This method identifies a binary weight or binary weight and activation subnetwork within a randomly initialized network that achieves performance comparable to, and sometimes better than, a weight-optimized network. The resulting binarized and pruned networks that achieve comparable performance are called Multi-Prize Tickets, abbreviated MPTs. The experiments conducted using biprop verify the following Multi-Prize Lottery Ticket Hypothesis:

A sufficiently over-parameterized neural network with random weights contains several subnetworks (winning tickets) that

1. Have comparable accuracy to a dense target network with learned weights (Prize 1)
2. Do not require any further training to achieve prize 1 (Prize 2)
3. Is robust to extreme forms of quantization (i.e., binary weights and/or activation) (Prize 3)

More extensive details and motivation can be found in our ICLR 2021 paper:

Multi-Prize Lottery Ticket Hypothesis: Finding Generalizable and Efficient Binary Subnetworks in a Randomly Weighted Neural Network

This implementation of biprop was built on top of the hidden-networks repository from the Allen Institute for AI.

The following updates have been added to biprop to reflect several implementation details that were developed for our NeurIPS 2021 paper A Winning Hand: Compressing Deep Networks Can Improve Out-Of-Distribution Robustness

The original implementation of biprop pruned the network in a layerwise fashion, that is, the fraction of unpruned parameters in each layer was equal to the prune_rate argument. This update includes an option to prune the network globally, that is, the fraction of unpruned parameters globally is equal to the prune_rate argument however the fraction of unpruned weights in each layer is not constrained to be equal to prune_rate. Our experiments in A Winning Hand (see Figure 5 in Appendix C) illustrate that globally pruned networks are capable of achieving higher accuracy at higher sparsity levels when compared to layerwise pruned models.

• Global pruning can be accomplished by adding the flag --conv-type GlobalSubnetConv to any new training run.

• Note that for models pruned at 50% sparsity or higher, the prune_rate is updated using a progressive scheduler to avoid layer collapse (i.e., when an entire layer is pruned). By default, this scheduler will reach the full sparsity at 10 epochs but this number of epochs can be specified by the user with the flag --prune_rate_epoch.

The Augmix and Gaussian data augmentation schemes utilized in A Winning Hand have been added to this implementation of biprop for public use and experimentation.

Augmix: We incorporated the official Augmix repo implementation of Augmix. The following arguments were added to facilitate the use of Augmix with biprop:

• Use --augmix when training to use Augmix.
• Use --jsd when training with Augmix to add the Jensen-Shannon divergence term to the loss function.
• Use --mixture-width to set the number of augmentation chains to mix per augmented example. By default, this value is 3.
• Use --mixture-depth to set the depth of augmentation chains. -1 denotes stochastic depth in [1, 3]. By default, this value is -1.
• Use --aug-severity to set the severity of base augmentation operators. By default, this value is 3.

Gaussian: The Gaussian implementation randomly adds gaussian noise to training images. The following arguments were added to control the standard deviation and probability of noise being added to images:

• Use --gaussian_aug when training to using this gaussian data augmentation method.
• Use --std_gauss to set the variance of the sampled gaussian noise. By default, this value is 0.1.
• Use --p_clean to set the probability that an image is clean (i.e., gaussian noise is not added to image). By default this value is 1 (all images will be clean).

From this version forward, all saved models now include fields containing the conv_type, prune_rate, and arguments relating to Augmix and Gaussian data augmentation schemes. The conv_type and prune_rate flags allow pretrained models to be properly loaded without requiring additional user flags. However, when loading pretrained models trained prior to this update a warning will be raised indicating that the conv_type and prune_rate should be specified to ensure proper loading of the model. Additionally, we include a train_augmentation field to enable the user to perform a quick check of which augmentation scheme was used during training. Additional augmentation settings (e.g. p_clean and jsd) are also included in the saved model file so that this information is preserved with the model and not just in the auxiliary settings.txt file.

Use the biprop.yml file to create a conda environment in which to run biprop.

1. Create a conda environment with python 3.7.4.
2. Use the requirements.txt file with pip install -r requirements.txt to install necessary requirements

Configurations for various experiments can be found as YAML files in the configs/ folder. Each of the configurations can be executed on a single node or multi-node (distributed) setup. It is likely that most users will require the single node configuration, the multi-node configuration was added for the larger experiments (ImageNet). Single node setups are sufficient for CIFAR-10 experiments.

