Emergent interactions lead to collective frustration in robotic matter

TL;DR

A paradigmatic model for robotic matter is studied: a stochastic many-particle system in which each particle is endowed with a deep neural network that predicts its transitions based on the particles' environments, which captures key features of more complex forms of robotic systems.

Abstract

Current artificial intelligence systems show near-human-level capabilities when deployed in isolation. Systems of a few collaborating intelligent agents are being engineered to perform tasks collectively. This raises the question of whether robotic matter, where many learning and intelligent agents interact, shows emergence of collective behaviour. And if so, which kind of phenomena would such systems exhibit? Here, we study a paradigmatic model for robotic matter: a stochastic many-particle system in which each particle is endowed with a deep neural network that predicts its transitions based on the particles' environments. For a one-dimensional model, we show that robotic matter exhibits complex emergent phenomena, including transitions between long-lived learning regimes, the emergence of particle species, and frustration. We also find a density-dependent phase transition with signatures of criticality. Using active matter theory, we show that this phase transition is a consequence of self-organisation mediated by emergent inter-particle interactions. Our simple model captures key features of more complex forms of robotic systems.

Figures (9)

• Figure 1: Figure 1. (a) Feedback between collective particle dynamics and the evolution of deep neural networks in stochastic many-particle systems driven by deep learning. (b) One-dimensional lattice gas implementation. (c) Numerical protocol of stochastic updating and learning.
• Figure 2: Representative trajectories showing the positions of particles over time in distinct temporal regimes (rows). Each column corresponds to a simulation at the specified particle density. The y-axis denotes the time in episodes divided by the typical time it takes for a particle to cross the system once. The starting time for each row is indicated in grey, and the final time is in the top-right corner of each panel. Line colours show the sign of the average relative velocity of that particle in the last 2e5 episodes of the simulations. Trajectories of representative particles are highlighted in bold. For densities 0.4, 0.5, and 0.6, we have randomly sampled 100 particles to make individual lines distinguishable.
• Figure 3: (a) Average velocity of particles relative to the average velocity of all particles in a simulation. Particles are grouped by their asymptotic velocity, which is calculated as an average over the final 2e5 episodes of the simulations. The inlay show the density $0.5$ between episodes $5e3$ and $6e5$. (b) Average absolute velocity of all particles for two representative densities (colours defined in (c)). The dashed lines on the time axis denote in this and in all other figures two characteristic times: $t_1\approx 1e4$ episodes mark the initial formation of global alignment at low densities; $t_2\approx 3e4$ episodes mark the initial formation of two groups of particles moving in opposite directions at high densities. (c) Log2-fold change of the standard deviation of the number of right-moving particles across simulations. The lower horizontal dashed line is the variance expected if the direction of movement were assigned by chance. The upper dashed line is the maximal variance expected for globally aligned motion. (d) Average reward for two representative densities as a function of time. The inlay is a magnification that shows a decrease in the reward for density 0.5. Colours as in (c).
• Figure 4: (a) Average distance to the nearest-neighbour particle rescaled by the nearest-neighbour distance (NND) expected for a spatially uniform distribution of particles (horizontal dashed line). Vertical dashed lines denote characteristic times defined in Fig. \ref{['fig:velocities']}. (b) Fraction of particles sharing a lattice site with at least one other particle rescaled by the expected value for a uniform distribution (horizontal dashed line). (c) Heatmaps of the pair correlation function for low and high particle densities. The pair correlation function is rescaled by the average density of particles (grey).
• Figure 5: Probability density functions of neural network parameters (black lines) for logarithmically spaced time points. Density functions are shown separately for two different densities, the actor and critic networks constituting the deep reinforcement learning algorithm and the weights and biases in the neural networks.