Meta-Skills

Definition

Meta-skills are second-order capabilities that operate on skills rather than tasks directly.

In the Literature

Fan et al. (2024) — Compositional Meta-skills

Meta-skill = high-level skill for composing basic ICL skills:

1. Identifying if samples come from a composite function
2. Identifying the needed combination of basic skills
3. Applying a composite skill on-the-fly

Lu (SELF, 2024) — Procedural Meta-skills

1. Self-Feedback: ${\tau }_{\varphi }(f|p,r)$ — evaluate own responses
2. Self-Refinement: ${\tau }_{\varphi }(\hat{r}|p,r,f)$ — optimize based on feedback

Arora (Talk) — Introspective Meta-skills

• Ability to recognize and classify own skill usage
• Naming and organizing skill taxonomies

In This Project

Types of Meta-skills

Type	Operation	Structure Used
Decomposition (${\mathcal{M}}_d$)	Break skills into parts	Mereological
Composition (${\mathcal{M}}_c$)	Combine skills	Algebraic
Analysis (${\mathcal{M}}_a$)	Evaluate task-skill fit	Fitness function

Formal Definition

$\mathcal{M}:2^{\mathcal{S}}\times 2^{\mathcal{S}}\times \mathcal{K}\to 2^{\mathcal{S}}$

Meta-skills as higher-order functions on skill sets, with context $\mathcal{K}$.

Key Distinctions

• Compositional meta-skills (Fan) — Operators for combining
• Procedural meta-skills (SELF) — Evaluation/refinement loops
• Introspective meta-skills (Arora) — Self-classification

Related Concepts

• skills — The objects meta-skills operate on
• composition — What compositional meta-skills do
• skills-algebra — Formal framework including meta-skills

References

• Literature Overview and Meta-Analysis
• Clarifying “Algebra of Skills Ontology”