AlgoTrace: Algorithmic Primitives and Compositional Geometry of Reasoning in Language Models

The paper introduces AlgoTrace, a framework that traces and steers algorithmic operations in large language models’ latent space during multi‑step reasoning. By clustering latent activations on tasks such as TSP, 3SAT, AIME, and Graph Navigation, the authors identify reusable primitive vectors that can be injected to elicit specific algorithmic behaviors, composed algebraically, and transferred across models and tasks. Fine‑tuning further improves the composition of these primitives, suggesting that LLM reasoning can be viewed as a walk through algorithmic primitives governed by compositional geometry.

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• llms
• diffusion
• fine-tuning
• benchmarks