BraiNCA: brain-inspired neural cellular automata and applications to morphogenesis and motor control
Authors: Léo Pio-Lopez, Benedikt Hartl, Michael Levin
Organizations: Allen Discovery Center at Tufts University, Medford, MA, USA · Wyss Institute for Biologically Inspired Engineering at Harvard University, Boston, MA, USA
Most of the Neural Cellular Automata (NCAs) defined in the literature have a common theme: they are based on regular grids with a Moore neighborhood (one-hop neighbour). They do not take into account long-range connections and more complex topologies as we can find in the brain. In this paper, we introduce BraiNCA, a brain-inspired NCA with an attention layer, long-range connections and complex topology. BraiNCAs shows better results in terms of robustness and speed of learning on the two tasks compared to Vanilla NCAs establishing that incorporating attention-based message selection together with explicit long-range edges can yield more sample-efficient and damage-tolerant self-organization than purely local, grid-based update rules. These results support the hypothesis that, for tasks requiring distributed coordination over extended spatial and temporal scales, the choice of interaction topology and the ability to dynamically route information will impact the robustness and speed of learning of an NCA. More broadly, BraiNCA provides brain-inspired NCA formulation that preserves the decentralized local update principle while better reflecting non-local connectivity patterns, making it a promising substrate for studying collective computation under biologically-realistic network structure and evolving cognitive substrates.
Figures & tables
Figure 1: Schematic illustration of the BraiNCA model. Every cell i not only integrates its local neighborhood Ni via attention, but also long-range signals from sparsely connected distant cells j,k∈Li for recurrent state updates. Flexible topologies are allowed, departing from NCAs with regular, e.g., square grid-layouts.
Figure 2: Flow-diagram of the BraiNCA architecture. Each cell’s state is updated by aggregating information from both local and long-range neighborhoods through attention-based context encoding. The combined signals are processed via a recurrent update function (GRU + MLP), enabling spatially distributed coordination in morphogenesis experiments and sensory-motor control of RL agents.
Figure 3: Morphogenesis conditions . Left: target pattern and cell labeling for the 3×3 neighborhood condition. Middle: target pattern for the 5×5 neighborhood condition. Right: example of long-range connections used in long-range variants. We made it sparse to mimic scale-free networks connectivity as we can find in the brain.
Figure 4: LunarLander connectivity schematics for the four conditions . Vanilla: 16 × 16 grid with quadrant action regions (NOOP/LEFT/MAIN/RIGHT). Vanilla+LR: same grid with additional long-range links under the selected long-range architecture. T-Shape: 24 × 16 grid with four active 8 × 8 zones in a T-shape. T-Shape+LR: same topology with patch-based cross-zone long-range messaging. Dots indicate individual cells in action regions (shaded blocks .
Figure 5: Long-range connections and size of neighborhood integration increase accuracy and speed of learning . A) Violin plots of the episodes to successes in the different conditions (3 × 3 Vanilla, 3 × 3 Long-Range, 5 × 5 Vanilla, and 5 × 5 Long-Range). B) Mean episodes to success in the different conditions. C) Relative speedup compared to the baseline (3 × 3 Vanilla).
Figure 6: Somatotopy increase robustness and speed of learning to the task . Left. Success rate in the different conditions (Vanilla, Long-Range with quadrant-patch connections, and T-Shape topology). Right. Mean survival time in the different conditions. *: p<0.05 , **: p<0.01 , ***: p<0.001
As Neural Cellular Automata (NCAs) are increasingly applied outside of the toy models in Artificial Life, there is a pressing need to understand how they behave and to build appropriate routes to interpret what they have learnt. By their very nature, the benefits of training NCAs are balanced with a lack of interpretability: we can engineer emergent behaviour, but have limited ability to understand what has been learnt. In this paper, we apply a variety of techniques to pry open the NCA black box and glean some understanding of what it has learnt to do. We apply techniques from manifold learning (principal components analysis and both dense and sparse autoencoders) along with techniques from topological data analysis (persistent homology) to capture the NCA's underlying behavioural manifold, with varying success. Results show that when analysis is performed at a macroscopic level (i.e. taking the entire NCA state as a single data point), the underlying manifold is often quite simple and can be captured and analysed quite well. When analysis is performed at a microscopic level (i.e. taking the state of individual cells as a single data point), the manifold is highly complex and more complicated techniques are required in order to make sense of it.
James Stovold, Mia-Katrin Kvalsund, Harald Michael Ludwig +2
University of York, UK · University of Oslo, Norway · Machine Learning Research Unit, TU Wien, Austria +2
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.
Meet Barot, Daniel Berenberg, Sina Khajehabdollahi
Mythos Scientific, New York, USA · Independent Scholar
Modern AI architectures used to solve visual reasoning tasks typically rely heavily on global connectivity and synchronization. As biological systems demonstrate, though, sophisticated computation can be performed in a more decentralized fashion. In this work, we test the reasoning capabilities of Neural Cellular Automata (NCAs), networks of recurrent cells that use strictly local connectivity and asynchronous updates. NCAs have been extensively studied in artificial life experiments, but it is unclear whether they can perform complex multi-step reasoning. We show that NCAs produce spatio-temporal dynamics capable of solving challenging visual reasoning tasks, including large mazes, Sudoku, and ARC-AGI-1. Furthermore, we provide evidence that NCAs generalize out-of-distribution when running with larger grids, longer rollouts, or parallel trials; and that the latter can be made more efficient via pruning of redundant trajectories. We find that these generalization capabilities depend on training with sample replay and stochastic perturbations, and that stochasticity remains beneficial at test time. Finally, we show that NCAs are robust reasoners capable of dynamically modulating compute to recover efficiently from damage, and that they can scale to solve reasoning in raw pixel space.
Mayalen Etcheverry, Pietro Miotti, Aidan Sirbu +7
Google Paradigms of Intelligence Team · School of Computer Science, McGill University · Mila - Quebec AI Institute +4