Indranil Halder is a Research Associate at the Harvard John A. Paulson School of Engineering and Applied Sciences in the Machine Learning Foundations Group. He is currently working with Cengiz Pehlevan. Previously, Indranil was the Harvard Quantum Initiative Fellow at the Center for the Fundamental Laws of Nature with Daniel Jafferis.

Research

Theoretical machine learning

Indranil is a theoretical machine learning researcher specializing in generative AI, with core interests in the interpretability of knowledge representations and the safety, robustness, and optimization of deep learning systems. His recent work focuses on inference-time sampling algorithms and on retrieval tasks for long-context windows.

Motivated by recent empirical successes of large language models that reallocate substantial computation from training to inference, Indranil studies the foundations of inference-time scaling. He has introduced an analytically tractable model based on Bayesian linear regression with a reward-weighted sampler and analyzed the generalization error when training data are drawn from a teacher model. This framework establishes the existence of an optimal temperature for the reward process, an optimal number of inference-time samples, and an optimal reward that can differ from the teacher. His analysis further characterizes the regimes in which scaling inference-time computation is provably preferable to collecting additional data, and shows how this advantage deteriorates as task difficulty increases. Some of these results have been reproduced in LLM-as-a-Judge setup.

Position bias is a well-documented limitation of modern long context language models, in which models systematically prioritize information based on its position in the input context—often manifesting as the “lost in the middle” phenomenon. Indranil’s ongoing work develops a theoretical account of this bias, analyzing how the temperature of the attention mechanism should scale with context length to induce different regimes of de-localized attention. His study reveals a novel connection between attention mechanism and the geometry of convex polytopes.

In the past, he has defined and studied an analytically tractable one-step diffusion model In the context of higher-dimensional statistics, using the method of deterministic equivalence, he has proved a theorem that presents an explicit formula for the Kullback-Leibler divergence between the generated and sampling distribution, taken to be isotropic Gaussian, showing the effect of finite diffusion time and noise scale. It shows that the monotonic fall phase of Kullback-Leibler divergence begins when the training dataset size reaches the dimension of the data points.

Theoretical physics

Before transitioning to machine learning, Indranil made notable contributions to theoretical physics.

During his early days at Harvard University, Indranil established a new strong-weak duality closely related to ER=EPR - the fascinating connection between entanglement and geometry. Using the duality, he has made distinct progress on the long-standing issue of thermal microstate counting of blackholes. He has also proposed a framework to evaluate the supersymmetric index in disordered systems in terms of bi-local fields closely related to wormhole-like physics.

During his graduate studies, Indranil worked extensively on theoretical developments of topological quantum computation, more precisely on Chern-Simons gauge theory coupled to matter. He discovered a condensed phase and pointed out an exact non-commutative structure in the presence of a background magnetic field.