Papers.
Research on learning, representing and
reasoning about dynamical systems.
Learning the Language of Dynamical Systems
A transformer learns to generate dynamical systems from observed trajectories. It represents systems as circuits in a typed compositional language whose combinators form a traced monoidal category. Trained by next-token prediction and refined with mutation-MCTS, the 23M-parameter model recovers explicit circuit structure on synthetic and classical systems.
Coming soonLearning Explicit Structure of Dynamical Systems
We train a foundation model to discover circuit structures from observed trajectories. Grammar-constrained decoding guarantees syntactic validity. Training progresses from supervised imitation through reward-ranked fine-tuning to AlphaZero-style search over circuit tokens.
Coming soonAsgard: Dynamical Systems as Programs
Asgard compiles mathematical equations into typed compositional circuits and executes them via JAX. It preserves explicit mathematical structure throughout, supporting formal composition, algebraic rewriting, and interchangeable semantics.
Read PDFThe Smoothness Hypothesis
Why does next-token prediction learn language so well, yet fail for dynamical systems? We propose an explanation based on the smoothness of the syntax-to-semantics map and discuss its implications for foundation models in structure-sensitive domains.
Read PDFSimulation Learning
An agent-based approach that extends the categorical proof system with simulation-guided reasoning. The agent interleaves strict symbolic rewrites with simulation-informed approximate rewrites to discover approximate closed-form solutions for systems where exact solutions do not exist.
Read PDFTrace Elimination as Closed-Form Discovery
We connect signal-flow circuits for dynamical systems to sequential programs. In this correspondence, finding a closed-form solution amounts to eliminating loops. We show that trace elimination is undecidable in general, formalising the intuition that most ODEs have no closed-form solution.
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