# Training Neural Networks with Optimal Double-Bayesian Learning

arXiv: https://arxiv.org/abs/2605.20009 · HTML: https://mlsanity.com/paper/2605.20009/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [Train faster, generalize better: Stability of stochastic gradient descent](https://mlsanity.com/paper/1509.01240/) (2015)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [MedGAN: Medical Image Translation using GANs](https://mlsanity.com/paper/1806.06397/) (2018)
- [Transformation Consistent Self-ensembling Model for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/1903.00348/) (2019)
- [Towards Theoretically Understanding Why SGD Generalizes Better Than ADAM in Deep Learning](https://mlsanity.com/paper/2010.05627/) (2020)
- [Improving Generalization Performance by Switching from Adam to SGD](https://mlsanity.com/paper/1712.07628/) (2017)
- [Covid-19: Automatic detection from X-Ray images utilizing Transfer Learning with Convolutional Neural Networks](https://mlsanity.com/paper/2003.11617/) (2020)
- [Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks](https://mlsanity.com/paper/1806.06763/) (2018)
- [Rethinking the Hyperparameters for Fine-tuning](https://mlsanity.com/paper/2002.11770/) (2020)
- [Adaptive Inertia: Disentangling the Effects of Adaptive Learning Rate and Momentum](https://mlsanity.com/paper/2006.15815/) (2020)
- [Double-Bayesian Learning](https://mlsanity.com/paper/2410.12984/) (2024)

## Abstract (arXiv)

Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely acknowledged that selecting appropriate parameters is crucial for avoiding overfitting and achieving unbiased outcomes, this choice remains largely based on empirical experiments and experience. This paper presents a new probabilistic framework for the learning rate, a key parameter in stochastic gradient descent. The framework develops classic Bayesian statistics into a double-Bayesian decision mechanism involving two antagonistic Bayesian processes. A theoretically optimal learning rate can be derived from these two processes and used for stochastic gradient descent. Experiments across various classification, segmentation, and detection tasks corroborate the practical significance of the theoretically derived learning rate. The paper also discusses the ramifications of the proposed double-Bayesian framework for network training and model performance.