Solving Inverse Problems in Stochastic Self-Organising Systems through Invariant Representations

Self-organising systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organisation central to understanding natural complexity. A fundamental challenge in modelling such systems is solving the inverse problem: finding the unknown causal parameters from macroscopic observations. This task becomes particularly difficult when observations have a strong stochastic component, yielding diverse yet equivalent patterns. Traditional inverse methods fail in this setting, as pixel-wise metrics cannot capture feature similarities between variable outcomes. In this work, we introduce a novel inverse modelling method specifically designed to handle stochasticity in the observable space, leveraging the capacity of visual embeddings to produce robust representations that capture perceptual invariances. By mapping the pattern representations onto an invariant embedding space, we can effectively recover unknown causal parameters without the need for handcrafted objective functions or heuristics. We evaluate the method on two canonical models--a reaction-diffusion system and an agent-based model of social segregation--and show that it reliably recovers parameters despite stochasticity in the outcomes. We further apply the method to real biological patterns, highlighting its potential as a tool for both theorists and experimentalists to investigate the dynamics underlying complex stochastic pattern formation.

Spectral Theory for Edge Pruning in Asynchronous Recurrent Graph Neural Networks

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning on graph-structured data, finding applications in numerous domains including social network analysis and molecular biology. Within this broad category, Asynchronous Recurrent Graph Neural Networks (ARGNNs) stand out for their ability to capture complex dependencies in dynamic graphs, resembling living organisms' intricate and adaptive nature. However, their complexity often leads to large and computationally expensive models. Therefore, pruning unnecessary edges becomes crucial for enhancing efficiency without significantly compromising performance. This paper presents a dynamic pruning method based on graph spectral theory, leveraging the imaginary component of the eigenvalues of the network graph's Laplacian.

Neural Cellular Automata for Decentralized Sensing using a Soft Inductive Sensor Array for Distributed Manipulator Systems

In Distributed Manipulator Systems (DMS), decentralization is a highly desirable property as it promotes robustness and facilitates scalability by distributing computational burden and eliminating singular points of failure. However, current DMS typically utilize a centralized approach to sensing, such as single-camera computer vision systems. This centralization poses a risk to system reliability and offers a significant limiting factor to system size. In this work, we introduce a decentralized approach for sensing and in a Distributed Manipulator Systems using Neural Cellular Automata (NCA). Demonstrating a decentralized sensing in a hardware implementation, we present a novel inductive sensor board designed for distributed sensing and evaluate its ability to estimate global object properties, such as the geometric center, through local interactions and computations. Experiments demonstrate that NCA-based sensing networks accurately estimate object position at 0.24 times the inter sensor distance. They maintain resilience under sensor faults and noise, and scale seamlessly across varying network sizes. These findings underscore the potential of local, decentralized computations to enable scalable, fault-tolerant, and noise-resilient object property estimation in DMS