q-bio.NCNov 4, 2026
SaveLearning Time-Varying Connectomes for Stable Behavior Across Development
Organizations: Neurobiology, Duke University, Durham, 27710, NC, USA.
Abstract
Neural circuits must maintain functionality to drive effective behavior while their size, topology, geometry, and intrinsic dynamics change across development. To model developing visuomotor circuits and behavior, we investigated whether a single compact generative encoding could produce functional recurrent controllers across such changes. Building on the HyperNEAT algorithm, we represented this program as a compositional pattern-producing network that received developmental time as an input to generate age-specific connectivity. The developmental substrate prescribed neuronal birth, position, sensory organization, and intrinsic time constants. We tested this approach using two geometrically distinct developmental substrates and two visuomotor tasks: optomotor responses and phototaxis. Controllers optimized at only the initial or mature substrate generally failed when evaluated at other ages. In contrast, controllers optimized across multiple developmental snapshots maintained substantially higher and more consistent performance across trained and unseen ages. Optimization at only three developmental snapshots was often sufficient to produce effective behavior across the tested developmental interval. The resulting connectomes changed substantially with age and did not converge on a single trajectory of sparsity or connection-weight statistics. Controllers also differed in whether they relied on neurons born later in development. These results demonstrate that a shared spatiotemporal time-varying connectivity program can produce recurrent neural networks that preserve behavior across substantial developmental changes. Together, these results provide a framework for studying how functional stability can emerge without requiring structural or dynamical stability.
Figures & tables
Figure 1: Parameterizing the connectome of a developing visuomotor system. (A) Three developmental snapshots illustrate the challenge of maintaining function as the neural substrate changes. The system must use sensory observations to produce survival-relevant actions while accommodating changes in network topology (e.g., neurogenesis) through local synaptic modifications without disrupting behavior. (B) A compositional pattern-producing network (CPPN) parameterizes the connectome. In HyperNEAT, source (src) and target (tgt) neuron coordinates determine directed synaptic weights, while an optional expression gate (expr.) promotes modularity ( Verbancsics and Stanley, 2011 ) . Our developmentally aware modification adds developmental time ( ) as a CPPN input, enabling time-varying generative rules. (C) CPPNs are optimized for optomotor response (OMR; top), in which the agent follows moving gratings, or phototaxis (bottom), in which it moves toward a stationary light source (purple rays indicate the retinal detection radius; see Methods). Although training uses only the three illustrated snapshots, performance is evaluated across the developmental trajectory. The example synaptic weight (yellow) between a source (red) and target (blue) in A may vary with substrate changes across the first two snapshots while in the third, the expression gate falls below threshold, clamping the weight to zero (dotted line). The objective is to maintain functionally stable behavior throughout development despite changes in the underlying connectome.
Figure 2: Results of Task Optimization and Fitness Stability. (A) Fitness trajectories across training conditions and substrate–task pairs. Five evolutionary runs with different random seeds were performed per condition; bold lines show mean fitness across seeds, with standard deviations overlaid. Rev. HyperNEAT achieved the highest fitness on both substrates, while the Ring substrate showed lower variability across seeds. (B) Fitness over the final 10 generations for the best seed in each condition, selected by mean fitness over those generations. (C) Developmental robustness of OMR-trained networks, evaluated over 11 evenly spaced developmental times, most unseen during training. Gray lines show mean fitness across 20 test trials per seed and time point; thick transparent lines show condition means, and dotted lines indicate the best seed’s fitness. HyperNEAT and Rev. HyperNEAT generally failed outside their optimized developmental times, whereas developmentally aware networks maintained more stable fitness. Notably, the highest training fitness rarely corresponded to the most fragile network. All five Ring seeds trained at three developmental time points (3pts) remained stable across development. (D) The same analysis for phototaxis reveals similar trends despite the task’s greater difficulty, attributable to substantial changes in sensory structure (see Methods).
Figure 3: Behavioral Stability Across Development for Best Seeds. (A) OMR performance during a fixed random trial, showing grating angle transitions (red) and error in desired orientation (black). Successful OMR drives orientation error toward zero. Flat lines indicate no change in orientation, sawtooth patterns indicate constant-rate spinning, and jumps at red lines reflect changes in grating angle. Although this metric cannot distinguish turning without movement, such behavior was never observed. Error trajectories are shown for three developmental times unseen during training (right). Despite learning OMR at their training times, HyperNEAT and Rev. HyperNEAT fail to turn in the correct direction at these unseen times. (B) Phototaxis performance during a fixed random trial, showing emitter position transitions (red) and the L2 distance between the agent and emitter center (black). Successful phototaxis drives this distance toward zero; jumps at red lines reflect changes in emitter position. As in OMR, HyperNEAT and Rev. HyperNEAT fail to generalize to the three unseen developmental times, with errors sometimes exceeding the plotted range. Oscillatory behavior, particularly on the Ring substrate, reflects circular movement of varying radii. We hypothesize that this strategy evolved because the emitter can move beyond the retina’s detection range, favoring continuous environmental scanning for luminance changes.
