Cognition without neurons: modelling anticipation in a basal reservoir computer

TL;DR

The paper tackles how non-neural organisms can anticipate periodic environmental changes. It introduces a basal reservoir computer—a spatially structured hexagonal network where local energy balance and allostatic adaptation reshape internal connections and targets, enabling unsupervised temporal pattern completion without a readout. Exposure to a periodic input yields internal reorganization that replays learned temporal structure even when input ceases, demonstrating memory and a fading-memory form of prediction. This work provides a minimal mechanism for memory and anticipation in basal cognition, highlighting how distributed, body-centered regulation can support predictive dynamics in non-neural systems.

Abstract

How do non-neural organisms, such as the slime mould \textit{Physarum polycephalum}, anticipate periodic events in their environment? We present a minimal, biologically inspired reservoir model that demonstrates simple temporal anticipation without neurons, spikes, or trained readouts. The model consists of a spatially embedded hexagonal network in which nodes regulate their energy through local, allostatic adaptation. Input perturbations shape energy dynamics over time, allowing the system to internalize temporal regularities into its structure. After being exposed to a periodic input signal, the model spontaneously re-enacts those dynamics even in the absence of further input -- a form of unsupervised temporal pattern completion. This behaviour emerges from internal homeodynamic regulation, without supervised learning or symbolic processing. Our results show that simple homeodynamic regulation can support unsupervised prediction, suggesting a pathway to memory and anticipation in basal organisms.

Figures (4)

• Figure 1: Schematic of the basal reservoir computer architecture. Input layer (left): $M$ input nodes $i_1,\dots,i_M$ deliver external signals into the reservoir via dashed, directed arrows representing input weights $W^{\mathrm{in}}_{n,m}$. Reservoir layer (right): $N$ processing nodes arranged on a hexagonal lattice. Between each neighbouring pair of nodes $n$ and $n'$ there are two solid, parallel arrows — one from $n$ to $n'$ (weight $W_{n',n}$) and one from $n'$ to $n$ (weight $W_{n,n'}$) — to indicate bidirectional energy flow (in general, $W_{n,n'}\neq W_{n',n}$). No readout layer is included: all computation and memory emerge from the reservoir’s internal dynamics.
• Figure 2: Reservoir weights on the first and last time step of training for a sample simulation. Weights are randomly sampled from a Gaussian distribution at initialization. Over the course of stimulus exposure, the weights adapt following local, homeodynamic regulation of activation, resulting in pruning and increased polarization of weight values.
• Figure 3: Reservoir state space during stimulus exposure. Activation manifold (top): Principal components analysis (PCA) of the reservoir's activation state space over training for a sample simulation. Reservoir activation exhibited a coherent routine, oscillating across a partition along the first principal component (PC1). Reservoir activity drifted through the state space over time while maintaining separation between two attractors corresponding to each possible state. Response over time (bottom): The first three principal components plotted over time for the last 20 time steps of training, averaged over 100 simulations. Very little variance in the oscillatory behaviour of PC1 indicates that across simulations the network successfully exhibited a stable response to the oscillatory signal. Greater variance along the second and third principal components is indicative of the drift of the oscillatory trajectory shown in the top figure, illustrating that the model maintains a stable behavioural response (PC1) to the signal despite underlying variance of the activation states producing the response over time.
• Figure 4: Fading memory of the reservoir. Correlation matrix (left): Correlations between the state of the reservoir on the last 12 time steps of training and four time steps into the future without further stimulation (the fading memory), averaged over 100 simulations. Time progresses from top to bottom along the y-axis and from left to right along the x-axis. The red, dashed box shows the correlation coefficients between each fading memory time step and the past 12 time steps of training. Higher correlations between fading memory states and training states indicate what input the network anticipated. The first row in the red box shows that the reservoir returned to a state most similar to past occurrences of "ON," indicating that the reservoir anticipated the next periodic phase even in the absence of the oscillatory stimulus. After this, the reservoir settled into a state unlike either oscillatory state as activation died out. Next state anticipation (right): The correlation coefficients between the reservoir state on the first time step of fading memory (corresponding to when "ON" would have appeared) and reservoir states from the last 12 time steps of training over 100 simulations. On average, the reservoir was more highly correlated with previous states associated with "ON" compared to "OFF," even in the absence of further input, indicating that the reservoir correctly anticipated the oscillatory signal one time step into the future.