I am a third year Ph.D. student in Computer Science at Columbia University. I study machine learning theory under the supervision of Professor Rocco Servedio and Professor Daniel Hsu. I graduated from Brown University in May 2018 with an joint Sc.B. in Applied Mathematics and Computer Science. In my "gap year" between Brown and Columbia, I lived in San Francisco as an Associate Data Scientist at LinkedIn and a Software Engineering Intern at Lumi Labs.

My goal in research is to make machine learning a more trustworthy and equitable tool built on rigorous mathematical foundations. To do so, I'm interested in studying why neural networks and other machine learning models work so well in practice, including work on generalization (how well a learning algorithm adapts to new data) and approximation (what kinds of learning rules can be represented by neural networks). I'm also interested in any topics on the overlap between dynamical systems and machine learning. (I briefly dabbled with dynamical systems research with Professor Bjorn Sandstede at Brown.)

I started the CS Theory Student Seminar at Columbia. I am currently a mentor of an Undergrad TCS Student Seminar on ML theory.

I am grateful for funding from an NSF GRFP fellowship, which I received in March 2021.

Email: clayton [AT] cs.columbia.edu
LinkedIn: claytonsanford
Github: chsanford


Clayton Sanford, Vaggos Chatziafratis. "Expressivity of Neural Networks via Chaotic Itineraries beyond Sharkovsky's Theorem." [arxiv]

Conference Publications

Navid Ardeshir*, Clayton Sanford*, Daniel Hsu. "Support vector machines and linear regression coincide with very high-dimensional features." NeurIPS 2021. [paper] [arxiv] [blog post] [reviews]

Daniel Hsu*, Clayton Sanford*, Rocco Servedio*, Emmanouil-Vasileios Vlatakis-Gkaragkounis*. "On the Approximation Power of Two-Layer Networks of Random ReLUs." COLT 2021. [paper] [arxiv] [blog post] [conference talks]

Undergraduate Publications

Clayton Sanford. "Applying Rademacher-Like Bounds to Combinatorial Samples and Function Selection." Honors Thesis, Brown Department of Computer Science, 2018. [thesis]

Kamil Cygan*, Clayton Sanford*, William Fairbrother. "Spliceman2 - A Computational Web Server That Predicts Sequence Variations in Pre-mRNA Splicing." Bioinformatics 33 (18), 2017. [paper]

Julia Gross*, Clayton Sanford*, Geoff Kocks*. "Projected Water Needs and Intervention Strategies in India." Undergraduate Mathematics and its Applications 37 (2), 2016. [paper] [article]


Lumi Labs

Software Engineering Intern

April 2019 - August 2019


Associate Data Scientist

August 2018 - April 2019

Data Analytics Intern

June 2017 - August 2017


Columbia University

Ph.D. Student in Computer Science

August 2019 -

GPA: 4.0 (out of 4.0)

M.S. in Computer Science

August 2019 - February 2021


  • Department Service Award (2020)

Selected Coursework

Randomized Algorithms; Optimization; ML Theory; Economics, AI, and Optimization; Computation and the Brain

Brown University

Sc.B. in Applied Mathematics-Computer Science

September 2014 - May 2018

GPA: 3.9 (out of 4.0)


  • Computer Science Senior Prize
  • Magna Cum Laude
  • Departmental Honors

Selected Coursework

Algorithms; Advanced Algorithms Seminar; ML; Information Theory; Prescriptive Analytics; Abstract Algebra; Cryptography; Real Analysis


Graduate Teaching Assistant

COMS 4252: Computational Learning Theory

Spring 2021

Head Teaching Assistant

CSCI 1570: Design and Analysis of Algorithms

Fall 2017

Undergraduate Teaching Assistant

APMA 1360: Topics in Chaotic Dynamics

Spring 2017

CSCI 1010: Theory of Computation

Fall 2016

CSCI 220: Discrete Structures and Probability

Spring 2016

CSCI 190: Accelerated Intro to CS

Fall 2015

A few random things...