string_data 2020

14 Dec 2020, 15:40 → 16 Dec 2020, 19:00 Europe/Zurich

Virtual only (CERN)

Fabian Ruehle (CERN)

Description

In the annual string_data workshop, scientists from the fields of string theory, mathematics, and computer science meet and exchange ideas and applications of machine learning, AI, and data science to open problems in fundamental physics and vice versa.

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Key speakers

David Berman (Queen Mary University London)	Magdalena Larfors (Uppsala University)
Nana Cabo Bizet (Universidad de Guanajuato)	Haggai Maron (Nvidia Research)
Michael Douglas (Simons Center)	Cody Long (Cornell University)
Harold Erbin (University of Turin)	Liam McAllister (Cornell University)
Sergei Gukov (Caltech)	Gary Shiu (University of Wisconsin)
Jim Halverson (Northeastern University & IAIFI)	Soledad Villar (New York University)
Yang-Hui He (City University of London)	Patrick Vaudrevange (TU Munich)
Vishnu Jejjala (Witwatersrand University)	Greg Yang (Microsoft Research)
Sven Krippendorf (LMU Munich)

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Organizers

Brent Nelson (Northeastern University & IAIFI)
Fabian Ruehle (CERN & University of Oxford)

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Monday, 14 December

1 Welcome

Speaker: Fabian Ruhle (CERN)

2 Numerical Calabi-Yau Metrics from Holomorphic Networks

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

Speaker: Mr Michael Douglas (Simons Center / CMSA Harvard )

Douglas-sd2020.pdf

Douglas-sd2020-video.mp4

3 Calabi-Yau Metrics from Machine Learning

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.

Speaker: Dr Sven Krippendorf (LMU Munich )

Krippendorf-sd2020.pdf

Krippendorf-sd2020-video.mp4

4 Reinforcement learning heterotic line bundle models

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.

Speaker: Dr Magdalena Larfors (Uppsala University )

Larfors-sd2020.pdf

Larfors-sd2020-video.mp4

17:15 Coffee break

5 NN-QFT Correspondence

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.

Speaker: Prof. Jim Halverson (Northeastern University)

Halverson-sd2020.pdf

Halverson-sd2020-video.mp4

6 Feature Learning in Infinite-Width Neural Networks

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.

Speaker: Mr Greg Yang (Microsoft Research)

Yang-sd2020.pdf

Yang-sd2020-video.mp4

Short talks

5 minute talks

short_talks-sd2020-video.mp4

7 Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology

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 scale or sublevel threshold is increased, to summarize multiscale and high-point correlations in a spin configuration. We employ vector representations of this information called persistence images to formulate and perform the statistical task of distinguishing phases. For the models we consider, a simple logistic regression on these images is sufficient to identify the phase transition. Interpretable order parameters are then read from the weights of the regression. This method suffices to identify magnetization, frustration, and vortex-antivortex structure as relevant features for phase transitions in our models. We also define "persistence" critical exponents and study how they are related to those critical exponents usually considered.

Speaker: Dr Alex Cole (University of Amsterdam)

Cole-sd2020.pdf

short-talks-sd2020-video

8 Algorithmically solving the Tadpole Problem

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 stabilization is well understood and can be formulated exclusively in terms of integer matrices and their eigenvalues and -vectors. In particular, there is no knowledge of complicated period integrals or the corresponding Picard-Fuchs equations required. This makes this example predestined for a computer aided search. Using differential evolution we show that there are no smooth compactifications on K3xK3 with arbitrarily small flux M2-charge, in tension with the tadpole bound.

Speaker: Dr Severin Lust (Harvard University)

Lust-sd2020.pdf

short-talks-sd2020-video

9 Baryons as Solitons in the Meson Spectrum: A ML Perspective

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 masses of pentaquarks and other exotic hadrons and demonstrate that machine learning is an effective tool for testing composition hypotheses. Our results surpass the benchmark constituent quark model both in terms of accuracy of predictions and hypothesis testing across all sectors of hadrons. We anticipate that our methods could yield a mass formula for hadrons from quark composition and other quantum numbers.

