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

Etienne Guichard; Stefano Nichele

cs.LGOct 6, 2026

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

Authors: Etienne Guichard, Stefano Nichele

Organizations: Department of Computer Science and Communication hiof.no

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.

Figures & tables

Figure 1 : The MetaLearnNCA interaction loop: Active-NCA computes forward task predictions on the support set, while Meta-NCA translates the residual error maps into an updated spatial program $\mathbf{S}_{\text{task}}$ .

		Gradient-Free Baselines			Gradient-Based	Ours
Dataset	Shot	MatchingNet	RelationNet	ProtoNet	FOMAML	MetaLearnNCA
Omniglot (In-Dist)	1	$63.47\pm 7.79$	$84.84\pm 3.74$	$\mathbf{92.26\pm 3.15}$	$87.84\pm 3.67$	$87.95\pm 4.16$
	5	$75.47\pm 4.54$	$92.73\pm 3.09$	$96.40\pm 3.09$	$\mathbf{96.93\pm 1.41}$	$95.20\pm 2.13$
	10	$77.40\pm 6.37$	$93.20\pm 2.65$	$97.40\pm 1.27$	$\mathbf{98.80\pm 0.94}$	$96.12\pm 0.70$
MNIST	1	$44.79\pm 4.93$	$51.17\pm 2.66$	$55.32\pm 1.87$	$48.16\pm 2.98$	$\mathbf{65.02\pm 3.07}$
	5	$58.93\pm 1.34$	$63.74\pm 1.39$	$75.17\pm 1.56$	$70.80\pm 1.72$	$\mathbf{84.12\pm 1.57}$

Table 1 : Few-shot adaptation performance (Accuracy %

\pm

95% CI) across 1-shot, 5-shot, and 10-shot regimes on in-domain Omniglot and cross-domain out-of-distribution transfer benchmarks. All models (except ours) employ the canonical Conv4 backbone on

28\times 28

inputs.

Figure 2 : Few-shot offline 10-shot adaptation trajectories of MetaLearnNCA evaluated on out-of-distribution character datasets across offline cellular optimization repeats ( $k\in\{0,\dots,5\}$ ). Solid curves depict mean accuracy across 42 independent meta-training runs and 42 independent testing seeds, with shaded regions denoting 95% confidence intervals.

Figure 3 : Resilience of MetaLearnNCA to physical spatial damage: test accuracy as a function of circular noise patches ( $r=4\text{ px}$ ) injected into the static program grid $S_{\text{task}}$ .

Figure 4 : Representative spatial and program channels during MNIST inference. (see Appendix C for the complete 46-channel atlas).

Appendix figures & tables12 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5 : Theoretical overview of the conditioning mechanism: the static spatial program $\mathbf{S}$ acts as a localized pre-activation bias, dynamically modulating information flow through the Active-NCA transition operator.

Figure 6 : Complete atlas of Active-NCA dynamic reasoning channels (Channels 10 through 31) during MNIST inference.

Figure 7 : Complete atlas of static spatial program channels ( $S_{\text{task}}$ , Channels 0 through 23) written by the Meta-NCA following support adaptation.

Panel of Figure 8 — Figure 8 : Ablation analysis on Omniglot: (a) test accuracy under Gaussian noise injection across dynamic reasoning channels ( $10\dots 31$ ), and (b) test accuracy when individual static program channels ( $0\dots 23$ ) are ablated to zero.

Figure 9 : Difference in $S_{task}$ across 2 independent testing runs on the same training seed

Figure 10 : MetaLearnNCA performance on MNIST under different levels of additive random noise to $S_{task}$ .

Figure 11 : MetaLearnNCA $S_{task}$ under different levels of noise.

Figure 12 : Cross dataset transfer, each model is trained on one dataset and tested on all the other ones. 50 repeats per dataset with 95% CI intervals.

Figure 13 : Dataset surfaces for seed 0, trained on OMNIGLOT across a combination of K-repeats and K-shots.

Dataset	Shift = 1 px	Shift = 2 px	Shift = 3 px	Shift = 4 px
Omniglot (In-Dist)	$93.47\pm 4.51\%$	$90.93\pm 4.56\%$	$83.33\pm 4.86\%$	$70.13\pm 8.81\%$
MNIST	$84.43\pm 1.41\%$	$82.93\pm 2.62\%$	$77.13\pm 2.86\%$	$59.01\pm 3.37\%$
USPS	$57.89\pm 7.27\%$	$51.67\pm 6.85\%$	$40.71\pm 5.31\%$	$30.83\pm 2.51\%$
Fashion-MNIST	$48.72\pm 4.56\%$	$42.85\pm 4.01\%$	$34.03\pm 5.16\%$	$24.72\pm 4.66\%$
KMNIST	$41.70\pm 3.88\%$	$37.47\pm 4.02\%$	$30.50\pm 3.55\%$	$22.73\pm 3.75\%$
MedMNIST	$18.55\pm 8.05\%$	$17.23\pm 7.92\%$	$14.98\pm 6.98\%$	$13.00\pm 5.90\%$

Appendix

Table 2 : Robustness of MetaLearnNCA to discrete spatial coordinate shifts (

\Delta\in\{1,2,3,4\}

pixels) in the 5-shot, 10-way transfer regime. Results report mean classification accuracy

\pm

95% confidence intervals evaluated over 5 independent testing runs on full test splits.

