Normalized Spatial Synchronization Analysis of Weight Corrections during Adam Optimization of Neural Networks

This dataset contains experimental results from a normalized spatial synchronization analysis of weight correction dynamics during training of neural networks optimized with the Adam algorithm. The dataset investigates neural network training as a high-dimensional nonlinear dynamical process, where adaptive weight updates generated by Adam optimization are analyzed through spatial organization, synchronization, and temporal evolution of neuron-wise correction patterns. The experiments were performed using multilayer perceptron (MLP) neural networks trained on the CIFAR-10 dataset. Binary classification tasks were constructed for individual CIFAR-10 classes, and the dynamics of Adam weight corrections were studied under different combinations of optimizer parameters: learning rate: α = 0.01; first momentum parameter: β₁ ∈ [0,1); second momentum parameter: β₂ ∈ [0,1). The dataset contains results obtained for different input dimensionalities: d = 32; d = 256; d = 2048. The analysis focuses on normalized spatial observables derived from neuron-wise Adam weight corrections: Normalized correction amplitude A_i(t) = (x_i(t)^2 + x_{i+1}(t)^2) / (2·mean(x(t)^2) + ε), which x_i(t) characterizes the local spatial distribution of correction amplitudes between neighboring neurons. Local synchronization-loss coefficient S_i(t) = |x_{i+1}(t) − x_i(t)| / (x_{i+1}(t) + x_i(t) + ε) which S_i(t) quantifies local desynchronization between neighboring weight corrections. Global Spatial Synchronization Coefficient (SSC) S(t) = sqrt(mean(S_i(t)^2)), which describes the overall level of spatial synchronization within the analyzed neural layer. Normalized neuron-wise correction profile X_norm_i(t) = x_i(t) / (sqrt(mean(x_j(t)^2)) + ε), used for studying spatial organization of adaptive weight updates. The dataset includes: dynamic regime maps in the (β1,β2) parameter space; three-dimensional surfaces of normalized spatial observables; full four-dimensional fields: F(i,β1,β2), where the neuron-pair index iii and Adam parameters define the spatial parameter domain, while the field value is represented by color intensity; spatial profiles of Ai, Si, and Xinorm; numerical matrices and CSV summaries for further statistical analysis. The data are intended for studying: adaptive optimization dynamics; spatial organization of neural network weight corrections; synchronization and desynchronization phenomena in learning processes; parameter-dependent regime transitions of Adam optimization; nonlinear dynamical interpretation of deep learning optimization algorithms. The accompanying files provide raw numerical results, generated figures, and metadata required for reproduction and further analysis. This dataset supports research on neural networks considered as complex adaptive dynamical systems and provides a basis for quantitative comparison of optimization regimes beyond conventional accuracy-based evaluation.