Growing Steerable Neural Cellular Automata

TL;DR

This paper introduces Steerable Neural Cellular Automata, enabling cells to control their orientation, which enhances pattern formation and symmetry properties, and simplifies training compared to isotropic variants.

Contribution

The paper presents a novel Steerable NCA model where cells can adjust their orientation, offering new capabilities and simpler training methods over previous isotropic NCA models.

Findings

Steerable NCA exhibits chirality and left-right symmetry.

Training can be simplified using symmetry-breaking seeds.

Rotation-invariant training with asynchronous updates is effective.

Abstract

Neural Cellular Automata (NCA) models have shown remarkable capacity for pattern formation and complex global behaviors stemming from local coordination. However, in the original implementation of NCA, cells are incapable of adjusting their own orientation, and it is the responsibility of the model designer to orient them externally. A recent isotropic variant of NCA (Growing Isotropic Neural Cellular Automata) makes the model orientation-independent - cells can no longer tell up from down, nor left from right - by removing its dependency on perceiving the gradient of spatial states in its neighborhood. In this work, we revisit NCA with a different approach: we make each cell responsible for its own orientation by allowing it to "turn" as determined by an adjustable internal state. The resulting Steerable NCA contains cells of varying orientation embedded in the same pattern. We observe how, while Isotropic NCA are orientation-agnostic, Steerable NCA have chirality: they have a predetermined left-right symmetry. We therefore show that we can train Steerable NCA in similar but simpler ways than their Isotropic variant by: (1) breaking symmetries using only two seeds, or (2) introducing a rotation-invariant training objective and relying on asynchronous cell updates to break the up-down symmetry of the system.