Improved Variational Online Newton (IVON)

We provide code of the IVON optimizer to train deep neural networks, along with a usage guide and small-scale examples.

Variational Learning is Effective for Large Deep Networks
Y. Shen*, N. Daheim*, B. Cong, P. Nickl, G.M. Marconi, C. Bazan, R. Yokota, I. Gurevych, D. Cremers, M.E. Khan, T. Möllenhoff
Paper: https://arxiv.org/abs/2402.17641

Installation of IVON

To install the IVON optimizer run: pip install ivon-opt

Dependencies

Install PyTorch as described here: pip3 install torch --index-url https://download.pytorch.org/whl/cu118

Usage guide

In Appendix A of the paper, we provide practical guidelines for choosing IVON hyperparameters.

Training loop

In the code snippet below we demonstrate the difference in the implementation of the training loop of the IVON optimizer compared to standard optimizers like SGD or Adam. The standard setting for weight sampling during training is to use one MC sample (train_samples=1).

import torch
+import ivon

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

-optimizer = torch.optim.Adam(model.parameters())
+optimizer = ivon.IVON(model.parameters(), lr=0.1, ess=len(train_dataset))

for X, y in train_loader:

+    for _ in range(train_samples):
+       with optimizer.sampled_params(train=True)
            optimizer.zero_grad()
            logit = model(X)
            loss = torch.nn.CrossEntropyLoss(logit, y)
            loss.backward()

    optimizer.step()

Prediction

There are two different ways of using the variational posterior of IVON for prediction:

(1) IVON can be used like standard optimizers:

for X, y in test_loader:
    logit = model(X)
    _, prediction = logit.max(1)

(2) A better way is to do posterior averaging. We can draw a total of test_samples weights from a Gaussian, predict with each one and average the predictions to obtain predictive probabilities.

for X, y in test_loader:
    sampled_probs = []
    for i in range(test_samples):
        with optimizer.sampled_params():
            sampled_logit = model(X)
            sampled_probs.append(F.softmax(sampled_logit, dim=1))
    prob = torch.mean(torch.stack(sampled_probs), dim=0)
    _, prediction = prob.max(1)

Examples

We include three Google Colab notebooks to demonstrate the usage of the IVON optimizers on small-scale problems.

1. MNIST image classification
   • We compare IVON to an SGD baseline.
2. 1-D Regression
   • IVON captures uncertainty in regions with little data. AdamW fails at this task.
3. 2-D Logistic Regression
   • SGD finds the mode of the weight posterior, while IVON converges to a region that is more robust to perturbation.

How to cite

@article{shen2024variational,
      title={Variational Learning is Effective for Large Deep Networks}, 
      author={Yuesong Shen and Nico Daheim and Bai Cong and Peter Nickl and Gian Maria Marconi and Clement Bazan and Rio Yokota and Iryna Gurevych and Daniel Cremers and Mohammad Emtiyaz Khan and Thomas Möllenhoff},
      journal={arXiv:2402.17641},
      year={2024},
      url={https://arxiv.org/abs/2402.17641}
}