Gimle Papers

A framework that compiles mathematical equations into typed compositional circuits and executes them via JAX. Unlike implicit approaches that learn black-box dynamics, Asgard maintains explicit mathematical structure throughout — enabling formal composition, algebraic rewriting, and interchangeable semantics.

Why does next-token prediction learn language so well, yet fail for dynamical systems? We propose an explanation rooted in the smoothness of the syntax-to-semantics map — and what it means for building foundation models in structure-sensitive domains.

A visual overview of the Gimle platform — why explicit mathematical structure matters for learning dynamical systems, how Asgard compiles equations into typed circuits, and the path from formal methods to practical simulation.

Most agent frameworks treat LLMs as agents. Hugin treats them as oracles — one component in a larger reasoning system. Built around an immutable stack architecture that makes branching, debugging, and multi-agent coordination natural.

We train a foundation model to discover circuit structures from observed trajectories, using grammar-constrained decoding to guarantee syntactic validity and a staged pipeline — from supervised imitation through end-to-end behavioural optimisation to AlphaZero-style search over circuit rewrites.

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.

A structural correspondence between signal-flow circuits for dynamical systems and sequential programs — where finding a closed-form solution corresponds to eliminating loops. We show trace elimination is undecidable in general, formalising the intuition that "most ODEs don't have closed-form solutions".