Speaker: Dr Damian Mayorga Pena (WITS University)

Mayorga-sd2020.pdf

short-talks-sd2020-video

10 Vector-like spectra in F-theory 1

I will elaborate on how data science helps uncover the structure of vector-like spectra in F-theory.

Speaker: Dr Martin Bies (University of Pennsylvania)

Bies-sd2020.pdf

short-talks-sd2020-video

11 Vector-like spectra in F-theory 2

I will talk about further challenges for realistic vector-like spectra in F-theory MSSM-constructions and how to overcome them in the future.

Speaker: Ms Muyang Liu (University of Pennsylvania)

Liu-sd2020.pdf

short-talks-sd2020-video

12 Output dimension effects in untrained Neural Networks

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 identity for n-point correlation functions of Gauss-net architecture in both GP and NGP limit in appropriate regime of validity of EFT description. Resulting SO(d) symmetry has interesting consequences on perturbative corrections to GP correlation functions, in terms of couplings corresponding to interaction terms of EFT action.

Speaker: Ms Anindita Maiti (Northeastern University)

Maiti-sd2020.pdf

short-talks-sd2020-video

13 Fixed Points in Neural Network Non-Gaussian Processes

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 leading non-Gaussian coefficients of the distribution, which are defined using the techniques of Wilsonian effective field theory.

Speaker: Mr Keegan Stoner (Northeastern University)

short-talks-sd2020-video

Stoner-sd2020.pdf

Tuesday, 15 December

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

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

Speaker: Prof. Gary Shiu (University of Wisconsin-Madison )

Shiu-sd2020.pdf

Shiu-sd2020-video.mp4

15 Towards the next level of string phenomenology using machine learning

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.

Speaker: Dr Patrick Vaudrevange (TU Munich)

Vaudrevange-sd2020.pdf

Vaudrevange-sd2020-video.mp4

16 Testing Swampland Conjectures with Machine Learning

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.

Speaker: Dr Nana Geraldine Cabo Bizet (Universidad de Guanajuato)

Cabo-Bizet-sd2020.pdf

Cabo-Bizet-sd2020-video.mp4

17:15 Coffee break

17 (K)not machine learning

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.

Speaker: Prof. Vishnu Jejjala (University of the Witwatersrand)

Jejjala-sd2020.pdf

Jejjala-sd2020-video.mp4

18 Can graph neural networks count substructures?

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.

Speaker: Prof. Soledad Villar (Johns Hopkins University)

Villar-sd2020.pdf

Villar-sd2020-video.mp4

19 Vacuum Selection in the Flux Landscape

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.

Speaker: Dr Cody Long (Harvard University)

Long-sd2020.pdf

Long-sd2020-video.mp4

Wednesday, 16 December

20 Towards Enumeration of Vacua

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.

Speaker: Prof. Liam McAllister (Cornell)

McAllister-sd2020.pdf

McAllister-sd2020-video.mp4

21 Machine learning for complete intersection Calabi-Yau manifolds

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.

Speaker: Dr Harold Erbin (MIT & CEA-LIST)

Erbin-sd2020.pdf

Erbin-sd2020-video.mp4

22 Machine-Learning Mathematical Structures

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.

Speaker: Prof. Yang-Hui He (City, U of London; Merton College, U of Oxford; & Nankai U)

He-sd2020.pdf

He-sd2020-video.mp4

17:15 Coffee break

23 Bayesian inference and quantum field theory

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

Speaker: Prof. David Berman (Queen Mary University of London)

Berman-sd2020.pdf

Berman-sd2020-video.mp4

Physics meets ML seminar

24 Leveraging Permutation Group Symmetries for the design of Equivariant Neural Networks

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 part of the talk, we will see that these architectures can be implemented using a simple parameter-sharing scheme. We will then demonstrate the applicability of the framework by devising neural architectures for two widely used irregular data types: (i) Graphs and hyper-graphs and (ii) Sets of structured elements.

Speaker: Haggai Maron (NVIDIA Research)

Maron-sd2020.pdf

Maron-sd2020-video.mp4

25 Learning to Unknot

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 giving the sequence of unknotting actions. Based on recent work with James Halverson, Fabian Ruehle, and Piotr Sulkowski.

Speaker: Sergei Gukov (California Institute of Technology)

Gukov-sd2020-video.mp4