Welcome

• Fabian Ruhle (CERN)

Room: Virtual only

Numerical Calabi-Yau Metrics from Holomorphic Networks

• Michael Douglas (Simons Center / CMSA Harvard )

Room: Virtual only We propose and implement machine learning inspired methods for computing numerical Ricci-flat Kahler metrics, and compare them with previous work.

Calabi-Yau Metrics from Machine Learning

• Sven Krippendorf (LMU Munich )

Room: Virtual only 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 approximations in terms of accuracy and speed. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties not accessible with previous numerical techniques. I comment on some applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical normalizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, and mention applications to mirror symmetry and the SYZ conjecture.

Reinforcement learning heterotic line bundle models

• Magdalena Larfors (Uppsala University )

Room: Virtual only 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.

NN-QFT Correspondence

• Jim Halverson (Northeastern University)

Room: Virtual only 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 the study of neural networks. In this talk, I will provide a new theoretical understanding of NNs in terms of Wilsonian effective field theory, complete with matches to experiment and renormalization. One insight gained is a duality between parameter space and function space treatments of NNs: as parameter complexity increases, Wilsonian RG flow and 1/N-corrections decrease the complexity of the function space distribution. This has the flavor of strong-weak dualities we are accustomed to in physics.

Feature Learning in Infinite-Width Neural Networks

• Greg Yang (Microsoft Research)

Room: Virtual only 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. features), which is crucial for pretraining and transfer learning such as with BERT. We propose simple modifications to the standard parametrization to allow for feature learning in the limit. Using the *Tensor Programs* technique, we derive explicit formulas for such limits. On Word2Vec and few-shot learning on Omniglot via MAML, two canonical tasks that rely crucially on feature learning, we compute these limits exactly. We find that they outperform both NTK baselines and finite-width networks, with the latter approaching the infinite-width feature learning performance as width increases. More generally, we classify a natural space of neural network parametrizations that generalizes standard, NTK, and Mean Field parametrizations. We show 1) any parametrization in this space either admits feature learning or has an infinite-width training dynamics given by kernel gradient descent, but not both; 2) any such infinite-width limit can be computed using the Tensor Programs technique.

The Topology of Data: from String Theory to Cosmology to Phases of Matter

• Gary Shiu (University of Wisconsin-Madison )

Room: Virtual only 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. I will discuss three applications of topological data analysis: 1) identifying structure of the string landscape, 2) constraining primordial non-Gaussianity from CMB measurements and large scale structures data, and 3) detecting and classifying phases of matter. Persistent homology condenses these datasets into their most relevant (and interpretable) features, so that simple statistical pipelines are sufficient in these contexts. This suggests that TDA can be used in conjunction with machine learning algorithms and improves their architecture. Based on: https://arxiv.org/abs/2009.14231 https://arxiv.org/abs/2009.04819 https://arxiv.org/abs/1907.10072 https://arxiv.org/abs/1812.06960 https://arxiv.org/abs/1712.08159

Towards the next level of string phenomenology using machine learning

• Patrick Vaudrevange (TU Munich)

Room: Virtual only 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 orbifold landscape is given, where various techniques from machine learning are applied: i) an autoencoder neural network to identify structures in this landscape, ii) contrast patterns to construct new MSSM-like string models and iii) neural networks to predict the stringy origin of the MSSM. Moreover, by analyzing parts of the string landscape some novel ideas on flavor, CP and dark matter will be uncovered.

Testing Swampland Conjectures with Machine Learning

• Nana Geraldine Cabo Bizet (Universidad de Guanajuato)

Room: Virtual only 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 small vacuum energy as well as unstable dS vacua with small tachyonic mass and large energy are absent, in accordance to the Refined de Sitter Conjecture. Hierarchical fluxes favor perturbative solutions with small values of the vacuum energy and moduli masses, as well as scenarios with the lightest modulus mass much smaller than the AdS vacuum scale.

(K)not machine learning

• Vishnu Jejjala (University of the Witwatersrand)

Room: Virtual only 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 language, the phase corresponds to a fractional level. We interpret this in terms of the analytic continuation of Chern-Simons theory.

Can graph neural networks count substructures?

• Soledad Villar (Johns Hopkins University)

Room: Virtual only 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 that examine their power in graph isomorphism testing and function approximation. No previous knowledge on graph neural networks is required.

Vacuum Selection in the Flux Landscape

• Cody Long (Harvard University)

Room: Virtual only 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 discuss an investigation into how these effects influence cosmological vacuum selection in a standard bubble nucleation cosmology.

Towards Enumeration of Vacua

• Liam McAllister (Cornell)

Room: Virtual only 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.

Machine learning for complete intersection Calabi-Yau manifolds

• Harold Erbin (MIT & CEA-LIST)

Room: Virtual only 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 perfect accuracy for h11 using much less data than other approaches. The same architecture also performs much better than any other algorithm for h21.

Machine-Learning Mathematical Structures

• Yang-Hui He (City, U of London; Merton College, U of Oxford; & Nankai U)

Room: Virtual only 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.

Bayesian inference and quantum field theory

• David Berman (Queen Mary University of London)

Room: Virtual only We will examine links between approaches to learning through Bayesian inference and properties of quantum field theories.