# Optimal Mini-Batch Size Selection for Fast Gradient Descent

arXiv: https://arxiv.org/abs/1911.06459 · HTML: https://mlsanity.com/paper/1911.06459/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2019.

## Built on by (most cited first, 3 of 3)

- [Phase transitions in the mini-batch size for sparse and dense two-layer neural networks](https://mlsanity.com/paper/2305.06435/) (2023)
- [Time-sensitive Learning for Heterogeneous Federated Edge Intelligence](https://mlsanity.com/paper/2301.10977/) (2023)
- [Integration of TinyML and LargeML: A Survey of 6G and Beyond](https://mlsanity.com/paper/2505.15854/) (2025)

## Abstract (arXiv)

This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and software implementation details, we reveal a robust empirical inverse law between mini-batch size and the average number of SGD updates required to converge to a specified error threshold. Combining this empirical inverse law with measured system performance, we create an accurate, closed-form model of average training time and show how this model can be used to identify quantifiable implications for both algorithmic and hardware aspects of machine learning. We demonstrate the inverse law empirically, on both image recognition (MNIST, CIFAR10 and CIFAR100) and machine translation (Europarl) tasks, and provide a theoretic justification via proving a novel bound on mini-batch SGD training.