Agentic Skill Optimization over Lie Algebroids

Source

• Source name: arXiv
• Source kind: paper
• Authors / organization: Sridhar Mahadevan
• Venue: arXiv: cs.LG
• Published: 2026-07-13
• Collected: 2026-07-14
• URL: http://arxiv.org/abs/2607.11493v1
• PDF: https://arxiv.org/pdf/2607.11493v1
• DOI: UNKNOWN

Plain-Language Brief

The text introduces LASKO, a new framework for optimizing skills in agentic systems. LASKO models skills as structured artifacts and edit policies as sections of a Lie algebroid. The framework achieves significant speedups in skill optimization by using quick Lie-bracket screening tests instead of expensive validations.

What the Document Says

• LASKO is a new framework for skill optimization.
• Skills are modeled as structured artifacts and edit policies as sections of a Lie algebroid with an anchor.
• The anchor maps an edit policy to its visible Markdown effect.
• The kernel represents latent template, routing, or implementation structure.
• The algebroid bracket measures non-commuting edit composition.
• LASKO achieves speedups in skill optimization due to inexpensive Lie-bracket screening tests and avoiding expensive validations.

Key Concepts Mentioned

• Agentic systems
• Skills optimization
• Lie Algebroid SKill Optimization (LASKO)
• Markdown
• Edit policies
• Lie algebroid
• Anchor
• Kernel
• Algebroid bracket

Claims Made by the Document

• LASKO achieves order-of-magnitude speedups in skill optimization.
• LASKO achieved a speedup of almost $15 imes$ compared to a brute-force approach.

Evidence Used

• Preliminary benchmark results showing speedups with LASKO.
• Comparison between LASKO and a brute-force approach on a causal extraction from natural language task.

Methods / Approach

• Using Lie algebroids for skill optimization
• Lie-bracket screening tests

Limitations Stated by the Authors

UNKNOWN

Limitations Noted by the Agent

Agent interpretation — not from the source.

UNKNOWN

Open Questions

UNKNOWN

Notes for Future Q&A

May include interpretation. Labeled where it does.

UNKNOWN

Raw Abstract / Excerpt

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.