# Navigating High Dimensional Concept Space with Metalearning

arXiv: https://arxiv.org/abs/2508.01948 · HTML: https://mlsanity.com/paper/2508.01948/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 17 references that are in the map.
- First posted on arXiv 28 Jul 2025.

## Builds on (most cited first, 6 of 6)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [Meta-Learning to Compositionally Generalize](https://mlsanity.com/paper/2106.04252/) (2021)
- [CURI: A Benchmark for Productive Concept Learning Under Uncertainty](https://mlsanity.com/paper/2010.02855/) (2020)
- [MAML is a Noisy Contrastive Learner in Classification](https://mlsanity.com/paper/2106.15367/) (2021)

## Abstract (arXiv)

Rapidly learning abstract concepts from limited examples is a hallmark of human intelligence. This work investigates whether gradient-based meta-learning can equip neural networks with inductive biases for efficient few-shot acquisition of discrete concepts. I compare meta-learning methods against a supervised learning baseline on Boolean concepts (logical statements) generated by a probabilistic context-free grammar (PCFG). By systematically varying concept dimensionality (number of features) and recursive compositionality (depth of grammar recursion), I delineate between complexity regimes in which meta-learning robustly improves few-shot concept learning and regimes in which it does not. Meta-learners are much better able to handle compositional complexity than featural complexity. I highlight some reasons for this with a representational analysis of the weights of meta-learners and a loss landscape analysis demonstrating how featural complexity increases the roughness of loss trajectories, allowing curvature-aware optimization to be more effective than first-order methods. I find improvements in out-of-distribution generalization on complex concepts by increasing the number of adaptation steps in meta-SGD, where adaptation acts as a way of encouraging exploration of rougher loss basins. Overall, this work highlights the intricacies of learning compositional versus featural complexity in high dimensional concept spaces and provides a road to understanding the role of 2nd order methods and extended gradient adaptation in few-shot concept learning.