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A reverse-process approach to synthetic data generation for training LLMs on mathematical reasoning, producing step-by-step solutions from worked examples.
A functorial framework that lifts algebraic structures into the encrypted domain, enabling secure computation that preserves mathematical properties.
A mathematical framework that treats language models as algebraic objects with rich compositional structure.
A C++ library for composable hash functions using algebraic structure over XOR, with template metaprogramming.
An R package treating MLEs as first-class algebraic objects with composable statistical properties.
An R package for treating probability distributions as first-class algebraic objects that compose through standard operations.
The same GCD algorithm works for integers and polynomials because both are Euclidean domains. This profound insight shows how algebraic structure determines algorithmic applicability.
Integers modulo N form a ring—an algebraic structure that determines which algorithms apply. Understanding this structure unlocks algorithms from cryptography to competitive programming.