# Stabilizing Backpropagation in 16-bit Neural Training with Modified Adam Optimizer

arXiv: https://arxiv.org/abs/2307.16189 · HTML: https://mlsanity.com/paper/2307.16189/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 18 references that are in the map.
- First posted on arXiv 30 Jul 2023.

## Builds on (most cited first, 8 of 8)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)

## Built on by (most cited first, 2 of 2)

- [Navigating LLM Valley: From AdamW to Memory-Efficient and Matrix-Based Optimizers](https://mlsanity.com/paper/2605.09176/) (2026)
- [Geometrical structures of digital fluctuations in parameter space of neural networks trained with adaptive momentum optimization](https://mlsanity.com/paper/2408.12273/) (2024)

## Abstract (arXiv)

In this research, we address critical concerns related to the numerical instability observed in 16-bit computations of machine learning models. Such instability, particularly when employing popular optimization algorithms like Adam, often leads to unstable training of deep neural networks. This not only disrupts the learning process but also poses significant challenges in deploying dependable models in real-world applications. Our investigation identifies the epsilon hyperparameter as the primary source of this instability. A nuanced exploration reveals that subtle adjustments to epsilon within 16-bit computations can enhance the numerical stability of Adam, enabling more stable training of 16-bit neural networks. We propose a novel, dependable approach that leverages updates from the Adam optimizer to bolster the stability of the learning process. Our contributions provide deeper insights into optimization challenges in low-precision computations and offer solutions to ensure the stability of deep neural network training, paving the way for their dependable use in various applications.