Hyperparameter	ProtoNet	MatchingNet	RelationNet	FOMAML
Backbone	Conv4-64	Conv4-64	Conv4-64	Conv4-64
Parameters	$\approx 115\text{k}$	$\approx 115\text{k}$	$\approx 225\text{k}$	$\approx 115\text{k}$
Output Head	Metric Centroid	Cosine Attention	Relation MLP	Linear ( $64\to 10$ )
BatchNorm Stats	Frozen Running	Frozen Running	Frozen Running	Shuffled Mini-Batch
Meta-Loss	Cross-Entropy	Neg. Log-Likelihood	Mean Squared Error	Cross-Entropy
Inner Steps ( $K_{\text{train}}/K_{\text{test}}$ )	–	–	–	3 / 5

Appendix

Table 3 : Architectural and optimization hyperparameters for canonical baselines.

Dataset	Domain	Transform Pipeline
Omniglot	Sparse Characters (In-Dist)	$\operatorname{Resize}(28)\to\operatorname{ToTensor}()\to\text{Invert }(1.0-x)\to\operatorname{Normalize}(0.5,0.5)$
MNIST / KMNIST / USPS	Digits / Calligraphy (OOD)	$\operatorname{Resize}(28)\to\operatorname{ToTensor}()\to\operatorname{Normalize}(0.5,0.5)$
Fashion / MedMNIST	Silhouettes / CT Organs (OOD)	$\operatorname{Resize}(28)()\to\operatorname{ToTensor}()\to\operatorname{Normalize}(0.5,0.5)$

Appendix

Table 4 : Dataset preprocessing and normalization pipelines (

28\times 28

grayscale).

Explore similar work

Architecture Generalization with MetaNCA
Jul 8, 2026Meet Barot, Daniel Berenberg, Sina KhajehabdollahiNeural Cellular Automata Brain-Inspired Synergistic Framework
Mythos Scientific, New York, USA · Independent Scholar
Online Task Adaptation via Self-Organisation
Sep 24, 2026Krsto ProrokovićEfficient Task Adaptation Neural Cellular Automata
Independent Researcher Montenegro
2D Spatial Reasoning with Adaptive Neural Cellular Automata
Oct 6, 2026Martin Spitznagel, Janis KeuperNeural Cellular Automata
Institute for Machine Learning and Analytics (IMLA), Offenburg University, Germany · University of Mannheim, Germany

Jul 8, 2026, cs.LGJ/K move · Enter open · S save

Architecture Generalization with MetaNCA

Meet Barot, Daniel Berenberg, Sina Khajehabdollahi

Mythos Scientific, New York, USA · Independent Scholar

Neural Cellular Automata Brain-Inspired Synergistic Framework Emergence Morphogenesis

Open paper AskPDF arXiv

Self-organization is an emergent property of life, driven by the collective behavior of individual components acting on local information. Biological neurons, through local interactions transmitted through synapses, are able to learn efficiently and can adapt their connections over an organism's lifespan. Motivated by these desirable properties of adaptability and local interaction, neural cellular automata (NCA) models have been successful at learning morphogenesis solely through local update rules, demonstrating stability over many updates and robustness to perturbations. In this work, we introduce Meta Neural Cellular Automata (MetaNCA), a framework that learns local rules which self-organize the weights of artificial neural networks. A learned rule network iteratively updates the weights of a task network using only local interactions on the computation graph. We propose a novel Weight Transformer architecture for the local rule network, which uses linear attention to aggregate signals from neighboring weights and hidden states. Once trained, the rule network generates task networks of diverse architectures without backpropagation. We show that MetaNCA generates weights for feedforward MLPs, CNNs, and ResNets on MNIST and CIFAR-100, scaling to networks of 2 million parameters. We further show that MetaNCA generalizes to architectures not seen during meta-training, and that architectural diversity in the training phase strengthens this generalization.

Abstract

Explore similar work

Architecture Generalization with MetaNCA

Online Task Adaptation via Self-Organisation

2D Spatial Reasoning with Adaptive Neural Cellular Automata