Dataset supports the research manuscript "NEAT-GAN Integration with Trainable Exponent Gates to Enhance Generative Search across Multi-Problem Benchmarks"

This dataset supports the research manuscript "NEAT-GAN Integration with Trainable Exponent Gates to Enhance Generative Search across Multi-Problem Benchmarks". ### Research Hypothesis Conventional neural network generators rely on fixed, purely additive computational graphs, which struggle to represent non-linear geometries (such as multiplicative, ratio-based, or power-law distributions) efficiently. We hypothesize that integrating the topology-evolving capabilities of the Neuroevolution of Augmenting Topologies (NEAT) algorithm with connection-level "trainable exponent gates" provides a powerful inductive bias. This allows the generator to dynamically transition between additive and multiplicative regimes, achieving superior representation with exceptional parameter efficiency. ### What the Data Shows & Notable Findings This database contains the complete performance sheets, ablation matrices, and feature-space generative validation logs across a total of 1,848 independent training runs: 1. Primary 768-Run Benchmark: Tracks performance across 8 distinct task families, 4 input dimensions (2, 3, 5, 8), and 2 training sizes (64, 256). Our model (NEAT Trainable Exponent) achieves a superior mean test accuracy of 93.03% and a normalized MAE of 0.0808 using only 69 parameters, significantly outperforming the standard MLP-16 baseline (91.76% accuracy, 105 parameters) and the standard NEAT-no-exponent baseline (91.75% accuracy, 40 parameters). 2. Reviewer-Driven 1,080-Run Ablation Suite: Systematically isolates the causal contributions of the exponent coordinate basis, exponent trainability, output branch, and sign path. The results confirm that the mathematical basis provides the core representation, while parameter trainability optimizes task-dependent degrees of freedom. 3. Feature-Space Generative Validation: Validates distribution matching on 10-dimensional handwritten digit statistics (mean, variance, skewness, and kurtosis) across 16 random seeds. Our model achieves excellent feature-space FID-like scores (0.0033 vs. 0.4101 for ablation) and high within-class diversity without suffering from mode collapse. ### How to Interpret and Use the Data Researchers can use this dataset to: - Compare the parameter efficiency of evolutionary architecture search (NAS) against conventional backpropagation baselines under tightly controlled budgets. - Analyze how different mathematical task structures (Product, Ratio, Fractional Power) interact with connection-level non-linear coordinate activations. - Replicate the statistical significance (paired effect size dz, win rates, and bootstrap 95% confidence intervals) reported in the paper.