Matthew S. Scott

PhD candidate in Applied Mathematics, University of British Columbia

I work on the mathematics of data, from theory to applications: convex analysis, high-dimensional probability and geometry, and the geometry of neural networks; compressed sensing with generative neural networks, sampling schemes for inverse problems, and average-case analysis of optimization problems. My PhD is supervised by Yaniv Plan and Özgür Yılmaz. Before UBC, I studied mathematics and physics at McGill University.

I also write software, mostly for research and note-taking, and I teach first-year calculus at UBC.

Email · CV · GitHub · Google Scholar · LinkedIn · Obsidian guides

Papers

• Exact signal recovery from generative priors with sigmoid output activation. With Y. Plan, Ö. Yılmaz. Submitted to Sampling Theory, Signal Processing, and Data Analysis.
• Convexity from order: a theory of faces and generalized separation. Sole author. Major revisions at Journal of Convex Analysis. arXiv:2609.05775
• Partially deterministic sampling for compressed sensing with denoising guarantees. With Y. Plan, Ö. Yılmaz. Submitted to Information and Inference: A Journal of the IMA. arXiv:2604.04802
• Average-case thresholds for exact regularization of linear programs. With M. P. Friedlander, S. Kubal, Y. Plan. Minor revisions, second round at SIAM Journal on Optimization. arXiv:2510.13083
• Bilateral facial reduction: qualification-free subdifferential calculus and exact duality. Sole author. Major revisions at Set-Valued and Variational Analysis. arXiv:2510.12244
• Denoising guarantees for optimized sampling schemes in compressed sensing. With Y. Plan, X. Sheng, Ö. Yılmaz. SIAM Journal on Mathematics of Data Science, 2026. arXiv:2504.01046
• Model-adapted Fourier sampling for generative compressed sensing. With A. Berk, S. Brugiapaglia, Y. Plan, X. Sheng, Ö. Yılmaz. Oral at NeurIPS 2023 Workshop on Deep Learning and Inverse Problems.
• A coherence parameter characterizing generative compressed sensing with Fourier measurements. With A. Berk, S. Brugiapaglia, B. Joshi, Y. Plan, Ö. Yılmaz. IEEE Journal on Selected Areas in Information Theory, 2022. arXiv:2207.09340

Also on Google Scholar · CV

Software

• Latex Exporter, 4,700+ downloads, 44 GitHub stars (TypeScript). An Obsidian plugin that infers a paper's LaTeX structure from the note graph: wikilinks become citations or references, embedded notes become theorems with proofs.
• Experiments on Slurm (Python, Bash). Experiments as a data frame, one row per run: input columns set the variables, output columns are filled by running the rows in parallel on a Slurm cluster, ready to plot.
• Research numerics (PyTorch, pandas, seaborn). Numerical experiments for signal recovery with sparse and generative priors.

• Cracker Craft, 10k+ Google Play Store downloads (C#, Unity, Blender). Design your own firework!

Video

• Balloons and the Legendre Transform: an animated video explaining the Legendre transform through balloons, 2022.

Blog posts

• Duality of faces in polar sets 31 August 2024

  Dual faces of polar convex sets as one instance of a general duality between sets, told through molds and pours.

• Bayesian signal recovery 29 April 2024

  Recovering a signal by sampling from its posterior, and when that works; a rigorous reading of Jalal et al. (2021).

• Obsidian for research: notes from my workshop on graph-based writing, with setup guides for citations, LaTeX and daily notes

Experience

• Teaching Assistant, Research Assistant and Small Class Instructor, University of British Columbia, 2021–present. Taught my own small classes in first-year calculus (MATH 100, MATH 180).
• Research Assistant in Computer Science, McGill University, with Prakash Panangaden, Summer 2020. Computational improvements to Yaida's FDR optimizer, and application to actor-critic RL.
• Machine Learning Intern, Decathlon Canada, Montreal, Summer 2018. Built a recurrent-network sales forecaster that beat four of five in-house models, the only one predicting long term.
• Mobile App Developer, GoRush, Montreal, Summer 2017. Sole developer of an on-demand lawn-mowing app (JavaScript, Meteor, MongoDB).

Talks

• Qualification-free duality via reduction to the joint supporting subspace. West Coast Optimization Meeting, UW Tacoma, 2026.
• Denoising guarantees for optimized sampling. SIAM Pacific Northwest Meeting, UW Seattle, 2025.
• Exact regularization of linear programs. SIAM Pacific Northwest Meeting, UW Seattle, 2025.
• Model-adapted Fourier sampling for generative compressed sensing. NeurIPS Workshop on Deep Learning and Inverse Problems, New Orleans, 2023.
• Generative recovery from subsampled Fourier measurements. CMS Winter Meeting, Montreal, 2023; UBC MILD seminar, 2022.