Figure 4: Changes in Connectome Across Development. (Top) Connectivity matrices at the beginning and end of development for the best seeds across substrate–task pairs. Each entry represents the weight from a source (x-axis) to a target neuron (y-axis). Red and blue indicate positive (excitatory) and negative (inhibitory) weights respectively, gray indicates weights set to zero by the expression gate, and white indicates connections prohibited by projection constraints. Axis colors denote neuron locations in the substrate. Thin gray lines separate regions, thick gray lines separate the left and right motor neurons (enlarged relative to other neurons for ease of visualization). (Bottom) Connectome visualizations at three developmental snapshots for the OMR Fish Dev. Aware–5pts condition (star). Red and blue indicate positive and negative weights. Only the 2,000 connections with the largest absolute weights are shown per snapshot, with the percentage indicating the fraction of the full connectome displayed. Stronger inputs to the right motor neuron bias the agent toward rightward turns.
Figure 5: Investigation of Developmental Strategies. (A) OMR–Fish pair. (Left) Developmental trajectories of connectome sparsity ratio, excitatory ratio, and mean nonzero connection weight. (Right) Fitness difference between the full growth model and a model without neurogenesis. Positive values indicate improved performance with neurogenesis, negative values indicate improved performance without it, and values near zero indicate little effect. All differences are zero at , when neurogenesis has not yet occurred. Gray lines show individual seeds, thick transparent lines show condition means, and dotted lines indicate the best seed. (B–D) The same analyses for the remaining substrate–task pairs.
| Parameter | Fish | Ring |
|---|---|---|
| Developmental interpolation, | ||
| Lateral assignment of recurrent cohort ranks | Outside to inside | Inside to outside |
| Middle-cohort birth-window bounds | ||
| Late-cohort birth-window bounds | ||
| Recurrent neurons, initial final | ||
| Brain width, initial final |
Table 1: HyperNEAT substrate parameter values for the Fish and Ring substrates 0 0 footnotetext: Recurrent counts include both hemispheres. Brain dimensions and eye radii are expressed in substrate coordinate units, phototaxis sensing distances in environment coordinate units, and in simulation time units. Phototaxis sampling parameters apply only to bipolar-like detectors; OMR input uses the directional signals defined above.
Figure 6: Substrate Growth Models. (A) Three developmental snapshots ( ) of the Fish and Ring substrates. Each differs in neuronal migration, neurogenesis schedules, and projection constraints. The number of neurons available to the CPPN is shown for each snapshot. Each substrate neuron corresponds to a CTRNN neuron, with motor neuron outputs determining the agent’s actions (see Methods). (B) Retinal models used for phototaxis (top) and OMR (bottom). Bipolar cells detect luminance averaged across points along a projected ray (see Methods); their number and effective detection range double across development. Direction-selective ganglion cells (DSGCs) detect local optic flow from moving gratings. Both substrates use the same initial and final cell counts for each retinal model.
| Substrate | Allowed source target projections |
|---|---|
| Fish | Sensory L Area 1 R; sensory R Area 1 L; Area 1 Area 1, Area 2, and Area 3; Area 2 Area 3; Area 3 motor. |
| Ring | Sensory L Area 2 R; sensory R Area 2 L; Area 2 R motor L, Area 1 L, and Area 3 L; Area 2 L motor R, Area 1 R, and Area 3 R; Area 1 L Area 3 R; Area 1 R Area 3 L; Area 3 L Area 1 R; Area 3 R Area 1 L. |
Table 2: Allowed source target projections for the Fish and Ring substrates 0 0 footnotetext: Note that the Fish and Ring substrates had exclusively contralateral retinal projections, which are present in the zebrafish visuomotor system ( Naumann et al., 2016 ) .
| Parameter | Value or rule |
|---|---|
| Initial input / hidden / output nodes | 7 / 2 / 2 |
| Weight-output activation | |
| Expression-output activation | |
| Connection expression criterion | Expression output |
| Decoded controller weight bounds | ; outgoing sensory weights in Fish: |
| Initial and mutated hidden-activation choices | Gaussian, sigmoid, , , , step, ReLU |
Table 3: CPPN encoding and neuroevolution parameters