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 WHAT THIS IS Y_LR is a deterministic, zero-overhead, zero-search neural-network training recipe built for one thing above all others: RELIABILITY. It is a single fixed learning-rate constant (0.031397115591219479) combined with adaptive per-parameter gradient clipping (ZClip) and Latest Weight Averaging (LAWA). You set one number and never touch it again. It is not the fastest method on every problem. It is the method that arrives at the destination - a trained model - safely, reproducibly, and without a hyperparameter search. WHY IT IS DIFFERENT FROM ADAPTIVE OPTIMIZERS Modern parameter-free optimizers (Schedule-Free, Prodigy, D-Adaptation) and hyperparameter search frameworks (Optuna) are excellent at finding a good learning rate. But they share three structural costs that a fixed constant does not have: 1. THEY BREAK BIT-FOR-BIT REPRODUCIBILITY. Their effective learning rate is a function of the optimization trajectory - it depends on data order, batch size, and hardware floating-point behavior. The same code on different hardware produces a different training run. A fixed deterministic constant produces the identical run on 1 GPU or 256 GPUs. 2. THEY ADD COMPUTE AND MEMORY OVERHEAD. Prodigy carries roughly 2.67x the optimizer state of plain AdamW; Schedule-Free adds a full extra copy of the weights. Y_LR is a scalar fed to stock AdamW - exactly 1.0x, zero overhead. 3. THEY REQUIRE TUNING OR SEARCH. Optuna runs training N times to find a value. Parameter-free methods still need their own betas tuned and have documented divergence modes at small batch sizes. Y_LR is one published number that needs no search. These are different tools for different jobs. Y_LR is for when reproducibility, auditability, simplicity, and zero overhead matter more than squeezing out the last fraction of peak accuracy. WHO THIS IS FOR Y_LR is built for training contexts where a locked, auditable, reproducible procedure is a requirement, not a nice-to-have: - Regulated machine learning: medical-device software (FDA Good Machine Learning Practice), banking and credit models (Federal Reserve SR 11-7 model risk management), insurance and fraud models, and EU AI Act high-risk systems (Annex IV training-process documentation).- Resource-constrained training: edge devices, on-device fine-tuning, and 7B-70B model training where optimizer-state memory is the bottleneck.- Teams without hyperparameter-search infrastructure: independent researchers, small teams, and domain experts who need a sensible default that just works. Many of these domains - credit scoring, fraud detection, medical risk models, insurance underwriting - are predominantly tabular / MLP workloads, which is exactly the domain in which Y_LR was validated. THE EVIDENCE Across a controlled 25,000-run empirical study (6 optimizers, 4 MLP architectures, 3 feature-dimensionality tiers, 2 task types, 2 data modalities, 9 learning rates, 15 random seeds), the Y_LR constant: - Produced ZERO training divergences across all 540 Tier-A ablation runs, against industry-standard divergence rates of 20 to 35 percent for aggressive learning rates.- Achieved the LOWEST seed-to-seed standard deviation of any tested learning rate (most reproducible).- Beat the canonical Adam/AdamW default (learning rate 0.001) in 67.5 percent of head-to-head comparisons (81 wins to 39 losses across 120 configurations).- Friedman omnibus chi-squared(8) = 127.4, p < 10 to the negative 22 (precise survival-function p approximately 9.82 x 10 to the negative 24).- Cross-domain replication on genomic single-nucleotide-polymorphism data reproduced the primary findings. The headline is not "fastest." The headline is "most reliable, fully reproducible, zero overhead, zero search - with a statistically decisive reliability advantage over the universal default." SCOPE AND HONEST LIMITS This release validates Y_LR on MLP-family architectures with tabular and genomic data. Transformer, convolutional, recurrent, graph, and reinforcement-learning architectures, and direct head-to-head comparison against parameter-free optimizers on transformers, are explicitly out of scope and are the subject of a separate pre-registered benchmark (in progress). Results, positive or negative, will be published per the pre-registration commitment. THE RECIPE 1. Set the learning rate to the exact value 0.031397115591219479 and hold it constant.2. Use AdamW or any standard optimizer (the recipe is optimizer-agnostic).3. Apply ZClip (adaptive per-parameter gradient clipping; EMA decay 0.95, z-threshold 2.5).4. Apply LAWA (Latest Weight Averaging over the final 25 percent of training, six snapshots).5. Do not apply a warmup-stable-decay scheduler - it degrades the constant (clustering significance p = 1.55 x 10 to the negative 4). The full reference implementation, including a deterministic-mode helper for bit-reproducible runs, is in 04_reference_implementation/y_lr_recipe.py. CONTENTS OF THIS ARCHIVE The release includes: the paper (PDF and markdown source), benchmark data (approximately 5 MB of JSON with SHA-256 integrity hashes covering more than 25,000 runs), 44 publication-grade figures, a reference implementation under PolyForm Noncommercial 1.0.0, and supporting reports. 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 CODE REPOSITORY 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.20417266 LICENSE AND PATENT NOTICE The source code 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 CC-BY 4.0. A U.S. patent application directed to the disclosed methods was filed in May 2026, with priority benefit from its earliest U.S. Provisional filing of May 26, 2026. This publication is protected by the priority claim and does not constitute prior art against the patent application. For commercial licensing inquiries: [email protected]