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Lecture

Optimal Errors and Phase Transitions

In course

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 discusses optimal errors and phase transitions in high dimensional generalized linear models. It covers the concept of generalized linear models, the significance of high dimensionality, and phase diagrams for estimation problems. The instructor explains the symmetric door perceptron model and its relation to achieving the minimum information-theoretic recovery threshold. Additionally, the lecture explores the link between these concepts and modern machine learning algorithms, emphasizing comparisons with GAMP and IT computations.

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Instructors (10)

Giuseppe Carleo is a computational quantum physicist, whose main focus is the development of advanced numerical algorithms tostudy challenging problems involving strongly interacting quantum systems.He is best known for the introduction of machine learning techniques to study both equilibrium and dynamical properties,based on a neural-network representations of quantum states, as well for the time-dependent variational Monte Carlo method.He earned a Ph.D. in Condensed Matter Theory from the International School for Advanced Studies (SISSA) in Italy in 2011.He held postdoctoral positions at the Institut d’Optique in France and ETH Zurich in Switzerland, where he alsoserved as a lecturer in computational quantum physics.In 2018, he joined the Flatiron Institute in New York City in 2018 at the Center for Computational Quantum Physics (CCQ), working as a Research Scientist and project leader, and also leading the development of the open-source project NetKet.Since September 2020 he is an assistant professor at EPFL, in Switzerland, leading the Computational Quantum Science Laboratory (CQSL).

Paolo De Los Rios

Paolo De Los Rios earned his master in Electronic Engineering at the Turin Institute of Technology (Politecnico di Torino) in May 1993. In November 1993 he moved to Trieste, Italy, to enter the PhD program in Theoretical Condensed Matter Theory at the International School for Advanced Studies (SISSA/ISAS) where he obtained the PhD degree in October 1996 for his work on the statistical physics of disordered systems. After a one year postdoc at the Max-Planck Institute for the Physics of Complex Systems in Dresden, Germany, in November 1997 he moved to the University of Fribourg, Switzerland, to join the group of Prof. Yi-Cheng Zhang. There he has worked on various applications of statistical physics to complex systems. In September 2000 he has been appointed Assistant Professor in Statistical Physics of Living Matter and Complex Systems at the Institute of Theoretical Physics of the University of Lausanne, Switzerland. Since April 2010 he is Associate Professor at the Institute of Theoretical Physics of the Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland.

Michele Ceriotti

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Related concepts (23)

Machine learning

Machine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.

Supervised learning

Supervised learning (SL) is a paradigm in machine learning where input objects (for example, a vector of predictor variables) and a desired output value (also known as human-labeled supervisory signal) train a model. The training data is processed, building a function that maps new data on expected output values. An optimal scenario will allow for the algorithm to correctly determine output values for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias).

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.

Self-supervised learning

Self-supervised learning (SSL) is a paradigm in machine learning for processing data of lower quality, rather than improving ultimate outcomes. Self-supervised learning more closely imitates the way humans learn to classify objects. The typical SSL method is based on an artificial neural network or other model such as a decision list. The model learns in two steps. First, the task is solved based on an auxiliary or pretext classification task using pseudo-labels which help to initialize the model parameters.

Artificial neural network

Artificial neural networks (ANNs, also shortened to neural networks (NNs) or neural nets) are a branch of machine learning models that are built using principles of neuronal organization discovered by connectionism in the biological neural networks constituting animal brains. An ANN is based on a collection of connected units or nodes called artificial neurons, which loosely model the neurons in a biological brain. Each connection, like the synapses in a biological brain, can transmit a signal to other neurons.

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