Agentic Skill Optimization over Lie Algebroids

2026-07-13

AI Summary

This work addresses the challenges of agent skill editing—namely, strong structural dependencies, sensitivity to operation order, and high verification costs—which render conventional approaches inefficient. To overcome these limitations, the authors propose LASKO, a novel framework that introduces controlled Lie algebroids into skill optimization for the first time. Skills are formally modeled as typed, anchor-equipped Markdown objects, enabling precise characterization of their non-commutative nature and implicit structure. A key innovation is the Lie bracket-based pre-screening mechanism, which drastically reduces the number of expensive verification calls to large language models. Experimental results on causal extraction tasks demonstrate that LASKO achieves nearly a 15-fold speedup over brute-force verification while substantially lowering computational overhead.

Abstract

Agentic systems increasingly improve themselves by editing skills: prompts, rubrics, plans, tool contracts, examples, validators, and traces. Skill edits are not independent coordinates in a vector space: they are local repairs to structured artifacts whose effects are observed only after rollout, validation, and critique. Distinct edits can have the same immediate visible effect while differing in routing context, template state, guardrail scope, or future composability. The order of edits can matter as well: repairing a schema before a normalization rule need not be equivalent to applying the same edits in the reverse order. This paper introduces a new framework for skill optimization called LASKO, for Lie Algebroid SKill Optimization. LASKO models typed, anchored Markdown skills as the base category and available edit policies as sections of a controlled Lie algebroid with anchor $ρ$. The anchor maps an edit policy to its visible Markdown effect; the kernel $\ker(ρ)$ represents latent template, routing, or implementation structure; and the algebroid bracket measures noncommuting edit composition. As shown in the paper, LASKO achieves order-of-magnitude speedups in skill optimization in our preliminary benchmark results, primarily because it substitutes inexpensive Lie-bracket screening tests that run in microseconds, before investing in expensive validations that require running large language models. On a causal extraction from natural language task, LASKO achieved a speedup of almost $15 \times$ compared to a brute-force approach that validated all edits by running them through a DeepSeek V3.1 4-bit model with 671B parameters.

Problem

• agentic systems
• skill optimization
• structured artifacts
• edit composition
• noncommuting edits

Innovation

• Lie algebroid
• skill optimization
• noncommutative editing
• anchor map
• efficient validation