The Lottery Ticket Hypothesis Finding Sparse, Trainable Neural Networks

• Pruning can reduce network by 90% without compromising accuracy
• Standard pruning naturally uncovers sub-networks whose initialization made them capable of training effectively
• They find "winning tickets" consistently for MNSIT and CIFAR10

Formally:

• $f(x, \theta)$ is some dense FF network where $\theta_0 \sim D_\theta$ for some distribution of parameters $D_\theta$
• $f$ reaches $l$ validation loss and test accuracy $a$ at some iteration $j$ from e.g. SGD
• Consider training $f(x, m \dot \theta)$ for some fixed mask $m \in \{0, 1\}^{\Vert{\theta}\Vert}$
  • This will reach some validation loss $l'$, at iteration $j'$ for some test accuracy $a'$
• LTH States: $\exists M$ where $j' \leq j$, $a' \leq a$

To find such $M$ they propose an algorithm:

1. Randomly initialize $f(x, \theta_0)$
2. Train for some fixed iterations
3. Prune p% of the network, to construct the mask $M$
4. Reset the parameters to $\theta_0$ and retrain the model

Repeat this procedure iteratively over n rounds, combining the mask over each round. They should empirically that this out-performs doing this once.

They have experimental results on MNIST and CIFAR10