William
Chang
PhD student in Applied Mathematics at UCLA.
About
I'm a PhD student in Applied Mathematics at the University of California, Los Angeles, where I've been since Fall 2023. Before that I earned a B.A. in Mathematics from the University of Southern California in 2022.
My research interests are broad and span mathematics and machine learning. See my papers below for more.
I'm also the founder of BruinML, a research group at UCLA where I mentor students on projects in machine learning and mathematics.
I enjoy tutoring and take students in math and physics at every level, from elementary school through university. Email me to book a session.
Outside of research I practice Taekwondo and sing. My covers are on YouTube and Spotify.
Research
Mentoring
I founded BruinML, a UCLA machine learning and mathematics research group, in January 2024. It's now led by Kenny Guo.
Since Spring 2024 I've mentored undergraduates through research projects from first idea to submission. Many of the papers above were led by students in the group, with work appearing at NeurIPS, UAI, EWRL, Asilomar and TMLR.
If you're a student interested in a project, send me an email with a bit about your background.
ProjectsSmall things I've built
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Robot Sumo
Two-wheeled robots shoving each other out of a ring. Small neural nets trained by evolution strategies and self-play. Drive one yourself and try to beat each level.
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Selfplay Chess
A chess engine that learned its own piece values by playing itself, starting from all pieces equal. Play against any of its four levels.
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Pianoify
Drop in a song and get a simplified piano arrangement: the chords, the melody and sheet music you can play. Beat, chord and melody detection run in your browser.
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Cover Me
Sing six notes and a few words, pick any song, and hear its melody sung back in your own voice. Pitch shifting by PSOLA, all in the browser.
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Unmix
Pull the singer out of a song, right in your browser: drop in a track and get the voice and the backing as separate files. No training data, nothing uploaded.
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Liner Lyric Studio
Load a song, paste timestamped lyrics (or tap along to time them), and turn them into an animated lyric video whose scene follows the song's mood, read by a small model that runs in your browser. Exports the finished video.
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Dataset Doctor
Drop in a CSV and find the problems that quietly break machine-learning models: leaking columns, test rows copied from training, contradictory labels, hidden placeholders. Then download the fix.
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Agent Blame
When a multi-step LLM pipeline gets an answer wrong, find which step caused it. Swap steps for better versions with the randomness held fixed, and watch Shapley values split the blame.
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Bandits Lab
Race bandit algorithms against the Lai–Robbins lower bound in your browser, and plan an A/B test: see whether a fixed split or Thompson sampling costs fewer conversions.
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Classifier Toolkit
See how far to trust a classifier: honest confidence, prediction sets with a coverage guarantee, abstention with a certified error rate and drift alarms. Try it on three models or your own CSV.
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Theory Demos
Five ideas from ML theory you can play with in the browser: double descent, high-dimensional geometry, diffusion models that copy their training data, private polls and certified robustness.
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Run List
A shared bucket list sorted like ski runs, from easy nights in to passport trips. Make an account, start a list and invite people to it.
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Figure Lab
Describe a math figure in words and get an interactive one you can rotate, slice and share. Starts with a drilled sphere, solids of revolution, Riemann sums and more.
TeachingTeaching assistant, UCLA Mathematics
- Fall 2024Math 131A Real Analysis
- Fall 2024Math 134 Linear and Nonlinear Systems of Differential Equations
- Spring 2024Math 156 Machine Learning
- Winter 2024Math 32B Calculus of Several Variables
- Fall 2023Math 31A Differential and Integral Calculus
I've also taught at the UCLA Math Circle since Fall 2023.
Background
Education
- University of California, Los Angeles 2023–2027PhD, Applied Mathematics. Passed qualifying exams in Basic (Fall 2023), Applied Differential Equations (Fall 2023) and Geometry/Topology (Spring 2024).
- University of Southern California 2018–2022B.A., Mathematics
Experience
- Northrop Grumman Summer 2022Intern, Communications Systems and Mission Payload, Space Systems. Analyzed slant ranges and channel losses.
- Baruch College Discrete Math REU Summer 2021Asymptotic bounds on cliques in Kt-minor-free graphs, with Fan Wei.
- UCLA Applied Math REU 2020–2021Thin-film equations for pleural fluid in the lungs, with Hangjie Ji.
- USC Math Center 2019–2020Tutor for linear algebra, calculus, probability, number theory and analysis.
Fellowships and awards
- NSF EAGER REU Fellowship 2021–2022Multi-agent bandits with information asymmetry, with Rahul Jain.
- USC CURVE Fellowship 2021, 2021–2022Decentralized multiplayer bandits (Rahul Jain); stability of physics-informed neural networks (Assad Oberai).
- USC Provost Undergraduate Research Fellowship 2020–2022Matrix varieties (Robert Guralnick); e-positivity of chromatic polynomials (Greta Panova).
- Putnam Competition 2018–2021Top 500 in 2020; USC representative four years.
Talks and service
- ReviewerICLR and NeurIPS (2023, 2024); IFAC and CDC (2023).
- IEEE CDC 2022Online learning for cooperative multi-player multi-armed bandits.
- Asilomar 2022Approximation capabilities of neural networks using morphological perceptrons.
- Joint Mathematics Meetings 2022Undergraduate poster: maximal cliques in Kt-minor-free graphs.