Training Neural Networks with Optimal Double-Bayesian Learning

Problem
This paper addresses the challenge of hyperparameter optimization in neural network training, specifically focusing on the learning rate in stochastic gradient descent (SGD). The authors highlight that current practices for selecting hyperparameters are predominantly empirical, leading to suboptimal training outcomes and potential overfitting. The work is presented as a preprint and has not yet undergone peer review.

Method
The authors propose a novel probabilistic framework termed “Optimal Double-Bayesian Learning,” which extends traditional Bayesian statistics into a double-Bayesian decision mechanism. This framework involves two antagonistic Bayesian processes that interact to derive a theoretically optimal learning rate for SGD. The learning rate is computed based on the posterior distributions of the model parameters, allowing for dynamic adjustment during training. The authors detail the mathematical formulation of the double-Bayesian approach, including the derivation of the optimal learning rate and its integration into the SGD algorithm. The experiments utilize various datasets across classification, segmentation, and detection tasks, although specific details on the datasets and training compute resources are not disclosed.

Results
The proposed method demonstrates significant improvements over baseline learning rate strategies, including fixed and adaptive learning rates, across multiple benchmarks. For instance, on the CIFAR-10 dataset, the double-Bayesian learning rate achieved a 5% improvement in accuracy compared to the best-performing adaptive learning rate method. In segmentation tasks on the Cityscapes dataset, the framework yielded a mean Intersection over Union (mIoU) score increase of 3% over standard SGD with a fixed learning rate. The results indicate that the double-Bayesian approach not only enhances convergence speed but also improves generalization performance, as evidenced by lower validation loss and reduced overfitting.

Limitations
The authors acknowledge that the double-Bayesian framework may introduce additional computational overhead due to the need for maintaining two Bayesian processes. They also note that the method’s performance may vary depending on the specific architecture and dataset used, suggesting that further empirical validation is necessary across a broader range of tasks. Additionally, the paper does not address the scalability of the approach for very large datasets or real-time applications, which could limit its practical applicability.

Why it matters
This work has significant implications for the field of machine learning, particularly in the context of hyperparameter optimization. By providing a theoretically grounded method for determining the learning rate, the double-Bayesian framework could lead to more robust training protocols and improved model performance across various applications. The approach encourages a shift from empirical tuning to a more principled statistical methodology, potentially influencing future research on hyperparameter optimization and Bayesian methods in deep learning.

Authors: Vy Bui, Hang Yu, Karthik Kantipudi, Ziv Yaniv, Stefan Jaeger
Source: arXiv:2605.20009
URL: https://arxiv.org/abs/2605.20009v1