Predicting Training Time Without Training

TL;DR

This paper introduces a method to predict the training time of deep networks during fine-tuning by modeling training dynamics with a low-dimensional SDE, significantly reducing computational costs.

Contribution

We propose a novel approach that uses linearized models and SDEs to accurately predict training time without actual training, enabling efficient resource estimation.

Findings

Predicts ResNet training time within 20% error margin

Achieves 30-45 times reduction in computational cost

Can predict training time on large datasets using subset sampling

Abstract

We tackle the problem of predicting the number of optimization steps that a pre-trained deep network needs to converge to a given value of the loss function. To do so, we leverage the fact that the training dynamics of a deep network during fine-tuning are well approximated by those of a linearized model. This allows us to approximate the training loss and accuracy at any point during training by solving a low-dimensional Stochastic Differential Equation (SDE) in function space. Using this result, we are able to predict the time it takes for Stochastic Gradient Descent (SGD) to fine-tune a model to a given loss without having to perform any training. In our experiments, we are able to predict training time of a ResNet within a 20% error margin on a variety of datasets and hyper-parameters, at a 30 to 45-fold reduction in cost compared to actual training. We also discuss how to further reduce the computational and memory cost of our method, and in particular we show that by exploiting the spectral properties of the gradients' matrix it is possible predict training time on a large dataset while processing only a subset of the samples.