The Lottery Ticket Hypothesis


This codebase was developed by Jonathan Frankle and David Bieber at Google during the summer of 2018.


This library reimplements and extends the work of Frankle and Carbin in "The Lottery Ticket Hypothesis: Finding Small, Trainable Neural Networks" ( Their paper aims to explore why we find large, overparameterized networks easier to train than the smaller networks we can find by pruning or distilling. Their answer is the lottery ticket hypothesis:

Any large network that trains successfully contains a subnetwork that is initialized such that - when trained in isolation - it can match the accuracy of the original network in at most the same number of training iterations.

They refer to this special subset as a winning ticket.

Frankle and Carbin further conjecture that pruning a neural network after training reveals a winning ticket in the original, untrained network. They posit that were pruned after training were never necessary at all, meaning they could have been removed from the original network with no harm to learning. Once pruned, the original network becomes a winning ticket.

To evaluate the lottery ticket hypothesis in the context of pruning, they run the following experiment:

  1. Randomly initialize a neural network.

  2. Train the network until it converges.

  3. Prune a fraction of the network.

  4. To extract the winning ticket, reset the weights of the remaining portion of the network to their values from (1) - the initializations they received before training began.

  5. To evaluate whether the resulting network at step (4) is indeed a winning ticket, train the pruned, untrained network and examine its convergence behavior and accuracy.

Frankle and Carbin found that running this process iteratively produced the smallest winning tickets. That is, the network found at step (4) becomes a new network to train and further prune again at steps (2) and (3). By training, pruning, resetting, and repeating many times, Frankle and Carbin achieved their best results.


This library reimplements Frankle and Carbin's core experiment on fully-connected networks for MNIST (Section 2 of their paper). It also includes several additional capabilities for further examining the behavior of winning tickets.

Getting Started

  1. Run to install library dependencies.

  2. Modify mnist_fc/ to determine where to store MNIST (MNIST_LOCATION) and the data generated by experiments (EXPERIMENT_PATH).

  3. Run to install MNIST in those locations.

Code Walkthrough

This codebase is divided into four top-level directories: foundations, datasets, analysis, and mnist_fc.


The foundations directory contains all of the abstractions and machinery for running lottery ticket experiments.

Dataset and Model

A learning task is represented by two components: a Model to train and a Dataset on which to train that network. Base classes for these abstractions are in foundations/ and foundations/ Any networks on which you wish to run the lottery ticket experiment must subclass the ModelBase class in foundations/; likewise, any datasets on which you wish to train data must subclass the DatasetBase class in foundations/ foundations.model_fc implements a generic fully-connected model.

Model objects in this codebase have two special features that distinguish them from normal models:

Masks are the mechanism by which weights are pruned. To prune a weight, set the value of the corresponding position in the mask to 0. Presets are the mechanism by which a network can be initialized to specific values, making it possible to perform the "reset" step of the lottery ticket experiment.

ModelBase has a dense method that mirrors the tf.layers.dense method but automatically integrates masks and presets. You should use this method when you build your networks so that weights can properly be managed during the course of the lottery ticket experiment, and you may desire to write similar methods for conv2d, etc. if you want to work with other kinds of layers.

Trainer, Pruner, and Experiment

To train a network, run the train function of foundations.trainer, providing it with a Model and Dataset.

A lottery ticket experiment comprises iteratively training a network, pruning it, resetting it, and training it again. The infrastructure for doing so is in the experiment function of foundations.experiment. This function expects four functions as arguments (in addition to other parameters).

At a high level, here is how an experiment is structured:

Paths, Saving, and Restoring

The foundations.paths module contains helper functions for managing the locations where data generated by the experiments is stored. Each experiment generates five outputs:

foundations.paths has functions that create the appropriate filenames for each of these records when provided with the directory in which they should be stored. It also has functions that structure where the results of a particular experiment, trial, and run are stored.

The foundations.save_restore module contains functions for saving networks, masks, and experimental results.

Networks and masks are stored as dictionaries whose keys are layer names and whose values are numpy arrays of the corresponding values for each layer. The standardize function of foundations.save_restore takes as input either a dictionary storing a network or the path to the location where such a network is stored; either way, it returns the dictionary. This function is used throughout the codebase to handle cases where a network could be represented by either a path or a dictionary.


The datasets directory stores specific datasets - children of the DatasetBase class. Right now, only dataset_mnist is present.

MNIST on a Fully-Connected Network

The mnist_fc directory contains the experimental infrastructure for instantiating the foundations on a fully-connected network for MNIST. It has three main components:

Top-level Files

The top-level files (,, etc.) contain the infrastructure for running MNIST experiments.

Support infrastructure:

Infrastructure for running experiments:


For each of the scripts for running experiments, there is a corresponding runner which uses Python Fire to make these scripts callable from the command line. For example, you can run runners/ to execute it from the command line by using its function arguments as flags.


The argfiles directory contains scripts that generate sets of flags for the runners to perform experiments. The script will run the experiments specified in an argfile on a particular runner. For example:

python runners/ argfiles/

will run the lottery experiment for each of the sets of flags generated by

Disclaimer: This is not an official Google product.