# Multilevel Initialization for Layer-Parallel Deep Neural Network Training

arXiv: https://arxiv.org/abs/1912.08974 · HTML: https://mlsanity.com/paper/1912.08974/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2019.

## Built on by (most cited first, 7 of 7)

- [Globally Convergent Multilevel Training of Deep Residual Networks](https://mlsanity.com/paper/2107.07572/) (2021)
- [Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training](https://mlsanity.com/paper/2302.07049/) (2023)
- [Parallel Training of GRU Networks with a Multi-Grid Solver for Long Sequences](https://mlsanity.com/paper/2203.04738/) (2022)
- [Training of deep residual networks with stochastic MG/OPT](https://mlsanity.com/paper/2108.04052/) (2021)
- [Layer-Parallel Training for Transformers](https://mlsanity.com/paper/2601.09026/) (2026)
- [Multilevel-in-Layer Training for Deep Neural Network Regression](https://mlsanity.com/paper/2211.06515/) (2022)
- [A Multi-Level Framework for Accelerating Training Transformer Models](https://mlsanity.com/paper/2404.07999/) (2024)

## Abstract (arXiv)

This paper investigates multilevel initialization strategies for training very deep neural networks with a layer-parallel multigrid solver. The scheme is based on the continuous interpretation of the training problem as a problem of optimal control, in which neural networks are represented as discretizations of time-dependent ordinary differential equations. A key goal is to develop a method able to intelligently initialize the network parameters for the very deep networks enabled by scalable layer-parallel training. To do this, we apply a refinement strategy across the time domain, that is equivalent to refining in the layer dimension. The resulting refinements create deep networks, with good initializations for the network parameters coming from the coarser trained networks. We investigate the effectiveness of such multilevel "nested iteration" strategies for network training, showing supporting numerical evidence of reduced run time for equivalent accuracy. In addition, we study whether the initialization strategies provide a regularizing effect on the overall training process and reduce sensitivity to hyperparameters and randomness in initial network parameters.