Machine learning methods are mostly based on calculus and probability and statistics on Euclidean spaces.

However, many interesting problems can be articulated as learning in lower dimensional embedded manifolds

and on Lie groups. This talk reviews how learning and Lie groups fit together, and how the machine learning community can benefit from modern mathematical developments. The topics...

We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties. The associated non-reflexive polytopes provide a generalization of Batyrev’s original work, allowing us to construct new pairs of mirror manifolds. In particular, this allows us to find new K3-fibered Calabi-Yau manifolds, relevant for string compactifications.

Curry-Howard correspondence is, roughly speaking, the observation that proving a theorem is equivalent to writing a program. Using this principle, I will present a unified survey of recent trends in the application of deep learning in program synthesis and automated theorem proving, with commentary on their applicability to the working mathematician and physicists.

I will discuss the two-fold relation between Quantum Computers and Machine Learning. On one hand Quantum Computers offer new algorithms to perform training tasks on classical or Quantum data. On the other hand, Machine Learning offers new tools to study Quantum Matter, and to control Quantum experiments.

Our understanding of any given complex physical system is made of not just one, but many theories which capture different aspects of the system. These theories are often stitched together only in informal ways. An exception is given by renormalization group techniques, which provide formal ways of hierarchically connecting descriptions at different scales.

In machine learning, the various...

Physical systems differing in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the renormalization group (RG) procedure, which systematically retains ‘slow’ degrees of freedom and integrates out the rest. We demonstrate a machine-learning...

Topological data analysis (TDA) is a multi-scale approach in computational topology used to analyze the ``shape” of large datasets by identifying which homological characteristics persist over a range of scales. In this talk, I will discuss how TDA can be used to extract physics from cosmological datasets (e.g., primordial non-Gaussianities generated by cosmic inflation) and to explore the...

I will review the Bousso-Polchinski model and aspects of its computational complexity. An asynchronous advantage actor-critic will be used to find small cosmological constants.

The Nelson-Seiberg theorem relates F-term SUSY breaking and R-symmetries in N=1 SUSY field theories. I will talk its several extensions including a revision to a necessary and sufficient condition, discrete R-symmetries and non-Abelian R-symmetries, relation to SUSY and W=0 vacua in the string landscape, and some possible machine learning applications in the searching for SUSY vacua.

Tensor network is both a theoretical and numerical tool, which has achieved great success in many body physics from calculating he thermodynamic property and quantum phase transition to simulations of black holes. As a general form of high dimensional data structure, tensors have been adopted in diverse branches of data analysis, such as in signal and image processing, psychometric, quantum...

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network...

Handling the large number of degrees of freedom with proper approximations, namely the construction of the effective Hamiltonian is at the heart of the (condensed matter) physics. Here we propose a simple scheme of constructing Hamiltonians from given energy spectrum. The sparse nature of the physical Hamiltonians allows us to formulate this as a solvable supervised learning problem. Taking a...

We present a deep neural network representation of the AdS/CFT correspondence, and demonstrate the emergence of the bulk metric function via the learning process for given data sets of response in boundary quantum field theories. The emergent radial direction of the bulk is identified with the depth of the layers, and the network itself is interpreted as a bulk geometry. Our network provides a...

A Convolutional Neural Network (CNN) is designed to study correlation between the temperature and the spin configuration of the 2 dimensional Ising model.

Our CNN is able to find the characteristic feature of the phase transition without prior knowledge. Also a novel order parameter on the basis of the CNN is introduced to identify the location of the critical temperature; the result is...

In this talk, I show some concepts in computing, Physics and Mathematics

focusing on High Energy Physics. I share some programming languages and

tools implemented for computing the amplitudes, decays and cross sections.

In particular, I explore the Two-Higgs Doublet Model and Extended Gauge Group

Model and some results using Artificial Inteligence.