01. PROFILE

Aakash Kumar

PhD Student in Theoretical Machine Learning
“Life is a Markov process.”
Aakash Kumar
02. Biography

I am a PhD student working on theoretical machine learning, with a focus on composition, memory and pruning.

Based in Nice, France, I am affiliated with COATI, 3IA Côte d’Azur, Inria, I3S, CNRS, and Université Côte d’Azur. Working under the supervision of Prof. Emanuele Natale, my research studies the mathematical principles behind model composition, sequence memory, and neural network pruning.

Prior to this, I completed my BS-MS in Physics at IISER Kolkata, giving me a strong foundation in the physical principles that often govern complex systems like Neural Networks.

03. Research Focus

Compositionality, Memory, and Network Structure

A central part of my research studies the Strong Lottery Ticket Hypothesis (SLTH), which asks whether sparse subnetworks hidden inside large randomly initialized models can already exhibit strong performance before training. My earlier work developed theoretical frameworks connecting pruning and quantization in these regimes.

More recently, I have been exploring how neural systems combine specialized behaviors without interference. One line of work develops a principled framework for composing autoregressive models, with guarantees on stability and compositional generalization.

Another line investigates asymmetric Hopfield networks and sequence memory, showing classical asymmetric Hopfield networks can support extremely large number of stable limit cycles, each with a very large period.

Keywords: Strong Lottery Ticket Hypothesis, Model Composition, Sequence Memory, Neural Network Theory
04. Publications
Beyond Fixed Points: Superpolynomial Capacity of Asymmetric Hopfield Networks
Aakash Kumar, Anatoly Khina, Frederik Mallmann-Trenn, Emanuele Natale
ArXiv Preprint (2026)
Compositional Generalization in Autoregressive Models via Logit Composition
Aakash Kumar, Maria Sofia Bucarelli, Emanuele Natale
ArXiv Preprint (2026)
Quantization vs Pruning: Insights from the Strong Lottery Ticket Hypothesis
Aakash Kumar, Emanuele Natale
ArXiv Preprint (2025)
More works in progress...
05. Academic Timeline
2025 — Present
PhD, Theoretical Machine Learning
Inria & Université Côte d’Azur, France

Team COATI. Advisor: Emanuele Natale.

Inria
2020 — 2025
BS-MS in Physical Sciences
IISER Kolkata, India

Thesis: "Phase transition in Artificial Neural Networks".
Teaching Assistant for Mathematical Methods I.

IISER
06. Connect

Let's Discuss Science

I am always open to discussion and welcome you to contact me.