Publications

My Google Scholar page can be found here. Below is a list of my preprints and publications, separated by subject.

Machine Learning and Optimization

Convergence and Margin of Adversarial Training on Separable Data. Zachary Charles, Shashank Rajput, Stephen Wright, Dimitris Papailiopoulos. [arXiv]

Does Data Augmentation Lead to Positive Margin? Shashank Rajput, Zhili Feng, Zachary Charles, Po-Ling Loh, Dimitris Papailiopoulos. ICML, 2019. [arXiv]

A Geometric Perspective on the Transferability of Adversarial Directions. Zachary Charles, Harrison Rosenberg, Dimitris Papailiopoulos. AISTATS, 2019. [link] [arXiv]

ErasureHead: Distributed Gradient Descent without Delays Using Approximate Gradient Codes. Hongyi Wang, Zachary Charles, Dimitris Papailiopoulos. [arXiv]

ATOMO: Communication-efficient Learning via Atomic Sparsification. Hongyi Wang, Scott Sievert, Zachary Charles, Shengchao Liu, Stephen Wright, Dimitris Papailiopoulos. NeurIPS, 2018. [link] [arXiv]

Stability and Generalization of Learning Algorithms that Converge to Global Optima. Zachary Charles, Dimitris Papailiopoulos. ICML, 2018. [link] [arXiv] [slides]

Approximate Gradient Coding via Sparse Random Graphs. Zachary Charles, Dimitris Papailiopoulos, Jordan Ellenberg. [arXiv]

DRACO: Robust Distributed Training via Redundant Gradients. Lingjiao Chen, Hongyi Wang, Zachary Charles, Dimitris Papailiopoulos. ICML, 2018. [link] [arXiv]

Gradient Coding Using the Stochastic Block Model. Zachary Charles, Dimitris Papailiopoulos. ISIT, 2018. [link] [arXiv] [slides]

Subspace Clustering with Missing and Corrupted Data. Zachary Charles, Amin Jalali, Rebecca Willett. IEEE Data Science Workshop, 2018. [link] [arXiv] [slides]

Applied and Computational Mathematics

Exploiting Algebraic Structure in Global Optimization and the Belgian Chocolate Problem. Zachary Charles, Nigel Boston. Journal of Global Optimization, 2018. [link] [arXiv]

Generating Random Factored Ideals in Number Fields. Zachary Charles. Mathematics of Computation, 2018. [link] [arXiv]

Distributions of the Number of Solutions to the Network Power Flow Equations. Alisha Zachariah, Zachary Charles, Nigel Boston, Bernard Lesieutre. ISCAS, 2018. [link]

Efficiently Finding All Power Flow Solutions to Tree Networks. Alisha Zachariah, Zachary Charles. Allerton, 2017. [link]

Nonpositive Eigenvalues of Hollow, Symmetric, Nonnegative Matrices. Zachary Charles, Miriam Farber, Charles R Johnson, Lee Kennedy-Shaffer. SIAM Journal on Matrix Analysis and Applications, 2013. [link]

Nonpositive Eigenvalues of the Adjacency Matrix and Lower Bounds for Laplacian Eigenvalues. Zachary Charles, Miriam Farber, Charles R Johnson, Lee Kennedy-Shaffer. Discrete Mathematics, 2013. [link]

The Relation Between the Diagonal Entries and the Eigenvalues of a Symmetric Matrix, Based upon the Sign Pattern of its Off-Diagonal Entries. Zachary Charles, Miriam Farber, Charles R Johnson, Lee Kennedy-Shaffer. Linear Algebra and its Applications, 2013. [link]

Dissertation

Algebraic and Geometric Structure in Machine Learning and Optimization Algorithms. Zachary Charles. University of Wisconsin-Madison PhD thesis, 2017. [link]