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Lecture

Phase Transitions in Physics and Machine Learning

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PHYS-754: Lecture series on scientific machine learning

This lecture presents ongoing work on how scientific questions can be tackled using machine learning. Machine learning enables extracting knowledge from data computationally and in an automatized way. We will learn on examples how this is influencing the v ...

Description

This lecture explores the concept of phase transitions, comparing the smooth transition in physics to the abrupt jumps in computational problems. The instructor discusses how first-order phase transitions occur in spin glass games and computational problems, leading to easy, hard, and impossible phases. The lecture delves into the relationship between phase transitions in physics and the computational hardness conjecture, highlighting the challenges faced by algorithms in the hard phase. Additionally, the lecture touches on compressing, a signal processing technique that aims to reconstruct images efficiently by capturing sparse features. The discussion extends to the application of physics principles in understanding neural networks, emphasizing the need for theoretical insights to bridge the gap between machine learning and scientific understanding.

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Instructors (10)

Michele Ceriotti

Michele Ceriotti received his Ph.D. in Physics from ETH Zürich in 2010. He spent three years in Oxford as a Junior Research Fellow at Merton College. Since 2013 he leads the laboratory for Computational Science and Modeling in the Institute of Materials at EPFL. His research revolves around the atomic-scale modelling of materials, based on the sampling of quantum and thermal fluctuations and on the use of machine learning to predict and rationalize structure-property relations. He has been awarded the IBM Research Forschungspreis in 2010, the Volker Heine Young Investigator Award in 2013, an ERC Starting Grant in 2016, and the IUPAP C10 Young Scientist Prize in 2018.

Anne-Florence Raphaëlle Bitbol

Lenka Zdeborová

Lenka Zdeborová is a Professor of Physics and of Computer Science in École Polytechnique Fédérale de Lausanne where she leads the Statistical Physics of Computation Laboratory. She received a PhD in physics from University Paris-Sud and from Charles University in Prague in 2008. She spent two years in the Los Alamos National Laboratory as the Director's Postdoctoral Fellow. Between 2010 and 2020 she was a researcher at CNRS working in the Institute of Theoretical Physics in CEA Saclay, France. In 2014, she was awarded the CNRS bronze medal, in 2016 Philippe Meyer prize in theoretical physics and an ERC Starting Grant, in 2018 the Irène Joliot-Curie prize, in 2021 the Gibbs lectureship of AMS. She is an editorial board member for Journal of Physics A, Physical Review E, Physical Review X, SIMODS, Machine Learning: Science and Technology, and Information and Inference. Lenka's expertise is in applications of concepts from statistical physics, such as advanced mean field methods, replica method and related message-passing algorithms, to problems in machine learning, signal processing, inference and optimization. She enjoys erasing the boundaries between theoretical physics, mathematics and computer science.

Anne-Clémence Corminboeuf

David Richard Harvey

Alexander Mathis

Alexander studied pure mathematics with a minor in logic and theory of science at the Ludwig Maximilians University in Munich. For his PhD also at LMU, he worked on optimal coding approaches to elucidate the properties of grid cells. As a postdoctoral fellow with Prof. Venkatesh N. Murthy at Harvard University and Prof. Matthias Bethge at Tuebingen AI, he decided to study olfactory behaviors such as odor-guided navigation, social behaviors and the cocktail party problem in mice. During this time, he increasingly got interested sensorimotor behaviors beyond olfaction and started working on proprioception, motor adaption, as well as computer vision tools for measuring animal behavior. In his group, he is interested in elucidating how the brain gives rise to adaptive behavior. One of the major goals is to synthesize large datasets into computationally useful information. For those purposes, he develops algorithms and systems to analyze animal behavior (e.g. DeepLabCut), neural data, as well as creates experimentally testable computational models.

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Related concepts (32)

Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.

Computational problem

In theoretical computer science, a computational problem is a problem that may be solved by an algorithm. For example, the problem of factoring "Given a positive integer n, find a nontrivial prime factor of n." is a computational problem. A computational problem can be viewed as a set of instances or cases together with a, possibly empty, set of solutions for every instance/case. For example, in the factoring problem, the instances are the integers n, and solutions are prime numbers p that are the nontrivial prime factors of n.

Phase (matter)

In the physical sciences, a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase. (See .) More precisely, a phase is a region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform.

Recurrent neural network

A recurrent neural network (RNN) is one of the two broad types of artificial neural network, characterized by direction of the flow of information between its layers. In contrast to uni-directional feedforward neural network, it is a bi-directional artificial neural network, meaning that it allows the output from some nodes to affect subsequent input to the same nodes. Their ability to use internal state (memory) to process arbitrary sequences of inputs makes them applicable to tasks such as unsegmented, connected handwriting recognition or speech recognition.

Polyamorphism

Polyamorphism is the ability of a substance to exist in several different amorphous modifications. It is analogous to the polymorphism of crystalline materials. Many amorphous substances can exist with different amorphous characteristics (e.g. polymers). However, polyamorphism requires two distinct amorphous states with a clear, discontinuous (first-order) phase transition between them. When such a transition occurs between two stable liquid states, a polyamorphic transition may also be referred to as a liquid–liquid phase transition.

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