Academic Papers

Research

Deep Learning Theory

Glasgow, M., Wu, D., Bruna, J. Mean-field analysis of polynomial-width two-layer neural network beyond finite time horizon. Working Paper. Under Review.

Glasgow, M. SGD Finds then Tunes Features in Two-Layer Neural Networks with near-Optimal Sample Complexity: A Case Study in the XOR problem. Arxiv. ICLR 2024 (Spotlight).

Mahankali, A., Haochen, J.,Dong, K., Glasgow, M., Ma, T. Beyond NTK with Vanilla Gradient Descent: A Mean-Field Analysis of Neural Networks with Polynomial Width, Samples, and Time. Arxiv. Neurips 2023.

Glasgow, M., Wei, C., Wootters, M., Ma, T. Max-Margin Works while Large Margin Fails: Generalization without Uniform Convergence Arxiv. ICLR 2023.

Distributed Optimization

Cheng, Z., Glasgow, M. Convergence of Distributed Adaptive Optimization with Local Updates Arxiv. ICLR 2025.

Patel, K., Glasgow, M., Wang, L., Joshi, N., Srebro, N. On the Still Unreasonable Effectiveness of Federated Averaging for Heterogeneous Distributed Learning Arxiv. COLT 2024.

Glasgow, M.*, Yuan, H.*, Ma, T. Sharp Bounds for Federated Averaging (Local SGD) and Continous Perspective Arxiv. AISTATS 2022.

Glasgow, M., Wootters, M. Asynchronous Distributed Optimization with Randomized Delays. Arxiv. AISTATS 2022.

Glasgow, M., Wootters, M. Approximate Gradient Coding with Optimal Decoding. Arxiv. IEEE JSAIT 2021.

Other ML Theory

Glasgow, M., Rakhlin, A. Tight Bounds for gamma-Regret via the Decision-Estimation Coefficient Arxiv 2023.

Tamkin, A., Glasgow, M., He, X., Goodman, N. Feature Dropout: Revisiting the Role of Augmentations in Contrastive Learning Arxiv. Neurips 2023.

Discrete Random Matrix Theory

(A-Z) Glasgow, M., Kwan, M., Sah, A., Sawhney, M. A central limit theorem for the matching number of a sparse random graph. Arxiv 2024.

(A-Z) Glasgow, M., Kwan, M., Sah, A., Sawhney, M. The Exact Rank of Sparse Random Graphs Arxiv 2023.

(A-Z) DeMichele, P., Glasgow, M., Moreira, A. On the Rank, Kernel, and Core of Sparse Random Matrices Arxiv 2022. RSA 2024.

Undergraduate Research

Tomezsko, P.J., Corbin, V.D.A., Gupta, P. et al. Determination of RNA structural diversity and its role in HIV-1 RNA splicing. Nature (2020) Nature
Summary of my personal contributions to this work. Undergraduate Research in Silvia Roukin's lab at the Whitehead Institue.

Glasgow, M. Unexpected transitions between repeating patterns in continued fractions. In preparation. Manuscript Undergraduate research with Henry Cohn.

Expository Writing

Trends in Machine Learning Theory Part of the ALT 2021 Highlights Series.

An Equivalence between Private Learning and Online Learning Part of the ALT 2021 Highlights Series.

Approximation Algorithms for Graphic TSP Final Project with Bertie Ancona for Advanced Algorithms (6.854) Fall ’17.

Matrix Groups in GL_n(Q) Final Project for Number Theory Seminar (18.784) Fall ’16.

Other

A lower bound for average linear embeddings L2^2 –> L1 Based on some work during my rotation with Moses Charikar in Fall ’18.

“A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.” - G. H. Hardy