[Paper Review] The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks

Jonathan Frankle, Michael Carbin|arXiv (Cornell University)|Mar 9, 2018

Adversarial Robustness in Machine Learning64 references1,319 citations

TL;DR

The paper shows dense neural networks contain sparse subnetworks (winning tickets) that, when initialized to their original values and trained from the start, can match the original's accuracy in similar iterations, often at 10–20% of the parameters.

ABSTRACT

Neural network pruning techniques can reduce the parameter counts of trained networks by over 90%, decreasing storage requirements and improving computational performance of inference without compromising accuracy. However, contemporary experience is that the sparse architectures produced by pruning are difficult to train from the start, which would similarly improve training performance. We find that a standard pruning technique naturally uncovers subnetworks whose initializations made them capable of training effectively. Based on these results, we articulate the "lottery ticket hypothesis:" dense, randomly-initialized, feed-forward networks contain subnetworks ("winning tickets") that - when trained in isolation - reach test accuracy comparable to the original network in a similar number of iterations. The winning tickets we find have won the initialization lottery: their connections have initial weights that make training particularly effective. We present an algorithm to identify winning tickets and a series of experiments that support the lottery ticket hypothesis and the importance of these fortuitous initializations. We consistently find winning tickets that are less than 10-20% of the size of several fully-connected and convolutional feed-forward architectures for MNIST and CIFAR10. Above this size, the winning tickets that we find learn faster than the original network and reach higher test accuracy.

Motivation & Objective

• Motivate why pruning-friendly sparse architectures are desirable for training efficiency and inference.
• Test whether sparse subnetworks exist that can be trained from their original initialization to achieve comparable performance.
• Empirically identify winning tickets across MNIST and CIFAR-10 using iterative pruning.
• Assess how initialization, sparsity, and architecture affect trainability and generalization of winning tickets.

Proposed method

• Train a dense network, prune smallest-magnitude weights, and reset surviving weights to their initial values to form a winning ticket.
• Iteratively prune a fraction p^(1/n) of remaining weights over n rounds to find smaller winning tickets.
• Compare training dynamics and test accuracy of winning tickets against the original network under SGD/momentum/Adam.
• Evaluate both fully-connected and convolutional architectures on MNIST and CIFAR-10.
• When reinitializing winning tickets, reset to random initializations and observe performance to test initialization importance.

Experimental results

Research questions

• RQ1 Do sparse subnetworks exist within randomly initialized dense networks that can be trained to comparable accuracy as the full network?
• RQ2 How does iterative pruning versus one-shot pruning affect the size and performance of winning tickets?
• RQ3 What is the role of initialization versus network structure in the success of winning tickets?
• RQ4 Do winning tickets generalize better than the original network, and under what sparsity levels?

Key findings

• Winning tickets exist at 10–20% of the original parameter count and can match or exceed test accuracy in comparable training iterations.
• Iterative pruning finds smaller winning tickets that learn faster and often achieve higher test accuracy than the original network.
• Random reinitialization of a winning ticket’s weights degrades performance, highlighting the importance of the initial initialization.
• Winning tickets show improved generalization, with smaller gaps between training and test accuracy at certain sparsities.
• The effect is observed across multiple architectures (Lenet, Conv-2/4/6, VGG-19, ResNet-18) and optimizers, though learning rate and warmup can influence success, especially in deeper nets.