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We present a tensorization algorithm for constructing tensor train representations of functions, drawing on sketching and cross interpolation ideas. The method only requires black-box access to the target function and a small set of sample points defining the domain of interest. Thus, it is particularly well-suited for machine learning models, where the domain of interest is naturally defined by the training dataset. We show that this approach can be used to enhance the privacy and interpretability of neural network models. Specifically, we apply our decomposition to (i) obfuscate neural networks whose parameters encode patterns tied to the training data distribution, and (ii) estimate topological phases of matter that are easily accessible from the tensor train representation. Additionally, we show that this tensorization can serve as an efficient initialization method for optimizing tensor trains in general settings, and that, for model compression, our algorithm achieves a superior trade-off between memory and time complexity compared to conventional tensorization methods of neural networks.

We are entering the golden age of multi-wavelength astronomical surveys. In the 2020s, a plethora of surveys (such as Euclid, eROSITA, Rubin-LSST, Simons Observatory, and CMB-S4) are underway or planned to provide unprecedented insights into cosmology and astrophysics. In this talk, I will discuss the significant scientific opportunities and challenges that arise in the era of big data, highlighting recent advances in computational modeling and the roles of artificial intelligence and machine learning.

Galaxies are the medium through which we study the structure of the universe. However, widely applied statistical models of galaxies are generally over-simplified: even recently proposed models cannot capture the dependencies on environment or formation history. To solve this problem, I will introduce Graph Neural Networks (GNNs), a general and ideal tool for physical modelling. Geometrically constrained GNNs vastly improve our models, and allow us to ask detailed questions about the importance of formation history and environment for cosmological galaxy modeling. I will also prove a surprising equivalence between these two aspects of galaxy formation.

We develop a Machine-Learning Renormalization Group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the $c$-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions. We demonstrate the MLRG method in two-dimensional lattice models with Ising symmetry and show that the algorithm correctly identifies and characterizes the Ising criticality.

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