We propose and implement machine learning inspired methods for computing numerical Ricci-flat Kahler metrics, and compare them with previous work.
The metric of the extra-dimensions in string theory contains crucial information about the low-energy dynamics of string theory systems. This talk reports on recent work (2012.04656) where we use machine learning to approximate Calabi-Yau and SU(3)-structure metrics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical...
Heterotic compactifications on CY 3-folds dressed with line bundle sums provide a fruitful setting for the construction of standard model like models for particle physics. However, the computational resources provide a stumbling block in systematic explorations. In this talk, I will report on experiments where reinforcement learning is used to search for such models. The talk is based on 2003.04817.
From a path integral perspective, the backbone of perturbative quantum field theory is a close-to-Gaussian distribution on function space that allows for the computation of correlators via expansion of the non-Gaussianities. Incidentally, many neural network (NN) architectures induce function space distributions with similar properties, allowing for direct import of techniques from QFT into...
As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the NTK parametrization). However, we show that the standard and NTK parametrizations of a neural network do not admit infinite-width limits that can learn representations (i.e....
We apply modern methods in computational topology to the task of discovering and characterizing phase transitions. As illustrations, we apply our method to four two-dimensional lattice spin models: the Ising, square ice, XY, and fully-frustrated XY models. In particular, we use persistent homology, which computes the births and deaths of individual topological features as a coarse-graining...
I demonstrate how to use differential evolutionary algorithms to find flux compactifications of M-theory on K3xK3. The assumption that large numbers of moduli can be stabilized with fluxes within the tadpole bound is one of the corner stones of the String Landscape. However, showing moduli stabilization for manifolds with many moduli explicitly is highly challenging. On K3xK3 moduli...
Inspired by Witten's idea that in the large N limit of QCD Baryons correspond to soliton states of mesons, we construct a model of hadronic masses using both Bayesian and non-Bayesian techniques in machine learning. From knowledge of the meson spectrum only, neural networks and Gaussian processes predict the masses of baryons with 90.3% and 96.6% accuracy, respectively. We also predict the...
I will elaborate on how data science helps uncover the structure of vector-like spectra in F-theory.
I will talk about further challenges for realistic vector-like spectra in F-theory MSSM-constructions and how to overcome them in the future.
Untrained asymptotically wide Neural Networks are Gaussian Processes, with a direct correspondence to Euclidean free field theory; deviations of the NN away from GP can be effectively described using Wilsonian EFT. Further, output dimension d shows up as the number of independent species in the free / interacting field corresponding to GP / non-GP NN outputs. Experimentally, we verify Ward...
We apply a recent correspondence between neural networks and quantum field theory to study RG fixed points of single-layer neural networks with exponential activation. Many architectures with a biased linear output layer exhibit a universal fixed point at large cutoff, and for some architectures, another fixed point at low cutoff. These fixed points are demonstrated at second-order in the...
We are faced with an explosion of data in many areas of physics, but very so often, it is not the size but the complexity of the data that makes extracting physics from big datasets challenging. As I will discuss in this talk, data has shape and the shape of data encodes the underlying physics. Persistent homology is a tool in computational topology developed for quantifying the shape of data....
String theory can be seen as the prime candidate for a consistent theory of gravity and particle physics. However, the task to explicitly construct a string model of particle physics that is in agreement with all experimental observations is very challenging due to the enormous size of the so-called string landscape of four-dimensional string models. In this talk, an overview of the heterotic...
We consider Type IIB string theory compactification on an isotropic torus with geometric and non geometric fluxes. Employing supervised machine learning, consisting of an artificial neural network coupled to a genetic algorithm, we determine more than sixty thousand flux configurations yielding a scalar potential with at least one critical point. Stable AdS vacua with large moduli masses and...
We present a simple phenomenological formula which approximates the hyperbolic volume of the knot complement based on an evaluation of the Jones polynomial at a complex phase. The error is 2.86% on the first 1.7 million knots. This approximate formula is obtained from reverse engineering a neural network which achieves a similar error after training on 10% of the data. In Chern-Simons...
The ability to detect and count certain substructures in graphs is important for solving many tasks on graph-structured data, especially in the contexts of computational chemistry and biology as well as social network analysis. In this talk we study the expressive power of popular graph neural networks (GNNs) via their ability to count attributed graph substructures, extending recent works...
The Ashok-Denef-Douglas method of counting flux vacua yields an enormous landscape of vacua, an overwhelming majority of which have a large number N of scalar fields. That same calculation suggests that the average density of vacua increases rapidly with N, leading to an increase in the bubble nucleation rates at large N, and therefore a decrease in the average lifetime of such vacua. I will...
I will describe efforts to automate the construction of flux vacua of type IIB string theory, and to find associated anti-de Sitter and de Sitter solutions.
In this talk, I will explain how to compute both Hodge numbers for complete intersection Calabi-Yau (CICY) 3-folds using machine learning. I will first make a tour of various machine learning algorithms and explain how exploratory data analysis can help in improving results for most of them. Then, I will describe a neural network inspired from the Google's Inception model which reaches nearly...
We report and summarize some of the recent experiments in supervised machine-learning of various structures from different fields of mathematics, ranging from geometry, to representation theory, to combinatorics, to number theory. We speculate on a hierarchy of inherent difficulty and where string theoretic problems tend to reside.
We will examine links between approaches to learning through Bayesian inference and properties of quantum field theories.
Learning of irregular data, such as sets and graphs, is a prominent research direction that has received considerable attention in the last few years. The main challenge that arises is which architectures should be used for such data types. I will present a general framework for designing network architectures for irregular data types that adhere to permutation group symmetries. In the first...
We will apply the tools of Natural Language Processing (NLP) to problems in low-dimensional topology, some of which have direct applications to the smooth 4-dimensional Poincare conjecture. We will tackle the UNKNOT decision problem and discuss how reinforcement learning (RL) can find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly...
