cv
Basics
Name | Karthik Viswanathan |
Label | Researcher |
vkarthik095@gmail.com | |
Phone | (31) 684103282 |
Url | https://karthikviswanathn.github.io/ |
Summary | Topological Data Analysis for Cosmology \( \to \) Interpretability in LLMs |
Education
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2021.09 - Present Amsterdam, NL
PhD
University of Amsterdam, Netherlands
Interpetability in LLMs and Applications of Topological Data Analysis
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2019.09 - 2021.08 Amsterdam, NL
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2013.09 - 2017.06 Chennai, India
Work
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2017.05 - 2019.05 Surveillance Analyst
Goldman Sachs, Bangalore, India
Developed ML models for anomaly detection in financial data.
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2016.05 - 2016.07 Summer Analyst
Goldman Sachs, Bangalore, India
Implemented fast Personalized PageRank in a MapReduce framework
Publications
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2025.01.17 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.
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2024.10.14 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.
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2024.09.18 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%.
Awards
- 2020.09.01
Sander Bais Prize
Institute for Theoretical Physics, Amsterdam
Awarded by Institute for Theoretical Physics Amsterdam for exceptional academic performance in the master’s program
- 2015.05.20
ACM ICPC World Finals 2015 (Honorable Mention)
Represented India in the international collegiate programming contest held in Marrakesh, Morocco.
Projects
- 2020.09 - 2021.08
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.
- 2017.01 - 2017.04
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.