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A single iteration of gradient descent can be parallelised across many worker nodes. We simple split the training set across the worker nodes, pass the parameters to each worker, each worker computes gradients for their subset of the training set, and then passes it back to the master to be averaged. With some effort, we can even use model parallelism.

However, stochastic gradient descent is an inherently serial proces. Each update must be performed sequentially. Each iteration, we must perform a broadcast and gather of all parameters. This is bad for performance. Ultimately, number of updates is the limiting factor of deep model training speed.

Why must we perform many updates? With how few updates can we achieve good accuracy?

What factors affect the minimum number of updates requires to reach some accuracy?

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In Don't Decay the Learning Rate, Increase the Batch Size, Smith et al. train ResNet-50 on ImageNet to 76.1% with only 2500 updates. Has anyone done it in less?

In The Impact of Neural Network Overparameterization on Gradient Confusion and Stochastic Gradient Descent Sankararaman et al. present the concept of gradient confusion which slows convergence, and show that depth increases gradient confusion while overparameterization on width and skip connections reduces gradient confusion.

In Massively Distributed SGD: ImageNet/ResNet-50 Training in a Flash, Mikami et al. train ResNet-50 on ImageNet to 75.29% with some number of updates, but I can't do the math to compute out how many updates they must have used.

To summarise:

  • Larger mini-batches help, but give diminishing returns and cause other issues.
  • Deeper models tend to require more updates.
  • Wider layers need fewer updates.
  • Skip connections, label smoothing, and batch norm might help.
  • The best I have found so far on ImageNet/ResNet-50 to >75% is 2500 updates.
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