Cross-Domain Production-Grade Neural-Network Training Reliability from a Single Mathematical Constant

Author: Robert Zemichiel - Independent Researcher - [email protected]: May 28, 2026License (Paper, figures, benchmark data): Creative Commons Attribution 4.0 International (CC-BY 4.0)License (Source code): PolyForm Noncommercial License 1.0.0 ABSTRACT We report the results of a controlled 25,000-run empirical study examining learning rate (LR) reliability in neural-network optimization. Across 6 optimizers, 4 architectures (SmallMLP, DeepMLP, WideMLP, BottleneckMLP), 3 feature-dimensionality tiers, 2 task types, 2 data modalities, 9 learning rates, and 15 random seeds, we identify a single mathematical constant, Y_2_LR equal to 1 divided by Y_2 approximately 0.0314, derived from a pre-defined Y-Sequence, that produces a winning head-to-head record against every other tested learning rate. Most notably, the constant achieves a 67.5 percent head-to-head win rate against the canonical Adam and AdamW default of LR equal to 0.001 (81 wins to 39 losses across 120 configurations; Holm-corrected p equals 3.16 times 10 to the negative 4). The statistical evidence is overwhelming: Friedman omnibus test chi-squared with 8 degrees of freedom equals 127.4 with p less than 10 to the negative 22 (precise survival-function p approximately 9.82 times 10 to the negative 24); Y_2's aggregate first-place dominance Z equals 5.69 with p equal to 6.5 times 10 to the negative 9; joint head-to-head probability under the null hypothesis equals 1.96 times 10 to the negative 35. When combined into a production recipe with adaptive per-parameter gradient clipping (ZClip) and Latest Weight Averaging (LAWA), Y_2_LR achieves zero training divergences across all 36 Tier-A ablation configurations (540 runs at 15 seeds each), against industry-standard divergence rates of 20 to 35 percent for aggressive learning rates. We further document that the warmup-stable-decay (WSD) scheduler, a near-universal component of 2024-2026 frontier training stacks, catastrophically degrades Y_2_LR performance (clustering significance p equals 1.55 times 10 to the negative 4), a previously unreported scheduler-learning-rate interaction. Cross-domain validation on genomic single-nucleotide-polymorphism data (the SNIPA benchmark) reproduces all primary findings. Transformer, convolutional, recurrent, graph-based, and reinforcement-learning architectures, and direct comparisons against modern parameter-free methods such as Schedule-Free AdamW, Prodigy, and D-Adaptation, are explicitly out of scope and listed as future work. WHAT IS IN THIS RELEASE The release includes: the paper (PDF and markdown source) comprising 13 sections, 4 appendices, and approximately 10,000 words; benchmark data of approximately 5 megabytes of JSON with SHA-256 integrity hashes covering per-run metadata for more than 25,000 training runs; 44 publication-grade figures in PNG format; a reference implementation under PolyForm Noncommercial License 1.0.0 consisting of a drop-in PyTorch recipe and statistical-tests reproduction script; and supporting reports with methodology and per-configuration leaderboards. SHA-256 INTEGRITY HASHES (anchored in the paper) 01_fullstack_master.json: 5821e03e3ee578efc19b7b59a78c00d5a6314368f089927d22b261a644ebd74402_fullstack_tier_B.json: 1025168074f043db1420498df4946119cbfa7cf7ffb28323626d9c94385e823603_fullstack_tier_C.json: d2bf62f45e0856a85c804b1ff88cce810b8a8b4671f47fac87b4cc959e34191504_ablation_results.json: ec9e973e29755467f0eb12b846716d6ec9d23179e802d41769c3736e69c222be05_ablation_checkpoint.json: a40075183a32e087a7afd32803e08f8dd84672da03df290dfaf52eaa7c56f34a QUICK ADOPTION The recipe consists of three components and one negative limitation. (1) Set the learning rate to the exact value 0.031397115591219479. (2) Use AdamW or any standard optimizer (the recipe is optimizer-agnostic). (3) Apply ZClip (adaptive per-parameter gradient clipping) and LAWA (Latest Weight Averaging over the final 25 percent of training). (4) Do not apply a warmup-stable-decay scheduler; the affirmative exclusion of WSD is a material element of the recipe. The full reference implementation with self-test is provided in 04_reference_implementation/y_lr_recipe.py. PATENT AND INTELLECTUAL PROPERTY A U.S. patent application directed to the methods disclosed in this archive was filed by the inventor in May 2026. The application enjoys priority benefit from its earliest U.S. Provisional filing of May 26, 2026. This Zenodo publication is protected by the priority claim and does not constitute prior art against the patent application. The empirical use of the Y_2_LR constant in research and academic contexts is permitted under the licenses set forth above. Commercial-scale deployment may invoke licensable claims; commercial inquiries should be directed to the correspondence email above. CODE REPOSITORY Active development and community engagement: https://github.com/Yolazega/Y-LR CITATION Zemichiel, R. (2026). The Y_2 Learning Rate Recipe: Cross-Domain Production-Grade Neural-Network Training Reliability from a Single Mathematical Constant. Zenodo. https://doi.org/10.5281/zenodo.20408085 LICENSE AND PATENT NOTICE The source code in this release is licensed under the PolyForm Noncommercial License 1.0.0, free for academic research, personal evaluation, and non-profit use; commercial use requires a separate commercial license from the inventor. The paper, figures, and benchmark data are licensed under the Creative Commons Attribution 4.0 International License (CC-BY 4.0). For commercial licensing inquiries: [email protected]