# At Stability's Edge: How to Adjust Hyperparameters to Preserve Minima Selection in Asynchronous Training of Neural Networks?

arXiv: https://arxiv.org/abs/1909.12340 · HTML: https://mlsanity.com/paper/1909.12340/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2019.

## Built on by (most cited first, 16 of 16)

- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Adaptive Gradient Methods at the Edge of Stability](https://mlsanity.com/paper/2207.14484/) (2022)
- [On Linear Stability of SGD and Input-Smoothness of Neural Networks](https://mlsanity.com/paper/2105.13462/) (2021)
- [Stochastic Training is Not Necessary for Generalization](https://mlsanity.com/paper/2109.14119/) (2021)
- [Beyond the Quadratic Approximation: the Multiscale Structure of Neural Network Loss Landscapes](https://mlsanity.com/paper/2204.11326/) (2022)
- [Second-order regression models exhibit progressive sharpening to the edge of stability](https://mlsanity.com/paper/2210.04860/) (2022)
- [DoCoFL: Downlink Compression for Cross-Device Federated Learning](https://mlsanity.com/paper/2302.00543/) (2023)
- [TimelyFL: Heterogeneity-aware Asynchronous Federated Learning with Adaptive Partial Training](https://mlsanity.com/paper/2304.06947/) (2023)
- [Acceleration via Fractal Learning Rate Schedules](https://mlsanity.com/paper/2103.01338/) (2021)
- [Ordered Momentum for Asynchronous SGD](https://mlsanity.com/paper/2407.19234/) (2024)
- [μ2-SGD: Stable Stochastic Optimization via a Double Momentum Mechanism](https://mlsanity.com/paper/2304.04172/) (2023)
- [DropCompute: simple and more robust distributed synchronous training via compute variance reduction](https://mlsanity.com/paper/2306.10598/) (2023)
- [On the Interplay Between Stepsize Tuning and Progressive Sharpening](https://mlsanity.com/paper/2312.00209/) (2023)
- [Tensor-Parallelism with Partially Synchronized Activations](https://mlsanity.com/paper/2506.19645/) (2025)
- [Delayed Momentum Aggregation: Communication-efficient Byzantine-robust Federated Learning with Partial Participation](https://mlsanity.com/paper/2509.02970/) (2025)
- [Bringing Order to Asynchronous SGD: Towards Optimality under Data-Dependent Delays with Momentum](https://mlsanity.com/paper/2605.02043/) (2026)

## Abstract (arXiv)

Background: Recent developments have made it possible to accelerate neural networks training significantly using large batch sizes and data parallelism. Training in an asynchronous fashion, where delay occurs, can make training even more scalable. However, asynchronous training has its pitfalls, mainly a degradation in generalization, even after convergence of the algorithm. This gap remains not well understood, as theoretical analysis so far mainly focused on the convergence rate of asynchronous methods. Contributions: We examine asynchronous training from the perspective of dynamical stability. We find that the degree of delay interacts with the learning rate, to change the set of minima accessible by an asynchronous stochastic gradient descent algorithm. We derive closed-form rules on how the learning rate could be changed, while keeping the accessible set the same. Specifically, for high delay values, we find that the learning rate should be kept inversely proportional to the delay. We then extend this analysis to include momentum. We find momentum should be either turned off, or modified to improve training stability. We provide empirical experiments to validate our theoretical findings.