Scalable mobile swarm network for reservoir computing using gaussian kernel density estimation

Swarm intelligence results from a collective behaviour of swarm network, which harnesses distributed and simple rules of swarm systems to address complex problems without a central controller. One potential approach to transform such swarm networks into valuable and practical computational resources is by applying the reservoir computing framework. However, technical challenges, such as permutation symmetry and instability, could emerge in these networks during the process, which significantly hinder the computational performance. In this paper, we explore the potential of mobile swarm networks in a reservoir computing framework to perform machine learning tasks. We propose an observation layer using Gaussian kernel density estimation to be inserted into the reservoir computing framework. Our approach not only addresses permutation symmetry but also stabilises swarm behaviours, resulting in a scalable swarm network. We explore variations in computational capacity across different swarm sizes and combinations with four benchmark computations. We prove the effectiveness of our observation layer in addressing permutation symmetry and discovered the improvement in performance in combining different swarm networks in parallel. We found that the best ratio between ants and birds reservoir is 8:2. The performance achieves a covariance of approximately 0.20 with a swarm size of 20, comparable to that of echo-state-network (ESN) with 16 nodes. As the swarm size increases to 60, the covariance value reaches around 0.21, matching the performance of ESN with 18 nodes. This indicates that our swarm network has a reasonable amount of memory and nonlinearly capacity in performing computation tasks. We also validate our method's effectiveness on a handwriting classification task, further highlighting its practical applicability. Our findings delve into the impacts of the swarm networks' computational abilities, offering insights into mechanisms in this alternative means of swarm intelligence and application to AI.