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Conditional Morphogenesis: Emergent Generation of Structural Digits via Neural Cellular Automata

Ali Sakour

TL;DR

This work tackles conditional structural generation with neural cellular automata by introducing a Conditional NCA (c-NCA) that grows MNIST digits from a single seed using a persistent, spatially broadcast class vector. It enforces locality and translation equivariance through a learnable perception and a stochastic, 1×1 update policy, enabling a single rule set to realize ten distinct digit topologies with high fidelity and robustness. Empirical results show strong discriminative validity (96.3% accuracy by an external classifier), notable structural stability and self-repair under degradation, and remarkable parameter efficiency (≈10k parameters) compared to traditional generators. The findings advance biologically plausible, decentralized generative AI and open pathways to scalable conditional morphogenesis on richer datasets.

Abstract

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.

Conditional Morphogenesis: Emergent Generation of Structural Digits via Neural Cellular Automata

TL;DR

This work tackles conditional structural generation with neural cellular automata by introducing a Conditional NCA (c-NCA) that grows MNIST digits from a single seed using a persistent, spatially broadcast class vector. It enforces locality and translation equivariance through a learnable perception and a stochastic, 1×1 update policy, enabling a single rule set to realize ten distinct digit topologies with high fidelity and robustness. Empirical results show strong discriminative validity (96.3% accuracy by an external classifier), notable structural stability and self-repair under degradation, and remarkable parameter efficiency (≈10k parameters) compared to traditional generators. The findings advance biologically plausible, decentralized generative AI and open pathways to scalable conditional morphogenesis on richer datasets.

Abstract

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.

Paper Structure

This paper contains 24 sections, 5 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Neural Cellular Automata (NCA)
  4. Conditional Generative Models
  5. Structural Morphogenesis vs. Texture Synthesis
  6. Conditional Control Mechanisms in NCA
  7. Advanced Conditional and Adaptive NCAs
  8. Methodology
  9. State Space Representation
  10. Learnable Perception
  11. Conditional Control Mechanism
  12. Stochastic Update Policy
  13. Living Mask and Loss Function
  14. Experimental Setup
  15. Dataset and Preprocessing
  16. ...and 9 more sections

Figures (5)

  • Figure 1: Architecture of the Conditional Neural Cellular Automata (c-NCA). The class-conditional vector $\mathbf{c}$ is injected into the local perception loop, guiding the update dynamics.
  • Figure 2: Complete morphogenetic evolution of MNIST digits. All digits originate from the same generic seed. The condition vector guides the cellular automata to diverge into distinct topological attractors by Step 64.
  • Figure 3: Recovery from 50% stochastic pixel dropout. The middle column depicts the state immediately after damage. The right column shows the successful reconstruction after 48 steps.
  • Figure 4: Confusion Matrix of the c-NCA model. The strong diagonal indicates high accuracy. The specific off-diagonal cluster (Row '1', Column '8') highlights the structural over-growth artifact discussed in the error analysis.
  • Figure 5: Ablation study on the update rule. Top: Standard stochastic update ($p=0.5$) results in sharp topology. Bottom: Deterministic update ($p=1.0$) leads to blurred edges and synchronization artifacts.