Breaking the Central Bias: Spatially Partitioned Experts for Coordinate-Based Neuroevolution
Authors: Romain Claret, Arthur Gygax, Michael O'Neill, Paul Cotofrei, Michael Palma Mendes, Pascal Felber
Abstract
Evolvable-Substrate HyperNEAT (ES-HyperNEAT), a bio-inspired indirect encoding that determines neuron placement and connection weights from spatial coordinates, exhibits a failure mode on MNIST as a diagnostic benchmark. Because input pixels map to a coordinate space centered at the origin, evolved networks converge on a small central cluster of input pixels, a spatial-concentration bias; prior work observed only 21% mean accuracy in this regime. Is this bias an optimization artifact or an architectural ceiling? Inspired by Mixture-of-Experts (MoE) principles, we partition the input into non-overlapping spatial segments, each assigned to a separately evolved specialist network. With 13 such experts, this design reaches 43% mean accuracy, a 106% relative improvement over the baseline. The architectural gain does not depend on data-driven aggregation: equal-weighted averaging, which uses no validation data, already yields a 70% improvement; the gain comes from partitioning, not the weighting. Receptive-field analysis shows the mechanism: partitioning forces evolution to discover features across the entire image, expanding active pixel coverage from 4% to 79%. Absolute accuracy stays below gradient-trained baselines, but the relative gain points to central bias, not the evolutionary search. Two tools are designed to generalize beyond MNIST: a receptive-field diagnostic for silent input-coverage collapse, and a spatial-partitioning remedy that restores coverage.
Indirectly encoded neural networks can assign different activation functions to individual nodes, but the right functions are rarely known in advance. When the available set contains only standard monotonic functions, problems like parity become unsolvable, yet an all-inclusive palette underperforms a curated one. How should evolution discover which functions to use? We address this as a meta-learning problem, designing 13 strategies (11 inspired by biological adaptation mechanisms, plus baseline and oracle controls) that modify the set of available activation functions during evolution. Each strategy translates a biological principle into an evolutionary operator: for example, circadian-inspired oscillatory gating cycles functions in and out of the palette on a fixed schedule, while immune-inspired Clonal Selection permanently protects functions that consistently correlate with fitness. We evaluate all strategies across more than 3,000 runs on parity and non-parity problems, first evolving the activation palette alone, then co-evolving a per-node aggregation palette on harder problems; an independent replication with new seeds confirms a stable high-reliability tier, with Circadian holding its top rank. Bio-inspired strategies match the solve rate of a tuned baseline but converge up to twice as fast, with Circadian halving total compute. Strategy rankings reverse across problem types, with no strategy dominating all domains. Strategy success is largely shaped by timescale compatibility: strategies whose characteristic timescale matches the evolutionary evaluation window consistently outperform those that operate too slowly. The practical guideline: match the mechanism's timescale to the evaluation budget. Rescaling the slowest strategy bypasses the oscillatory barrier entirely: all nine solutions solve parity with non-oscillatory activations paired with min or max aggregation.
Evolutionary optimization of spiking neural networks (SNNs) becomes increasingly difficult as task complexity grows because they must search a combined topology--parameter space that grows super-exponentially with network size. We address this scaling challenge through a co-evolutionary ensemble framework in which a population of candidate SNNs is evolved with fitness defined by each network's marginal contribution to group performance. Grounded in cooperative game theory and difference evaluation functions from multiagent systems, this credit assignment rewards networks that consistently improve ensemble performance and penalizes redundancy, encouraging complementary specialization during evolution rather than relying on post-hoc combination of independently trained networks. We evaluate the approach on classification, regression, and control tasks under μCaspian neuromorphic hardware constraints. Co-evolved ensembles achieve statistically significant improvements over both single-network evolution and post-hoc ensembles across all tasks, with the most pronounced gains in control, where standard evolution fails to discover effective policies and co-evolution enables a qualitative transition to near-optimal performance.
Neuroevolution is a representative neural architecture search paradigm that evolves both network topology and weights through evolutionary algorithms. In this paper, we propose Seq103, a unified NEAT-style neuroevolution framework for compact sequence architecture discovery. Seq103 consists of a shared evolutionary backbone and an optional recurrent extension. The shared backbone includes an elementary node-and-connection representation, per-class RMSE-based evaluation, mutation-based evolution with class-wise recombination, and elitism. The optional hidden-state mechanism extends the search space with hidden-state nodes and hidden connections, enabling temporal memory when step-wise recurrent inference is required. With this design, Seq103 applies the same core search pipeline to both step-wise recurrent and sample-wise feedforward sequence classification. In recurrent tasks, the hidden-state extension is enabled to provide temporal memory; in feedforward tasks, it is disabled while the shared evolutionary backbone remains unchanged. We evaluate Seq103 on 8 text classification datasets and the full UCRArchive2018 benchmark with 128 univariate time-series datasets. On step-wise tasks, Seq103 retains 86.96% of the best-baseline accuracy on average while using 34.6x to 3218.0x fewer parameters. On sample-wise tasks over the full UCRArchive2018 benchmark, Seq103 retains 81.95% of the best-baseline accuracy on average while using 11.8x to 160,601.0x fewer parameters.