Related papers: RG inspired Machine Learning for lattice field the…

Accurately determining the underlying physical parameters of individual elements in integrated photonics is increasingly difficult as device architectures become more complex. Inferring these parameters directly from spectral measurements…

Graph convolution operator of the GCN model is originally motivated from a localized first-order approximation of spectral graph convolutions. This work stands on a different view; establishing a \textit{mathematical connection between…

Sampling from known probability distributions is a ubiquitous task in computational science, underlying calculations in domains from linguistics to biology and physics. Generative machine-learning (ML) models have emerged as a promising…

Knowing that the generative capabilities of large language models (LLM) are sometimes hampered by tendencies to hallucinate or create non-factual responses, researchers have increasingly focused on methods to ground generated outputs in…

The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…

The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient descent (GD) algorithm, implicit gradient descent (IGD)…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…

Centered Kernel Alignment (CKA) was recently proposed as a similarity metric for comparing activation patterns in deep networks. Here we experiment with the modified RV-coefficient (RV2), which has very similar properties as CKA while being…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

The Renormalization Group (RG) is one of the central and modern techniques in quantum field theory. Indeed, quantum field theories can be understood as flows between fixed points of the RG flow, which represent Conformal Field Theories…

The recent introduction of machine learning techniques, especially normalizing flows, for the sampling of lattice gauge theories has shed some hope on improving the sampling efficiency of the traditional HMC algorithm. Naive use of…

Following the earlier formalism of the categorical representation learning (arXiv:2103.14770) by the first two authors, we discuss the construction of the "RG-flow based categorifier". Borrowing ideas from theory of renormalization group…

High-dimensional data often exhibit dependencies among variables that violate the isotropic-noise assumption under which principal component analysis (PCA) is optimal. For cases where the noise is not independent and identically distributed…

Continual learning, focused on sequentially learning multiple tasks, has gained significant attention recently. Despite the tremendous progress made in the past, the theoretical understanding, especially factors contributing to catastrophic…

Machine learning techniques are increasingly powerful, leading to many breakthroughs in the natural sciences, but they are often stochastic, error-prone, and blackbox. How, then, should they be utilized in fields such as theoretical physics…

We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce…

In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…

High-dimensional multimodal sampling problems from lattice field theory (LFT) have become important benchmarks for machine learning assisted sampling methods. We show that GPU-accelerated particle methods, Sequential Monte Carlo (SMC) and…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Recently, Retrieval Augmented Generation (RAG) has shifted focus to multi-retrieval approaches to tackle complex tasks such as multi-hop question answering. However, these systems struggle to decide when to stop searching once enough…