AI 4 Math

The stories behind two independent research projects

These are two independent research stories. One began with the problem of keeping a geometric search valid at every step; the other began with a mixture of exact and bounded arithmetic data. I focus on the obstacles we met, the decisions that changed the direction, and what the experiments taught us.

COMBINATORIAL GEOMETRY

Geometry-aware MCTS

How can MCTS construct valid grid configurations when each move changes the feasible set and symmetry creates duplicate branches?

Making every rollout valid solved one problem and created another: maintaining the feasible set became the bottleneck. The rest of the story is about buying back that runtime with incremental updates, symmetry, and subtree reuse.

Read how we built the search →

ARITHMETIC GEOMETRY

Learning ℚ-gonality

What can tabular models learn from modular-curve invariants, and how can theoretical bounds become training signal when an exact label is unavailable?

The 5,800 bounded cases were not merely missing data: their intervals could become weak supervision. That shift led from tabular prediction to distribution-shift tests and a search for readable formulas.

Read how the project developed →