This repository contains code that demonstrate practical applications of Bayesian principles to Deep Learning. Our implementation contains an Adam-like optimizer, called VOGN, to obtain uncertainty in Deep Learning.

• 2D-binary classification (see toy example)
• Image classification (MNIST, CIFAR-10/100, and ImageNet)
• Continual learning for image classification (permuted MNIST)
• Per-pixel semantic labeling & segmentation (Cityscapes)

This repository uses PyTorch-SSO, a PyTorch extension for second-order optimization, variational inference, and distributed training.

$ git clone [email protected]:cybertronai/pytorch-sso.git
$ cd pytorch-sso
$ python setup.py install

Please follow the Installation of PyTorch-SSO for CUDA/MPI support.

Decision boundary and entropy plots on 2D-binary classification by MLPs trained with Adam and VOGN. VOGN optimizes the posterior distribution of each weight (i.e., mean and variance of the Gaussian). A model with the mean weights draws the red boundary, and models with the MC samples from the posterior distribution draw light red boundaries. VOGN converges to a similar solution as Adam while keeping uncertainty in its predictions.

With PyTorch-SSO (torchsso), you can run VOGN training by changing a line in your train script:

import torch
+import torchsso

train_loader = torch.utils.data.DataLoader(train_dataset) 
model = MLP()

-optimizer = torch.optim.Adam(model.parameters())
+optimizer = torchsso.optim.VOGN(model, dataset_size=len(train_loader.dataset))

for data, target in train_loader:

    def closure():
        optimizer.zero_grad()
        output = model(data)
        loss = F.binary_cross_entropy_with_logits(output, target)
        loss.backward()
        return loss, output

    loss, output = optimizer.step(closure)

To train MLPs by VOGN and Adam and create GIF

$ cd toy_example
$ python main.py

For detail, please see VOGN implementation in PyTorch-SSO.

This repository contains code for the NeurIPS 2019 paper "Practical Deep Learning with Bayesian Principles," [poster] which includes the results of Large-scale Variational Inference on ImageNet classification.

VOGN achieves similar performance in about the same number of epochs as Adam and SGD. Importantly, the benefits of Bayesian principles are preserved: predictive probabilities are well-calibrated (rightmost figure), uncertainties on out-of-distribution data are improved (please refer the paper), and continual-learning performance is boosted (please refer the paper, an example is to be prepared).

See classification (single CPU/GPU) or distributed/classification (multiple GPUs) for example scripts.

NeurIPS 2019 paper

@article{osawa2019practical,
  title = {Practical Deep Learning with Bayesian Principles},
  author = {Osawa, Kazuki and Swaroop, Siddharth and Jain, Anirudh and Eschenhagen, Runa and Turner, Richard E. and Yokota, Rio and Khan, Mohammad Emtiyaz},
  journal = {arXiv preprint arXiv:1906.02506},
  year = {2019}
}