Computer Science · Harvard University
I’m a PhD student at Harvard University, advised by Yue Lu.
My research connects machine learning, optimization, and statistics. My recent work focuses on enabling fast decision-making for foundation models on unstructured data.
My earlier work explored Riemannian optimization and high-dimensional learning dynamics. I also developed interpretable models with provable guarantees for large-scale tabular data, applying them to problems in national security and healthcare.
During my master’s, I was advised by Courtney Paquette and Elliot Paquette. I also completed my bachelor’s in Statistics and Computer Science at McGill.
My work has been supported in part by the NSERC Postgraduate Scholarship, Harvard’s Dean’s Competitive Fund for Promising Scholarship, NSF, and FQRNT.
· Incoming
Quantitative research intern
Voloridge
Quantitative research
Lawrence Livermore National Laboratory
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Machine learning for national security problems in energy.
Valence Labs
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Generative AI models for drug discovery.
n = 4096 · d/n fixed
A decision request becomes probabilities over its options in one forward pass.
Scroll across the diagram, or tap to enlarge.
Figure 1 · source paperWe show how open language models can make probabilistic decisions in a single forward pass, without generating text. We study a simple fine-tuning recipe and release models, serving code, and the OpenDecisions benchmark.
OpenWebText 10⁹ training examples
Full Figure 1
After 5 updates
| Query | Selected words |
|---|---|
| democracy | authoritarian, dictatorship, political, legitimacy, revolution |
| bank | deposits, fargo, deposit, central, banks |
| moose | deer, hunters, wolves, elephants, turtle |
| translates | phrases, implies, dictionary, meaning, translated |
| converting | convert, converted, conversion, generates, storing |
| kidnapping | charged, pleaded, convicted, counts, felony |
| influx | migrants, migration, refugees, asylum, refugee |
Selected cosine neighbors from the learned embedding at t = 5.
Original plots and word lists from Figure 1. Stable rank measures spectral concentration; trajectory error is relative to a 10⁹-example reference.
Figure 1 · source paperWe characterize how an iterative method alternating ridge regression with average gradient outer product (AGOP) updates learns task-relevant features for multi-output regression. We explain how these features evolve and how much data is needed to reliably recover their learning trajectory.
An expression tree certifying geodesic convexity through composition rules.
Figure 2 · source paperA symbolic framework for checking geodesic convexity on Hadamard manifolds. We identify composition rules and matrix-valued building blocks, and implement automated verification in the Julia package SymbolicAnalysis.jl.
Gaussian optimistic likelihood with side information, n = 100 and d = 30. Larger β pulls toward the supplied estimate, which need not be the true covariance.
Figure 7 · source paperWe design regularizers from symmetric gauge functions to handle constraints on positive definite matrices. These regularizers can preserve convexity or difference-of-convex structure, enabling efficient unconstrained optimization on the manifold.
SGD + momentum: published 90% bands for n = 64, 256, 1024, and 4096 around the deterministic Volterra prediction.
Figure 1 · source paperWe characterize high-dimensional mini-batch learning dynamics for regularized least squares. A deterministic discrete Volterra equation describes quadratic statistics of SGD, stochastic Nesterov, and momentum methods.
Under the assumptions in the paper, quadratic statistics \( \mathcal{R}: \mathbb{R}^d \to \mathbb{R} \), including training loss and excess risk, concentrate around deterministic predictions as sample size and dimension grow. The analysis concerns \( \ell_2 \)-regularized least-squares problems.
We describe how batch size controls momentum dynamics on high-dimensional least-squares problems. An implicit conditioning ratio identifies when mini-batch momentum can match the accelerated convergence rate of full-batch momentum.
The complete Figure 4. Horizontal axes: momentum Δ; vertical axes: learning rate γ. Axis ranges and color scales differ across panels.