year: 2025/09
paper: https://arxiv.org/pdf/2509.11131
website:
code:
connections: Benedikt Hartl, michael levin
The concept of embedding spaces for morphogenetic processes was introduced through the NCA Manifold framework [52], enabling the representation of different developmental trajectories in structured latent spaces. Tesfaldet et al. incorporated self-attention mechanisms directly into the cellular update rules, allowing individual cells to selectively focus on relevant neighborhood features [53]. Information-theoretic principles were integrated into NCA design (2022), by introducing empowerment as an auxiliary objective function to encourage coordinated cellular behaviors that enhance system robustness and adaptability [54, 55]. The stochastic modeling of emergent dynamics was advanced by Palm et al. through their Variational Neural Cellular Automata framework, which employs variational inference to capture the probabilistic nature of pattern formation processes [56]. Multi-scale emergent phenomena were developed by Pande and Grattarola (2023), who proposed hierarchical NCA architectures capable of systematically modeling intercellular behaviors across different levels of resolution of hierarchically stacked NCAs [11].
Limiatations / Future work required
NCAs can still be difficult to train, as solutions can collapse into trivial attractors (especially with gradient-based methods via pool-poisoning) or get trapped in suboptimal solutions that lack feature precision (predominantly in the case of neuroevolution training).
They suffer from limitations in storage capacity (of multiple system-level target outcomes, or functional modalities) and in scaling; simulating realistic organ-level complexity at unicellular resolutions is currently infeasible.
Relations of NCAs with reinforcement learning, active inference, or neuroevolution techniques remain underexplored. Moreover, their descriptive power, especially of biological systems, is still largely oversimplified: NCAs treat cells largely as homogeneous units and their numerical states and interactions are at best abstractions (or model composites) of most biological processes. And while progress has been made, it is difficult to integrate (and identify) NCA dynamics with molecular pathways, gene regulatory networks, or biomechanical forces.
Training NCAs is mostly concerned with the accuracy of the final system-level outcomes, largely neglecting energetic, metabolic, or other physical/chemical/biological constraints necessary for developing viable morphologies; the learned update rules are still largely opaque black-boxes and difficult to interpret at the parameter and interaction level; update dynamics don’t follow physical or biologically relevant ODEs; it is unclear how to implement reasonable multiscale coupling principles in HNCAs; in robotics, real-world experimental realization are in their infancies; and improving our theoretical understanding in stability, conditional dynamics, universality, criticality, and hierarchical phase-transitions still requires significant effort.
stopped min 27:40
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