Metaskill (𝓜)

Formal Definition

A metaskill is a skill about skills - the ability to reason about, compose, and manipulate skills. Metaskills operate at a higher level of abstraction, taking skills as input and producing new or modified skills as output.

Formally, a metaskill is a function:

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

Where:

• $2^{\mathcal{S}}$ is the power set of skills (sets of skills)
• $\mathcal{K}$ represents composition constraints and domain knowledge

Types of Metaskills

The ontology defines five fundamental types of metaskills:

1. Composition Metaskills (${\mathcal{M}}_c$)

Creates new skills from existing ones: ${\mathcal{M}}_c({\mathcal{S}}_1,{\mathcal{S}}_2)\to {\mathcal{S}}_{new}$

Example: Combining “text analysis” and “code generation” skills to create “code documentation” skill.

2. Decomposition Metaskills (${\mathcal{M}}_d$)

Breaks complex skills into constituent subskills: ${\mathcal{M}}_d({\mathcal{S}}_{complex})\to \{{\mathcal{S}}_1,{\mathcal{S}}_2,\dots ,{\mathcal{S}}_n\}$

Example: Breaking down “full-stack development” into “frontend”, “backend”, and “database” skills.

3. Analysis Metaskills (${\mathcal{M}}_a$)

Evaluates skill effectiveness and relationships: ${\mathcal{M}}_a(\mathcal{S},\mathcal{T})\to [0,1]$

Example: Assessing how well a “translation” skill performs on specific language pairs.

4. Optimization Metaskills (${\mathcal{M}}_o$)

Improves existing skill combinations: ${\mathcal{M}}_o(\{{\mathcal{S}}_i\})\to \{{\mathcal{S}}_i^{\prime }\}$

Example: Refining a set of problem-solving skills to improve efficiency.

5. Abstraction Metaskills (${\mathcal{M}}_{ab}$)

Generalizes from specific skills to broader patterns: ${\mathcal{M}}_{ab}(\{{\mathcal{S}}_i\})\to {\mathcal{S}}_{general}$

Example: Abstracting from “Python debugging” and “JavaScript debugging” to “general debugging principles”.

Key Properties and Characteristics

1. Higher-Order Nature: Metaskills operate on skills rather than tasks
2. Closure: Metaskill operations produce valid skills
3. Composability: Metaskills can be composed with each other
4. Self-Application: Some metaskills can operate on other metaskills
5. Fixed Points: Optimal metaskills exist for task optimization (Theorem 3)

Research Context and Applications

Metaskills are crucial for autonomous skill development:

• Self-Improvement: Agents can develop new capabilities without external guidance
• Transfer Learning: Metaskills enable knowledge transfer across domains
• Adaptive Learning: Systems can adapt their skill sets to new challenges
• Meta-Learning: Learning to learn through metaskill development

In LLM applications:

• Prompt engineering as a composition metaskill
• Few-shot learning as an abstraction metaskill
• Chain-of-thought as a decomposition metaskill
• Self-critique as an analysis metaskill

Connections to Other Concepts

• Skills (𝒮): Metaskills operate on the skill space
• Composition Operator (∘): Implemented through composition metaskills
• Decomposition Operator (↓): Implemented through decomposition metaskills
• Fitness Functions (φ, Φ): Used by analysis metaskills
• Metaskill Fixed Points: Optimal metaskills for task performance
• Metaskill Application Operator (⊙): Applies metaskills to skills

Metaskill Application Operator

The operator $\odot$ applies a metaskill to a skill: ${\mathcal{M}}_i\odot {\mathcal{S}}_j={\mathcal{S}}^{\prime }\text{where}{\mathcal{S}}^{\prime }={\mathcal{M}}_i({\mathcal{S}}_j)$

Open Research Questions

1. Primitive Metaskills: What is the minimal complete set of primitive metaskills?
2. Metaskill Hierarchies: Do metaskills themselves form a hierarchical structure?
3. Self-Reference: Can metaskills improve themselves through self-application?
4. Convergence: Do metaskill applications converge to optimal skill configurations?
5. Computational Complexity: What is the complexity of metaskill operations?
6. Metaskill Learning: How can agents learn new metaskills autonomously?
7. Cross-Domain Transfer: How do metaskills transfer across different domains?