Algebra

Advancing Mathematical Reasoning in AI: Introducing Reverse-Process Synthetic Data Generation

Check out the (early) project and source code on GitHub.

Abstract:

This paper introduces a methodology for generating high-quality, diverse training data for Language Models (LMs) in complex problem-solving domains. Our approach, termed …

Alga: Algebraic Parser Composition through Monadic Design A C++20 Template Library for Type-Safe Text Processing

Algebraic Cipher Types: Computing on Encrypted Data While Preserving Structure

A functorial framework that lifts algebraic structures into the encrypted domain, enabling secure computation that preserves mathematical properties.

An Algebraic Framework for Language Model Composition: Unifying Projections, Mixtures, and Constraints

Language Calculus: An Algebraic Framework for LLM Composition

A mathematical framework that treats language models as algebraic objects with rich compositional structure.

Algebraic Hashing A Modern C++20 Library for Composable Hash Functions Version 2.0

Algebraic Hashing: Composable Hash Functions Through XOR

Most hash libraries treat hash functions as black boxes. Algebraic Hashing exposes their mathematical structure, letting you compose hash functions like algebraic expressions—with zero runtime overhead.

The Core Insight

Hash functions form an abelian …

algebraic.mle: The Foundation of a Statistical Inference Ecosystem

An R package treating MLEs as first-class algebraic objects with composable statistical properties.

algebraic.dist: Treating Distributions as First-Class Algebraic Objects in R

Most statistical software treats probability distributions as static parameter sets you pass to sampling or density functions. algebraic.dist takes a different approach: distributions are algebraic objects that compose, transform, and combine using …