How does this integrate with other AI workflows?

It serves as a foundational layer for compositional architecture, providing the framework for other high-level AI tasks and formal verification processes.

What mathematical foundations does this skill use?

It is based on established category theory principles from works by Mac Lane, Fong & Spivak, and modern research in category theory for machine learning.

What is the primary focus of the Categorical Composition skill?

It focuses on providing mathematical frameworks like Kan extensions and adjunctions to build modular and adaptable AI systems through category theory.

Which programming language is supported?

The current implementation examples and primitives are designed for the Julia programming language, focused on categorical computation.

Can this skill help with model generalization?

Yes, it uses functorial parameter transfer and categorical reasoning to facilitate compositional and zero-shot generalization across different parameter spaces.

Categorical Composition Architecture

Name: Categorical Composition Architecture
Author: plurigrid

byplurigrid

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データサイエンスとML

Implements mathematical category theory abstractions to enable compositional learning and structured parameter transfer in AI models.

This skill provides a foundational framework for building complex AI systems from simpler components using rigorous category theory principles. It enables developers to apply Kan extensions for problem adaptation, utilize adjoint functors for bidirectional transformations, and execute functorial parameter transfer to preserve structural integrity across neural network architectures. By formalizing compositional generalization, it helps researchers and engineers create more modular, adaptable, and theoretically grounded machine learning models using advanced mathematical primitives.

主な機能

017 GitHub stars

02Facilitates functorial parameter transfer to preserve structure across spaces

03Provides adjoint functor pairs for seamless bidirectional transformations

04Offers category theory primitives including functors and natural transformations

05Implements Left and Right Kan extensions for automated problem adaptation

06Supports verification of triangle identities and adjunction laws

ユースケース

01Adapting pre-trained models to new task domains using Kan extensions

02Building modular neural network architectures with guaranteed structural preservation

03Formalizing zero-shot generalization through categorical reasoning and parameter transfer

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi categorical-composition

For use in Claude.ai and ChatGPT

Download Skill