FaceBook: 1 hour training ImageNet

Accurate, Large Minibatch SGD

Training ImageNet in 1 Hour

Main Idea

  • Higher training speed requires larger mini-batch size.

8192 images one batch, 256 GPUs

  • Larger mini-batch size leads to lower accuracy

  • Linear scaling rule for adjusting learning rates as a function of minibatch size

  • Warmup scheme overcomes optimization challenges early in training

Background

  • mini-batch SGD

  • Larger mini-batch size lead to lower accuracy.

mini-batch SGD

mini-batch SGD

  • Iteration(in FaceBook Paper):

  • Convergence:

    • Learning Rate:

    • Converge Speed:

    M: batch size, K: iteration number, σ²: stochastic gradient variance

Goal

  • Use large minibatches

    • scale to multiple workers

  • Maintaining training and generalization accuracy

Solution

  • Linear Scaling Rule: When the minibatch size is multiplied by k, multiply the learning rate by k.

Analysis

  • k iteration, minibatch size of n:

  • 1 iteration, minibatch size of kn:

  • Assume gradients of the above fomulas are equal

    • Two updates can be similar only if we set the second learning rate to k times the first learning rate.

Conditions that assumption not hold

  • Initial training epochs when the network is changing rapidly.

  • Results are stable for a large range of sizes, beyond a certain point

Warm Up

  • Low learning rate to solve rapid change of the initial network.

  • Constant Warmup: Sudden change of learning rate causes the training error to spike.

  • Gradual warmup: Ramping up the learning rate from a small to a large value.

  • start from a learning rate of η and increment it by a constant amount at each iteration such that it reaches η̂ = kη after 5 epochs.

Reference