Training Neural Networks with Optimal Double-Bayesian Learning

2026-05-20 · Source: cs.NE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Health & Medical Research · Depth: Expert, extended

Summary

A new probabilistic framework, called double-Bayesian learning, has been developed to derive an optimal learning rate for neural network training with Stochastic Gradient Descent (SGD). This framework conceptualizes training as two antagonistic Bayesian processes, drawing parallels to the golden ratio and the Pythagorean identity. The derived optimal learning rate is approximately 0.016, with a corresponding momentum weight of 0.874. Extensive experiments across handwritten digit classification (MNIST), tuberculosis classification (TBX11K), lung segmentation (COVID19 dataset), and malaria parasite detection tasks (NLM Malaria Data) validated these theoretical values. The study compared SGD with the Adam optimizer, demonstrating that SGD, when optimally tuned with the derived hyperparameters, consistently outperformed Adam in generalization and robustness to noise, despite Adam's faster convergence.

Key takeaway

For AI Engineers optimizing neural network training, consider adopting the theoretically derived SGD learning rate of approximately $0.016$ and a momentum weight of $0.874$. Your models will likely achieve better generalization performance and increased robustness to noisy data compared to using Adam, especially in critical applications like medical image analysis where data quality can vary. While Adam may converge faster, SGD's superior generalization can lead to more reliable and less biased models.

Key insights

A double-Bayesian framework theoretically derives optimal SGD hyperparameters, showing superior generalization over Adam.

Principles

• Optimal hyperparameters can be theoretically derived.
• Uncertainty in measurements drives double-Bayesian processes.
• The golden ratio defines equilibrium in Bayesian processes.

Method

The double-Bayesian approach involves two parallel Bayesian processes that resolve intrinsic uncertainties in measurements, leading to the derivation of an optimal learning rate (0.016) and momentum weight (0.874) for SGD.

In practice

• Use $\eta \approx 0.016$ and $\alpha \approx 0.874$ for SGD.
• Prefer SGD over Adam for noise robustness.
• Consider SGD for better generalization on unseen data.

Topics

• Double-Bayesian Learning
• Neural Network Training
• Stochastic Gradient Descent
• Hyperparameter Optimization
• Adam Optimizer

Code references

• v7labs/covid-19-xray-dataset
• ultralytics/ultralytics

Best for: AI Engineer, NLP Engineer, Computer Vision Engineer, AI Scientist, Machine Learning Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.NE updates on arXiv.org.