A high-bias, low-variance introduction to Machine Learning for physicists

Abstract

Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute.

Neural Network flows of low q-state Potts and clock Models

“…Machine learning (ML) methods outperform humans in specific tasks and have been applied successfully in a wide range of modern physics [1][2][3][4][5][6][7]. Of particular interest are applications of ML on identifying and classifying different phases of matter including the topological ones [8][9][10][11][12][13][14][15][16][17][18][19][20]. The identification of the phase transitions of spin systems, is in practice an accessible task where the spin states can be mapped to neural network states and in a sense one retains physical information during the training of the neural network.…”

“…Thus, it is quite remarkable that the RBM can flow all the microstates to the ones at the critical point. This unsupervised feature is in contrast to other supervised learning of the phase transitions [8][9][10][11][12][13][14][15][16][17][18][19][20]. A further impressive application of the RBM flow is that its fixed-point microstates, has been used to compute successfully the critical exponents of the spin models [15] and the scaling dimensions of operators [17].…”

Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning

“…Applications include predictive objectives, such as detecting phase transitions from lattice configurations, as well as generative modeling . We recommend [36] as an introduction to ML for physicists and [37] as a general review for ML applications in physics.…”

Thermodynamics and Feature Extraction by Machine Learning

“…Moreover, attempts to understand the mechanism of the emergence of bulk geometries in the gauge/gravity correspondence have been also proposed in [24,25]. While most of these physical applications are summarized in an analytic review of [26].…”