Joseph Park
I work on the mathematics underneath machine learning, and I teach it.
Category theory, topological data analysis, and quantum computation, applied to how AI systems represent and move data. That is my doctoral direction. Alongside it I tutor mathematics and physics, and I build things for clients who need the analysis done rather than described.
- Now Combined M.S. and Doctor of Engineering in Artificial Intelligence, Johns Hopkins University. Graduate certificate in Applied and Computational Mathematics.
- Research Quantum gravity and noncommutative geometry with Matilde Marcolli at Caltech. Mathematical physics with Sergei Shabanov at the University of Florida. Computational biophysics with Nikolay Dokholyan at UNC Chapel Hill.
- Published First author on climate forecasting work at NASA Wallops Flight Facility, results in a NASA Technical Memorandum.
- Degrees B.S. Mathematics and B.A. Physics, both with honors, University of Florida. Graduate coursework in quantum field theory, complex analysis, and numerical linear algebra.
- Teaching Tutoring mathematics and physics since 1997. GRE quantitative 169 of 170.
Two ways to work with me
Tutoring
University mathematics and physics, the mathematics behind machine learning, graduate qualifying material, and test preparation.
Consulting
Data analysis, forecasting, retrieval and agent systems, and the unglamorous work of getting a messy dataset into a state where a model can use it.
Recent work
A marketing and retention analysis for a math tutoring franchise, worked end to end and published with the code. Eight write-ups, each ending on a decision rather than a summary, and each one containing at least one result I did not expect when I started it.
- Survival The churn rate falls steeply over time even though no individual student's risk ever changes. Two readings, opposite interventions. Read it.
- Causal Targeting retention calls by churn probability turns out to be worse than calling at random. Read it.
- Modelling Gradient boosting lost to logistic regression, and the ceiling is computable: 56% of the signal above chance was unobservable. The recommendation was to stop tuning and collect a different variable.
- Engineering Drift monitoring, a CLI that validates before it predicts and exits non-zero on a retrain signal, and 38 tests that check claims rather than smoke.
Data throughout is artificial, for privacy. The analyses are the ones I ran against real records. Code: github.com/Wassaw-io/tutoring-center-analytics.
Catena
Catena is my doctoral research direction: a database whose schema is a category, where the maps between physical systems are typed morphisms that carry what they preserve, and where composing a path through the graph composes the guarantees along with it. The bet is that a good deal of what we currently ask a language model to infer is structure that could be represented exactly instead.
Spivak solved the exact case in 2010 and CQL implements it; Markov categories handle the probabilistic case. What neither does is let an approximate retrieval system propose a structural correspondence and then verify it against the categorical constraints before accepting it. That is the part I am building.
It is early. The first working slice is a verifier rather than a database, and the interesting output is the plausible-looking analogy it rejects.