Operational Training Budget for Large-Scale Neural Networks: Dynamic Cost Principle Analysis of Gradient Descent Convergence and Overfitting Thresholds (2024–2025)

This report introduces an operational framework for neural network training based on the Dynamic Cost Principle (DCP), which models each training epoch as a consumption of finite generalization capacity. Using controlled empirical validation on language (GPT-2/WikiText-2) and vision (ResNet-18/CIFAR-10) benchmarks, the work demonstrates that training should be stopped when accumulated cost (K_tot) approaches a practitioner-defined generalization budget (K_max). Applied to 2024–2025 large language models (GPT-4, Chinchilla, DeepSeek V3, Llama 3), the framework explains why ~1-epoch training is optimal, quantifies trade-offs between learning rate, data augmentation and batch size, and enables 10–30% compute savings through predictive early stopping. The method provides real-time budget tracking (N_remaining = (K_max − K_tot) / k_epoch) and cost-per-useful-epoch accounting, transforming training from reactive to predictive budget management. Validated across five domains (spin qubits, enzyme catalysis, lithium-ion batteries, NAND flash, and neural networks), DCP emerges as a universal operational law for sequential systems with finite tolerance. TECHNICAL COVER NOTE ^0 LICENSE TERMS.pdf Operational Lifetime Budgeting Across Four Physical Domains.pdf Fifth domain application of the Dynamic Cost Principle (DCP), extending the cross-domain validation from "Operational Lifetime Budgeting Across Four Physical Domains" (2025).