On Growth and Form, and Function: Reusable Regulatory Handles Control Phenotypic Variation
cs.NE, cs.LG
Submitted: 2026-09-24
Updated: 2026-09-24
Project page: https://umu1729.github.io
License: http://creativecommons.org/licenses/by/4.0/
The gist: How phenotypic transformations are implemented by changes in underlying regulatory dynamics remains a central question in developmental biology.
Terminology
Abstract
How phenotypic transformations are implemented by changes in underlying regulatory dynamics remains a central question in developmental biology. Inspired by D'Arcy Thompson's 1917 "On Growth and Form", we ask whether coherent large-scale transformations of morphology can be encoded as low-dimensional modulations of a self-organizing developmental system. We use neural cellular automata (NCAs) as bio-inspired models of distributed development, in which a shared local regulatory network grows target morphologies from a single cell. We apply low-rank adaptation (LoRA) to pretrained NCAs, representing each adapted developmental program as a low-rank modulation of a fixed regulatory scaffold. Horizontal and vertical scaling of a fully grown 2D emoji phenotype can each be implemented by rank-one adaptations. Their linear combinations parametrically control phenotype size, generalize beyond the training distribution, and compose with target-specific adapters. Strikingly, adaptations learned for one phenotype transfer zero-shot across structurally and semantically diverse phenotypes sharing the same reference scaffold, while largely preserving internal features. This suggests reusable system-level hyper-directions of scale rather than morphology-specific transformations. From approximately 25,000 independently trained phenotype-specific NCA adapters with a shared scaffold, we further identify latent low-dimensional directions that functionally control phenotypic variation including scaling, style, and symmetrical fission. Together, our results provide a computational realization of D'Arcy Thompson's remarkable grid transformations in a 2D NCA---a minimal cybernetic tissue in which variations of fully grown emoji phenotypes can be encoded, combined, and controlled through low-dimensional directions in regulatory weight space.
Sources
- HyperNCA: Growing Developmental Networks with Neural Cellular Automata
- Questioning Representational Optimism in Deep Learning: The Fractured Entangled Representation Hypothesis
- Classifier-Free Diffusion Guidance
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