Normalized Spatial Synchronization and Early-Warning Regime Maps of AdamW Weight Corrections on CIFAR-10: A Multidimensional Dataset

Dataset Description This dataset provides numerical simulation outputs, multidimensional regime maps, normalized spatial synchronization characteristics, and early-stage training indicators obtained from neural networks trained with the AdamW optimization algorithm on CIFAR-10. The dataset extends the methodological framework presented in the research article "Normalized Spatial Synchronization Analysis of Adaptive Weight Corrections for Regime Mapping in Adam Optimization of Neural Networks" to the AdamW optimizer, incorporating decoupled weight decay into the analysis of adaptive weight corrections. 1. Scientific Objectives The primary objective is to investigate the spatial organization, synchronization properties, and dynamical regimes of neural network weight corrections under variations in the AdamW optimizer parameters β₁ and β₂. Particular attention is given to identifying heterogeneous correction patterns, localized synchronization losses, and changes in training dynamics that may serve as potential early-warning indicators of unstable optimization regimes. The dataset supports comparative studies of Adam and AdamW, parameter-dependent regime mapping, nonlinear training dynamics, and the development of interpretable optimization diagnostics. 2. Mathematical Observables The analysis is based on normalized, dimensionless observables calculated from the magnitudes of weight corrections associated with individual neurons. Normalized pairwise correction amplitude: Aᵢ(t) = [xᵢ²(t) + xᵢ₊₁²(t)] / [2⟨x²(t)⟩ + ε] This observable characterizes the relative magnitude of weight corrections for adjacent neurons. Local spatial synchronization-loss coefficient: Sᵢ(t) = |xᵢ₊₁(t) − xᵢ(t)| / [xᵢ₊₁(t) + xᵢ(t) + ε] This coefficient measures the local mismatch between adjacent neuronal weight-correction magnitudes. Global spatial synchronization-loss measure: S(t) = √⟨Sᵢ²(t)⟩ The global measure summarizes spatial synchronization loss across the analyzed neural network layer. Normalized neuron-wise correction: Xᵢⁿᵒʳᵐ(t) = xᵢ(t) / [RMSⱼ(xⱼ(t)) + ε] Together, these observables describe the amplitude distribution, spatial heterogeneity, and synchronization characteristics of adaptive weight corrections. 3. Experimental Configuration The numerical experiments employ: Dataset: CIFAR-10. Optimization algorithm: AdamW with decoupled weight decay. Neural network: multilayer perceptron with one hidden layer. Hidden layer size: 50 neurons. Activation function: sigmoid. Training duration: 5 epochs per parameter configuration. Batch size: 64. Weight decay coefficient: 0.01. Optimizer parameters: β₁ and β₂ sampled over a two-dimensional grid. Grid spacing: 0.002 for both β₁ and β₂. Input dimensionalities supported by the code: 32, 256, and 2048. Classification protocol: binary one-versus-rest tasks for the ten CIFAR-10 classes. The uploaded simulation archives correspond to selected learning rates α = 0.0001, 0.001, 0.01, 0.1, and 0.3. 4. Dataset Contents The deposited archives contain computational outputs organized by experimental configuration. The generation program supports the following data products: A. Parameter-dependent regime maps Maps of neural network weight-correction regimes in the (β₁, β₂) parameter space. B. Normalized amplitude characteristics Statistical representations of Aᵢ, including mean values, maximum amplitudes, and spatial dispersion. C. Spatial synchronization characteristics Local and global synchronization-loss measures, including Sᵢ and the root-mean-square global coefficient S. D. Multidimensional normalized fields Spatial fields Aᵢ(i, β₁, β₂) and Sᵢ(i, β₁, β₂), represented using three spatial/parameter coordinates and color-coded observable values. E. Three-dimensional surfaces and neuronal profiles Parameter-dependent surfaces, individual adjacent-neuron pair surfaces, and normalized correction profiles. F. Conventional training diagnostics Training loss, classification accuracy, gradient norms, update norms, and associated statistical characteristics. G. Early-stage training indicators Indicators computed over the initial 30% of training steps, including normalized amplitude statistics, synchronization-loss statistics, gradient norms, update norms, and update variability. These measurements enable retrospective comparisons between early training behavior and final optimization outcomes. They do not, by themselves, establish validated predictive performance. 5. Data Formats and Reproducibility The Python implementation generates numerical data and visualizations using NumPy and Matplotlib. Generated outputs include: CSV files containing parameter-dependent numerical summaries. NPZ files containing multidimensional numerical arrays and normalized fields. PNG files containing regime maps, surfaces, and spatial visualizations. Python source code implementing the AdamW experiments. The supplied Python script enables reconstruction of the experimental methodology, calculation of normalized observables, and generation of parameter-dependent regime maps. 6. Scientific Applications The dataset can be used for: Comparative investigation of Adam and AdamW optimization dynamics. Analysis of spatial synchronization and heterogeneity in neural network weight corrections. Detection and characterization of parameter-dependent dynamical regimes. Exploration of early-warning indicators for potentially unstable training behavior. Investigation of the effects of learning rate and optimizer hyperparameters on normalized spatial observables. Development and evaluation of interpretable diagnostics for adaptive neural network optimization. 7. Related Research This dataset is associated with the research article: "Normalized Spatial Synchronization Analysis of Adaptive Weight Corrections for Regime Mapping in Adam Optimization of Neural Networks." It provides an AdamW-based experimental extension of the normalized spatial synchronization framework originally investigated for Adam optimization. The deposited source code and numerical outputs are intended to support reproducibility, independent verification, and further research into neural network training dynamics.