High-Order Deep Meta-Learning with Category-Theoretic Interpretation

TL;DR

This paper presents a hierarchical deep meta-learning framework that uses category theory to generate virtual tasks, enabling neural networks to learn across task hierarchies and improve generalisation without solely relying on human data.

Contribution

It introduces a novel hierarchical meta-learning approach with a category-theoretic interpretation, allowing autonomous task generation and structured knowledge transfer.

Findings

Framework generates synthetic tasks to improve learning

Meta-learner refines constraints through active exploration

Category theory unifies and guides meta-learning design

Abstract

We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative mechanism that creates \emph{virtual tasks} -- synthetic problem instances designed to enable the meta-learner to learn \emph{soft constraints} and unknown generalisable rules across related tasks. Crucially, this enables the framework to generate its own informative, task-grounded datasets thereby freeing machine learning (ML) training from the limitations of relying entirely on human-generated data. By actively exploring the virtual point landscape and seeking out tasks lower-level learners find difficult, the meta-learner iteratively refines constraint regions. This enhances inductive biases, regularises the adaptation process, and produces novel, unanticipated tasks and constraints required for generalisation. Each meta-level of the hierarchy corresponds to a progressively abstracted generalisation of problems solved at lower levels, enabling a structured and interpretable learning progression. By interpreting meta-learners as category-theoretic \emph{functors} that generate and condition a hierarchy of subordinate learners, we establish a compositional structure that supports abstraction and knowledge transfer across progressively generalised tasks. The category-theoretic perspective unifies existing meta-learning models and reveals how learning processes can be transformed and compared through functorial relationships, while offering practical design principles for structuring meta-learning. We speculate this architecture may underpin the next generation of NNs capable of autonomously generating novel, instructive tasks and their solutions, thereby advancing ML towards general artificial intelligence.