Artificial Theory of Mind and Self-Guided Social Organisation

One of the challenges artificial intelligence (AI) faces is how a collection of agents coordinate their behaviour to achieve goals that are not reachable by any single agent. In a recent article by Ozmen et al this was framed as one of six grand challenges: That AI needs to respect human cognitive processes at the human-AI interaction frontier. We suggest that this extends to the AI-AI frontier and that it should also reflect human psychology, as it is the only successful framework we have from which to build out. In this extended abstract we first make the case for collective intelligence in a general setting, drawing on recent work from single neuron complexity in neural networks and ant network adaptability in ant colonies. From there we introduce how species relate to one another in an ecological network via niche selection, niche choice, and niche conformity with the aim of forming an analogy with human social network development as new agents join together and coordinate. From there we show how our social structures are influenced by our neuro-physiology, our psychology, and our language. This emphasises how individual people within a social network influence the structure and performance of that network in complex tasks, and that cognitive faculties such as Theory of Mind play a central role. We finish by discussing the current state of the art in AI and where there is potential for further development of a socially embodied collective artificial intelligence that is capable of guiding its own social structures.

Theory of Mind Enhances Collective Intelligence

Collective Intelligence plays a central role in a large variety of fields, from economics and evolutionary theory to neural networks and eusocial insects, and it is also core to much of the work on emergence and self-organisation in complex systems theory. However, in human collective intelligence there is still much more to be understood in the relationship between specific psychological processes at the individual level and the emergence of self-organised structures at the social level. Previously psychological factors have played a relatively minor role in the study of collective intelligence as the principles are often quite general and applicable to humans just as readily as insects or other agents without sophisticated psychologies. In this article we emphasise, with examples from other complex adaptive systems, the broad applicability of collective intelligence principles while the mechanisms and time-scales differ significantly between examples. We contend that flexible collective intelligence in human social settings is improved by our use of a specific cognitive tool: our Theory of Mind. We identify several key characteristics of psychologically mediated collective intelligence and show that the development of a Theory of Mind is a crucial factor distinguishing social collective intelligence from general collective intelligence. We then place these capabilities in the context of the next steps in artificial intelligence embedded in a future that includes an effective human-AI hybrid social ecology.

A Novel Use of Pseudospectra in Mathematical Biology: Understanding HPA Axis Sensitivity

The Hypothalamic-Pituitary-Adrenal (HPA) axis is a major neuroendocrine system, and its dysregulation is implicated in various diseases. This system also presents interesting mathematical challenges for modeling. We consider a nonlinear delay differential equation model and calculate pseudospectra of three different linearizations: a time-dependent Jacobian, linearization around the limit cycle, and dynamic mode decomposition (DMD) analysis of Koopman operators (global linearization). The time-dependent Jacobian provided insight into experimental phenomena, explaining why rats respond differently to perturbations during corticosterone secretion's upward versus downward slopes. We developed new mathematical techniques for the other two linearizations to calculate pseudospectra on Banach spaces and apply DMD to delay differential equations, respectively. These methods helped establish local and global limit cycle stability and study transients. Additionally, we discuss using pseudospectra to substantiate the model in experimental contexts and establish bio-variability via data-driven methods. This work is the first to utilize pseudospectra to explore the HPA axis.

Rigged Dynamic Mode Decomposition: Data-Driven Generalized Eigenfunction Decompositions for Koopman Operators

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex nonlinear dynamics into a linear framework suitable for spectral analysis. While powerful, traditional Dynamic Mode Decomposition (DMD) techniques often struggle with continuous spectra. Rigged DMD addresses these challenges with a data-driven methodology that approximates the Koopman operator's resolvent and its generalized eigenfunctions using snapshot data from the system's evolution. At its core, Rigged DMD builds wave-packet approximations for generalized Koopman eigenfunctions and modes by integrating Measure-Preserving Extended Dynamic Mode Decomposition with high-order kernels for smoothing. This provides a robust decomposition encompassing both discrete and continuous spectral elements. We derive explicit high-order convergence theorems for generalized eigenfunctions and spectral measures. Additionally, we propose a novel framework for constructing rigged Hilbert spaces using time-delay embedding, significantly extending the algorithm's applicability. We provide examples, including systems with a Lebesgue spectrum, integrable Hamiltonian systems, the Lorenz system, and a high-Reynolds number lid-driven flow in a two-dimensional square cavity, demonstrating Rigged DMD's convergence, efficiency, and versatility. This work paves the way for future research and applications of decompositions with continuous spectra.