Emergent E-I Structure in Performance-Evolved Reservoir Networks of Neuronal Population Dynamics

Abstract

Understanding how network structure gives rise to neuronal dynamics and whether compact computational models can recover that structure from data alone is a central challenge in computational neuroscience. We apply the performance-dependent network evolution (PDNE) framework to model the dynamics of the Wilson-Cowan (WC) neuronal system, a canonical two-population model of excitatory-inhibitory (E-I) interaction underlying physiological rhythms. Starting from a minimal seed network, PDNE iteratively grows and prunes a reservoir computing (RC) network based solely on prediction performance, yielding compact, task-optimized reservoirs networks. The evolved networks accurately predict both excitatory $E(t)$ and inhibitory $I(t)$ population activities across unseen stimulus amplitudes and generalize in a zero-shot manner to novel stimulus configurations: varying pulse number, position and amplitude without retraining. Structural analysis of the evolved networks reveals a consistent functional organization with nodes specialized for E, I, and shared E-I representations. Importantly, the population-level connectivity of the evolved reservoirs spontaneously recovers the correct excitatory-inhibitory sign pattern of the WC model for three of four interaction types, without this being imposed by design. These results demonstrate that performance-driven network evolution can produce not only accurate but structurally interpretable models of physiological rhythms, opening a path toward compact, data-efficient digital twins of neuronal systems.

Figures (5)

• Figure 1: Performance-dependent network evolution for learning Wilson-Cowan neuronal dynamics. (a) The reservoir computing (RC) model with input layer receiving pulse stimulus $s(t)$, recurrent reservoir layer $W^{\text{res}}$, and output layer predicting excitatory ($E$, red) and inhibitory ($I$, green) population activities. (b) The PDNE algorithm iteratively evolves the reservoir via node addition ($A$) and deletion ($D$) modules driven by prediction performance, from a minimal seed network $G_{s_0}$ toward a task-optimized topology. Right: the target WC model with coupling weights $W_{EE}$, $W_{EI}$, $W_{IE}$, and $W_{II}$.
• Figure 2: Prediction performance on unseen test stimuli.Top two rows: Predictions of excitatory $E(t)$ (red: original, blue: $E_p$) and inhibitory $I(t)$ (black: original, green: $I_p$) for test amplitudes $S_{\mathrm{amp}} = 2.35$ (left) and $S_{\mathrm{amp}} = 3.15$ (right), both absent from the training set. Bottom row: Peak amplitude predictions (blue circles) vs. original peak values (gray diamonds) across 10 model repetitions. Arrows indicate systematic over- or under-estimation where present. The pulse input $s(t)$ is scaled by $1/20$ for visualization.
• Figure 3: Zero-shot generalization to novel stimulus configurations. Models trained exclusively on two-pulse sequences are tested on stimuli with varying number of pulses, positions, and amplitudes without retraining. Each panel pair shows $E(t)$ (top: red original, blue dashed $E_p$) and $I(t)$ (bottom: black original, green dashed $I_p$). (a,b) Single-pulse reference at $S_{\mathrm{amp}} = 2.35$ and $3.25$. (c--l) Multi-pulse stimuli at $S_{\mathrm{amp}} = 2.20,\, 2.45,\, 3.15,\, 3.25,\, 3.32$ with varying pulse counts and temporal positions. The pulse input $s(t)$ is scaled by $1/20$ for visualization.
• Figure 4: PDNE evolution dynamics and network topology across 10 model repetitions. (a,b) Training NMSE for $\varepsilon_E$ and $\varepsilon_I$ vs. evolution step $t$. Orange: initial seed; blue: final evolved network. (c) Reservoir node count $N(t)$ reflecting iterative addition and deletion. (d) Evolution trajectory in the density-node parametric space. (e,f) Representative initial and final network topologies. Green: input nodes $\mathcal{I}$; red: output nodes $\mathcal{O}_{E,I}$; gray: hidden nodes. Edge colors: connection weight (colorbar). (g,h) Distributions of node gain values $\mathbf{g}$ and edge weights for initial (orange) and evolved (blue) networks.
• Figure 5: Structural analysis of evolved reservoirs and comparison with the Wilson-Cowan E-I architecture. (a) Node classification counts per repetition: E-specific (blue), I-specific (red), Shared (cyan), Peripheral (gray). Dashed lines: cross-repetition means. (b) Stacked percentage node composition per repetition. (c) Representative evolved network colored by functional role: E-specific (blue), I-specific (red), Shared (cyan), Input (orange). (d) Edge polarity: % of E$\rightarrow$I connections that are excitatory (blue) and I$\rightarrow$E connections that are inhibitory (red) per repetition. (e) Mean shortest path lengths E$\rightarrow$I (blue) and I$\rightarrow$E (red) per repetition. (f) WC ground truth connectivity matrix (top) and mean evolved network population connectivity matrix (bottom), showing sign correspondence for three of four E-I interaction types.