Vision Transformers (ViTs) demonstrate remarkable performance in image classification through visual-token interaction learning, particularly when equipped with local information via region attention or convolutions. Although such architectures improve the feature aggregation from different granularities, they often fail to contribute to the robustness of the networks. Neural Cellular Automata (NCA) enables the modeling of global visual-token representations through local interactions, with its training strategies and architecture design conferring strong generalization ability and robustness against noisy input. In this paper, we propose Adaptor Neural Cellular Automata (AdaNCA) for Vision Transformers that uses NCA as plug-and-play adaptors between ViT layers, thus enhancing ViT's performance and robustness against adversarial samples as well as out-of-distribution inputs. To overcome the large computational overhead of standard NCAs, we propose Dynamic Interaction for more efficient interaction learning. Using our analysis of AdaNCA placement and robustness improvement, we also develop an algorithm for identifying the most effective insertion points for AdaNCA. With less than a 3% increase in parameters, AdaNCA contributes to more than 10% absolute improvement in accuracy under adversarial attacks on the ImageNet1K benchmark. Moreover, we demonstrate with extensive evaluations across eight robustness benchmarks and four ViT architectures that AdaNCA, as a plug-and-play module, consistently improves the robustness of ViTs.

Neural Cellular Automata (NCAs) offer a way to study the growth of two-dimensional artificial organisms from a single seed cell. From the outset, NCA-grown organisms have had issues with stability, their natural boundary often breaking down and exhibiting tumour-like growth or failing to maintain the expected shape. In this paper, we present a method for improving the stability of NCA-grown organisms by introducing an 'identity' layer with simple constraints during training. Results show that NCAs grown in close proximity are more stable compared with the original NCA model. Moreover, only a single identity value is required to achieve this increase in stability. We observe emergent movement from the stable organisms, with increasing prevalence for models with multiple identity values. This work lays the foundation for further study of the interaction between NCA-grown organisms, paving the way for studying social interaction at a cellular level in artificial organisms. Code/Videos available at: https://github.com/jstovold/ALIFE2025

Biological systems exhibit remarkable morphogenetic plasticity, where a single genome can encode various specialized cellular structures triggered by local chemical signals. In the domain of Deep Learning, Differentiable Neural Cellular Automata (NCA) have emerged as a paradigm to mimic this self-organization. However, existing NCA research has predominantly focused on continuous texture synthesis or single-target object recovery, leaving the challenge of class-conditional structural generation largely unexplored. In this work, we propose a novel Conditional Neural Cellular Automata (c-NCA) architecture capable of growing distinct topological structures - specifically MNIST digits - from a single generic seed, guided solely by a spatially broadcasted class vector. Unlike traditional generative models (e.g., GANs, VAEs) that rely on global reception fields, our model enforces strict locality and translation equivariance. We demonstrate that by injecting a one-hot condition into the cellular perception field, a single set of local rules can learn to break symmetry and self-assemble into ten distinct geometric attractors. Experimental results show that our c-NCA achieves stable convergence, correctly forming digit topologies from a single pixel, and exhibits robustness characteristic of biological systems. This work bridges the gap between texture-based NCAs and structural pattern formation, offering a lightweight, biologically plausible alternative for conditional generation.

Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise transformations and few-shot generalization, using the Abstraction and Reasoning Corpus for Artificial General Intelligence (ARC-AGI) as a domain that challenges their capabilities in ways not previously explored. Specifically, this paper uses gradient-based training to learn iterative update rules that transform input grids into their outputs from the training examples and then applies them to the test inputs. Results suggest that gradient-trained NCA models are a promising and efficient approach to a range of abstract grid-based tasks from ARC. Along with discussing the impacts of various design modifications and training constraints, this work examines the behavior and properties of NCAs applied to ARC to give insights for broader applications of self-organizing systems.

This paper presents a rotation-invariant embedded platform for simulating (neural) cellular automata (NCA) in modular robotic systems. Inspired by previous work on physical NCA, we introduce key innovations that overcome limitations in prior hardware designs. Our platform features a symmetric, modular structure, enabling seamless connections between cells regardless of orientation. Additionally, each cell is battery-powered, allowing it to operate independently and retain its state even when disconnected from the collective. To demonstrate the platform's applicability, we present a novel rotation-invariant NCA model for isotropic shape classification. The proposed system provides a robust foundation for exploring the physical realization of NCA, with potential applications in distributed robotic systems and self-organizing structures.

Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive self-regulatory dynamics of living matter. By embedding Artificial Neural Networks (ANNs) as local decision-making centers and interaction rules between localized agents, NCA can simulate processes across molecular, cellular, tissue, and system-level scales, offering a multiscale competency architecture perspective on evolution, development, regeneration, aging, morphogenesis, and robotic control. These models not only reproduce biologically inspired target patterns but also generalize to novel conditions, demonstrating robustness to perturbations and the capacity for open-ended adaptation and reasoning. Given their immense success in recent developments, we here review current literature of NCAs that are relevant primarily for biological or bioengineering applications. Moreover, we emphasize that beyond biology, NCAs display robust and generalizing goal-directed dynamics without centralized control, e.g., in controlling or regenerating composite robotic morphologies or even on cutting-edge reasoning tasks such as ARC-AGI-1. In addition, the same principles of iterative state-refinement is reminiscent to modern generative Artificial Intelligence (AI), such as probabilistic diffusion models. Their governing self-regulatory behavior is constraint to fully localized interactions, yet their collective behavior scales into coordinated system-level outcomes. We thus argue that NCAs constitute a unifying computationally lean paradigm that not only bridges fundamental insights from multiscale biology with modern generative AI, but have the potential to design truly bio-inspired collective intelligence capable of hierarchical reasoning and control.

When working with tabular data, missingness is always one of the most painful problems. Throughout many years, researchers have continuously explored better and better ways to impute missing data. Recently, with the rapid development evolution in machine learning and deep learning, there is a new trend of leveraging generative models to solve the imputation task. While the imputing version of famous models such as V ariational Autoencoders or Generative Adversarial Networks were investigated, prior work has overlooked Neural Cellular Automata (NCA), a powerful computational model. In this paper, we propose a novel imputation method that is inspired by NCA. We show that, with some appropriate adaptations, an NCA-based model is able to address the missing data imputation problem. We also provide several experiments to evidence that our model outperforms state-of-the-art methods in terms of imputation error and post-imputation performance. Introduction There is no doubt that data plays a crucial role in this modern world. In numerous business and scientific applications, data is the foundation for decision-making process, enabling experts to detect noticeable patterns and take advantage of them. One of the most common types of data is tabular data, which presents in almost every domains from economics, finance to healthcare, demography. Being organized in structured rows and columns, one can straightforwardly apply statistical methods, perform calculations and draw meaningful insights from this data. Moreover, many machine learning algorithms, especially those used in supervised learning tasks, are designed to work optimally on tabular data.

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of real-world biological and physical systems. We propose the Mixture of Neural Cellular Automata (MNCA), a novel framework incorporating the idea of mixture models into the NCA paradigm. By combining probabilistic rule assignments with intrinsic noise, MNCAs can model diverse local behaviors and reproduce the stochastic dynamics observed in biological processes. We evaluate the effectiveness of MNCAs in three key domains: (1) synthetic simulations of tissue growth and differentiation, (2) image morphogenesis robustness, and (3) microscopy image segmentation. Results show that MNCAs achieve superior robustness to perturbations, better recapitulate real biological growth patterns, and provide interpretable rule segmentation. These findings position MNCAs as a promising tool for modeling stochastic dynamical systems and studying self-growth processes.

This paper introduces Differentiable Logic Cellular Automata (DiffLogic CA), a novel combination of Neural Cellular Automata (NCA) and Differentiable Logic Gates Networks (DLGNs). The fundamental computation units of the model are differentiable logic gates, combined into a circuit. During training, the model is fully end-to-end differentiable allowing gradient-based training, and at inference time it operates in a fully discrete state space. This enables learning local update rules for cellular automata while preserving their inherent discrete nature. We demonstrate the versatility of our approach through a series of milestones: (1) fully learning the rules of Conway's Game of Life, (2) generating checkerboard patterns that exhibit resilience to noise and damage, (3) growing a lizard shape, and (4) multi-color pattern generation. Our model successfully learns recurrent circuits capable of generating desired target patterns. For simpler patterns, we observe success with both synchronous and asynchronous updates, demonstrating significant generalization capabilities and robustness to perturbations. We make the case that this combination of DLGNs and NCA represents a step toward programmable matter and robust computing systems that combine binary logic, neural network adaptability, and localized processing. This work, to the best of our knowledge, is the first successful application of differentiable logic gate networks in recurrent architectures.

Vision Transformers (ViTs) demonstrate remarkable performance in image classification through visual-token interaction learning, particularly when equipped with local information via region attention or convolutions. Although such architectures improve the feature aggregation from different granularities, they often fail to contribute to the robustness of the networks. Neural Cellular Automata (NCA) enables the modeling of global visual-token representations through local interactions, with its training strategies and architecture design conferring strong generalization ability and robustness against noisy input. In this paper, we propose Adaptor Neural Cellular Automata (AdaNCA) for Vision Transformers that uses NCA as plug-and-play adaptors between ViT layers, thus enhancing ViT's performance and robustness against adversarial samples as well as out-of-distribution inputs. To overcome the large computational overhead of standard NCAs, we propose Dynamic Interaction for more efficient interaction learning.