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Make your PyTorch faster

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Variational Dropout Sparsifies NN (Pytorch)

license PyPI version

Make your neural network 300 times faster!

Pytorch implementation of Variational Dropout Sparsifies Deep Neural Networks (arxiv:1701.05369).


The discovered approach helps to train both convolutional and dense deep sparsified models without significant loss of quality. Additive Noise Reparameterization and the Local Reparameterization Trick discovered in the paper helps to eliminate weights prior's restrictions () and achieve Automatic Relevance Determination (ARD) effect on (typically most) network's parameters. According to the original paper, authors reduced the number of parameters up to 280 times on LeNet architectures and up to 68 times on VGG-like networks with a negligible decrease of accuracy. Experiments with Boston dataset in this repository proves that: 99% of simple dense model were dropped using paper's ARD-prior without any significant loss of MSE. Moreover, this technique helps to significantly reduce overfitting and helps to not worry about model's complexity - all redundant parameters will be dropped automatically. Moreover, you can achieve any degree of regularization variating regularization factor tradeoff (see reg_factor variable in and scripts)


import torch_ard as nn_ard
from torch import nn
import torch.nn.functional as F

input_size, hidden_size, output_size = 60, 150, 1

model = nn.Sequential(
    nn_ard.LinearARD(input_size, hidden_size),
    nn_ard.LinearARD(hidden_size, output_size)

reg_factor = 1.0
criterion = lambda input, target: F.binary_cross_entropy(input, target) + reg_factor*nn_ard.get_ard_reg(model)
print('Sparsification ratio: %.3f%%' % (100.*nn_ard.get_dropped_params_ratio(model)))


pip install pytorch-ard


All experiments are placed at examples folder and contains baseline and implemented models comparison.

Boston dataset

Two scripts were used in the experiment: and Training procedure for each experiment was 100000 epoches, Adam(lr=1e-3). Baseline model was dense neural network with single hidden layer with hidden size 150.

Baseline (nn.Linear) LinearARD, no reg LinearARD, reg=0.0001 LinearARD, reg=0.001 LinearARD, reg=0.1 LinearARD, reg=1
MSE (train) 1.751 1.626 1.587 1.962 17.167 33.682
MSE (test) 22.580 16.229 15.957 8.416 25.695 30.231
Compression, % 0 0.38 52.95 64.19 97.29 99.29

You can see on the table above that variating regularization factor any degree of compression can be achieved (for example, ~99.29% of connections can be dropped if reg_factor=1 will be used). Moreover, you can see that training with LinearARD layers with some regularization parameters (like reg=0.001 in the table above) not only significantly reduces number of model parameters (>64% of parameters can be dropped after training), but also significantly increases quality on test, reducing overfitting.


  1. Despite the high performance of implemented layers in "end-to-end" mode, authors recommends to use in fine-tuning pretrained models without ARD prior. In this case the best performance could be achieved. Moreover, it will be faster - despite of comparable convergence speed of this layers optimization, each training epoch takes more time (approx. twice longer - ~2 times more parameters in *ARD implementations). This fact well describable - using ARD prior in earlier stages can drop useful connections with unobvious dependencies.
  2. Model's sparsification takes almost no any speed-up effects until You convert it to the sparse one! (TODO)


  • PyTorch >= 0.4.0
  • SkLearn >= 0.19.1
  • Pandas >= 0.23.3
  • Numpy >= 1.14.5


  • [X] LinearARD layer implementation
  • [X] Conv2dARD layer implementation
  • [ ] Learnable bias for Conv2dARD
  • [ ] Implement to_sparse(model) utility


  title={Variational Dropout Sparsifies Deep Neural Networks},
  author={Molchanov, Dmitry and Ashukha, Arsenii and Vetrov, Dmitry},
  journal={arXiv preprint arXiv:1701.05369},

Original implementation (Theano/Lasagne)


  author = {Artem Ryzhikov},
  title = {HolyBayes/pytorch_ard},
  url = {},
  year = {2018}


Artem Ryzhikov, LAMBDA laboratory, Higher School of Economics, Yandex School of Data Analysis




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