# Mini-batch descent in semiflows

arXiv: https://arxiv.org/abs/2407.07556 · HTML: https://mlsanity.com/paper/2407.07556/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2024.

## Built on by (most cited first, 1 of 1)

- [Convergence, design and training of continuous-time dropout as a random batch method](https://mlsanity.com/paper/2510.13134/) (2025)

## Abstract (arXiv)

This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss functions over time, defining a piecewise flow. We prove that, under suitable assumptions on the potential generating the semiflow, the textitmini-batch descent flow trajectory closely approximates the original semiflow trajectory on average. In addition, we study a randomized minimizing movement scheme that also approximates the semiflow of the full loss function. We illustrate the versatility of this approach across various problems, including constrained optimization, sparse inversion, and domain decomposition. Finally, we validate our results with several numerical examples.