The command to run a single node experiment is of the form:

python main.py --config <path/to/config> <override-args>

and a multi-node experiment is of the form:

python parallel_main.py --config <path/to/config> <override-args>

Note that the single node configuration should work as-is while the multi-node configuration will likely require minor configuration based on specific details of the user's distributed computing set up.

All override-args can be found in the args.py file. Examples include --multigpu=<gpu-ids seperated by commas, no spaces> to run on GPUs on a single node, and --prune-rate to set the prune rate, which denotes the fraction of weights remaining in the identified MPT. For example, a prune_rate of 0.4 will result in a MPT in which 40% of the weights are binarized and 60% are pruned.

For each model, there are configuration files for identifying Multi-Prize Tickets with binary weights and full precision activations, called MPT-1/32, and Multi-Prize Tickets with binary weights and binary activations, called MPT-1/1. Below we provide the naming conventions for configuration files corresponding to MPT-1/32 and MPT-1/1 experiments:

<network>_<initialization>.yml --------> MPT-1/32 (Binary weights and full precision activation)
<network>_BinAct_<initialization>.yml -> MPT-1/1  (Binary weights and binary activation)

Additionally, embedded in each configuration file name is the initialization used for that configuration. Below is a list of all initializations already implemented for use and the corresponding abbreviation found in the configuration file. While all of these initializations are available, note that the experiments involving MPT-1/32 and MPT-1/1 make use of the Kaiming normal and signed constant initializations.

(u)uc -> (unscaled) unsigned constant
(u)sc -> (unscaled) signed constant
(u)kn -> (unscaled) kaiming normal

If affine is in the configuration filename, it indicates a batchnorm configuration with trainable parameters. Batchnorm training can be turned on with the --learn_batchnorm flag.

Below is a sample call to identify a MPT-1/1 within the Conv4 network that has binarized 20% of the original weights and pruned the remaining 80%. In this call, a MPT-1/1 will be identified using two GPUs on a single node with the network weights initialized using a scaled Kaiming normal initialization:

python main.py --config configs/smallscale/conv4/conv4_BinAct_kn_unsigned.yml \
               --multigpu 0,1 \
               --name conv4_mpt_1_1 \
               --data <path/to/data-dir> \
               --prune-rate 0.2

To identify a MPT-1/32 within the same network, one can use the following call. Note that the only necessary change is the configuration file but that we have also changed the name of the run so that it matches the identified MPT.

python main.py --config configs/smallscale/conv4/conv4_kn_unsigned.yml \
               --multigpu 0,1 \
               --name conv4_mpt_1_32 \
               --data <path/to/data-dir> \
               --prune-rate 0.2

The file mpt_cifar_script.sh will identify MPT-1/32 and MPT-1/1 networks in the Conv2/4/6/8 architectures on CIFAR-10 from the aforementioned paper for prune rates of 0.8, 0.6, 0.5, 0.4, 0.2, and 0.1. This script will require at least minimal modifications to run (such as providing user specific DATA and LOG directory information) but may require some additional modifications depending on the user's configuration.

Below we state the best performing MPT-1/32 and MPT-1/1 networks for CIFAR-10 and ImageNet. Note that +BN indicates subnetworks in which the batchnorm parameters were learned when identifying the subnetwork using BIPROP.

Below we state the best performing MPT-1/32 networks for ImageNet on various networks.

To use a pretrained model use the --pretrained=<path/to/pretrained-checkpoint> flag. Pretrained models are provided in the pretrained directory. To evaluate a pretrained model on the test dataset, add the --evaluate flag.

tensorboard --logdir runs/ --bind_all

When your experiment is done, a CSV entry will be written (or appended) to runs/results.csv. Your experiment base directory will automatically be written to runs/<config-name>/prune-rate=<prune-rate>/<experiment-name> with checkpoints/ and logs/ subdirectories. If your experiment happens to match a previously created experiment base directory then an integer increment will be added to the filepath (eg. /0, /1, etc.). Checkpoints by default will have the first, best, and last models. To change this behavior, use the --save-every flag.

BIPROP has been tested with Python 3.7.4, CUDA 10.0/10.1 and PyTorch 1.3.0/1.3.1. Below is a list of requirements that can be used to install requirements (other than Python and CUDA):

absl-py==0.8.1
grpcio==1.24.3
Markdown==3.1.1
numpy==1.17.3
Pillow==6.2.1
protobuf==3.10.0
PyYAML==5.1.2
six==1.12.0
tensorboard==2.0.0
torch==1.3.0
torchvision==0.4.1
tqdm==4.36.1
Werkzeug==0.16.0

SPDX-License-Identifier: (Apache-2.0)

LLNL-CODE-817561