MetaLearnNCA: Few-Shot Offline Meta-Learning via Interacting Neural Cellular Automata

2026-10-06

AI Summary

This study addresses the high computational cost of gradient backpropagation in few-shot meta-learning and the susceptibility to geometric information loss in two-dimensional spaces. To overcome these limitations, this work proposes a decentralized neural cellular automata framework built upon a non-von Neumann substrate. By coupling dynamic cellular interactions with a spatial procedural memory grid, the approach achieves gradient-free inference for task adaptation, further enhanced by a local error residual diffusion mechanism that improves learning robustness. This research presents the first utilization of decentralized cellular dynamics to realize gradient-free learning strategies. Empirical evaluations demonstrate that the proposed method attains 96.12% accuracy on the Omniglot benchmark, with cross-dataset transfer performance significantly surpassing that of Prototypical Networks and FOMAML.

Abstract

Few-shot meta-learning traditionally formulates task adaptation either as analytical gradient descent through unrolled computational graphs or as metric-based distance comparisons over flattened 1D fea- ture vectors, which either incur costly test-time backpropagation or discard native 2D spatial geometry. In this work, we propose METALEARNNCA, a decentralized framework that achieves few-shot adapta- tion through the dynamical interaction of coupled Neural Cellular Automata (NCAs) without computing analytical gradients during inference. MetaLearnNCA decomposes task adaptation into an Active- NCA, which executes task inference conditioned on a continuous 2D spatial memory grid termed the spatial program, and a learned Meta-NCA, which acts as a decentralized cellular optimizer by diffusing spatial error residuals across local neighborhoods to dynamically update this program. METALEARN- NCA is competitive against canonical meta-learners in-distribution (96.12% on Omniglot) with Out-Of- Distribution transfer gains on MNIST, KMNIST, and Fashion-MNIST transfer across 10 independent testing seeds across 1-, 5-, and 10-shot regimes (e.g., surpassing Prototypical Networks by +10.54% on 10-shot MNIST and a +3.87% gain on 10-shot Fashion-MNIST over FOMAML). Our results establish that robust, gradient-free learning-to-learn can emerge from decentralized cellular dynamics on non-von Neumann substrates.

Problem

• Few-shot meta-learning
• Task adaptation
• Test-time backpropagation
• 2D spatial geometry
• Gradient-free learning

Innovation

• Neural Cellular Automata
• Few-Shot Meta-Learning
• Gradient-Free Learning
• Decentralized Optimization
• Spatial Program