properties of complex systems pose a challenge to identifying general laws in the same manner that has been so successful in simpler physical systems. In Anderson's seminal work on why…
The task of semi-supervised classification aims at assigning labels to all nodes of a graph based on the labels known for a few nodes, called the seeds. One of the most popular algorithms relies on the principle of heat diffusion, where the…
We survey in this article the connections between Machine Learning and Control Theory. Control Theory provide useful concepts and tools for Machine Learning. Conversely Machine Learning can be used to solve large control problems. In the…
Using machine learning, we explore the utility of various deep neural networks (NN) when applied to high harmonic generation (HHG) scenarios. First, we train the NNs to predict the time-dependent dipole and spectra of HHG emission from…
Thermodynamics has a clear arrow of time, characterized by the irreversible approach to equilibrium. This stands in contrast to the laws of microscopic theories, which are invariant under time-reversal. Foundational discussions of this…
As the role played by statistical and computational sciences in climate and environmental modelling and prediction becomes more important, Machine Learning researchers are becoming more aware of the relevance of their work to help tackle…
The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on…
Although a plethora of architectural variants for deep classification has been introduced over time, recent works have found empirical evidence towards similarities in their training process. It has been hypothesized that neural networks…
The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…