cv

PhD

University of Amsterdam, Netherlands

Interpetability in LLMs and Applications of Topological Data Analysis

MSc

University of Amsterdam, Netherlands

Theoretical Physics

B.Tech

Indian Institute of Technology, Madras

Engineering Physics

Surveillance Analyst

Goldman Sachs, Bangalore, India

Developed ML models for anomaly detection in financial data.

Summer Analyst

Goldman Sachs, Bangalore, India

Implemented fast Personalized PageRank in a MapReduce framework

The Geometry of Tokens in Internal Representations of Large Language Models

arXiv

We investigate the relationship between the geometry of token embeddings and their role in next token prediction within transformer models. Our analysis reveals a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Persistent Topological Features in Large Language Models

arXiv

We present a novel framework based on zigzag persistence, a method in topological data analysis (TDA) to describe data undergoing dynamic transformations across layers of a large language models. As a practical application, we leverage persistence similarity to identify and prune redundant layers, demonstrating comparable performance to state-of-the-art methods across several benchmark datasets.

Cosmology with Persistent Homology: a Fisher Forecast

Journal of Cosmology and Astroparticle Physics

We apply persistent homology to the dark matter halo catalogs, and build a summary statistic for comparison with the joint power spectrum and bispectrum statistic regarding their information content on cosmological parameters and primordial non-Gaussianity. Through a Fisher analysis, we find that constraints from persistent homology are tighter for 8 out of the 10 parameters by margins of 13–50%.

Sander Bais Prize

Institute for Theoretical Physics, Amsterdam

Awarded by Institute for Theoretical Physics Amsterdam for exceptional academic performance in the master’s program

ACM ICPC World Finals 2015 (Honorable Mention)

Represented India in the international collegiate programming contest held in Marrakesh, Morocco.

Exploring the Spectral Theory/Topological Strings Duality (Master's Thesis)

This thesis analyzes the ST/TS duality, linking topological strings on toric Calabi-Yau manifolds to quantum mechanical spectral theory and highlighting how this duality, developed by Marcos Mariño and collaborators, enables a non-perturbative description of topological strings, which we verify using resurgence techniques.

Real Space Renormalization and Applications to Machine Learning (Bachelor's Thesis)

We explore the application of renormalization group (RG) theory to understand the success of Restricted Boltzmann Machines (RBMs), drawing parallels between RG's iterative coarse-graining in physics and feature extraction in deep learning, where theoretical understanding remains limited despite impressive empirical success across domains.