Fishr: Invariant Gradient Variances for Out-of-distribution Generalization

Official PyTorch implementation of the Fishr regularization for out-of-distribution generalization, ICML 2022 | paper

Alexandre Ramé, Corentin Dancette, Matthieu Cord

Abstract

Learning robust models that generalize well under changes in the data distribution is critical for real-world applications. To this end, there has been a growing surge of interest to learn simultaneously from multiple training domains - while enforcing different types of invariance across those domains. Yet, all existing approaches fail to show systematic benefits under fair evaluation protocols.

In this paper, we propose a new learning scheme to enforce domain invariance in the space of the gradients of the loss function: specifically, we introduce a regularization term that matches the domain-level variances of gradients across training domains. Critically, our strategy, named Fishr, exhibits close relations with the Fisher Information and the Hessian of the loss. We show that forcing domain-level gradient covariances to be similar during the learning procedure eventually aligns the domain-level loss landscapes locally around the final weights.

Extensive experiments demonstrate the effectiveness of Fishr for out-of-distribution generalization. In particular, Fishr improves the state of the art on the DomainBed benchmark and performs significantly better than Empirical Risk Minimization.

Installation

Requirements overview

Our implementation relies on the BackPACK package in PyTorch to easily compute gradient variances.

• python == 3.7.10
• torch == 1.8.1
• torchvision == 0.9.1
• backpack-for-pytorch == 1.3.0
• numpy == 1.20.2

Procedure

1. Clone the repo:

$ git clone https://github.com/alexrame/fishr.git

2. Install this repository and the dependencies using pip:

$ conda create --name fishr python=3.7.10
$ conda activate fishr
$ cd fishr
$ pip install -r requirements.txt

With this, you can edit the Fishr code on the fly.

Overview

This github enables the replication of our two main experiments: (1) on Colored MNIST in the setup defined by IRM and (2) on the DomainBed benchmark.

Colored MNIST in the IRM setup

We first validate that Fishr tackles distribution shifts on the synthetic Colored MNIST.

Main results (Table 2 in Section 6.A)

To reproduce the results from Table 2, call python3 coloredmnist/train_coloredmnist.py --algorithm $algorithm where algorithm is either:

• erm for Empirical Risk Minimization
• irm for Invariant Risk Minimization
• rex for Out-of-Distribution Generalization via Risk Extrapolation
• fishr for our proposed Fishr

Results will be printed at the end of the script, averaged over 10 runs. Note that all hyperparameters are taken from the seminal IRM implementation.

    Method | Train acc. | Test acc.  | Gray test acc.
   --------|------------|------------|----------------
    ERM    | 86.4 ± 0.2 | 14.0 ± 0.7 |   71.0 ± 0.7
    IRM    | 71.0 ± 0.5 | 65.6 ± 1.8 |   66.1 ± 0.2
    V-REx  | 71.7 ± 1.5 | 67.2 ± 1.5 |   68.6 ± 2.2
    Fishr  | 71.0 ± 0.9 | 69.5 ± 1.0 |   70.2 ± 1.1

Without label flipping (Table 5 in Appendix C.2.3)

The script coloredmnist.train_coloredmnist also accepts as input the argument --label_flipping_prob which defines the label flipping probability. By default, it's 0.25, so to reproduce the results from Table 5 you should set --label_flipping_prob 0.

Fishr variants (Table 6 in Appendix C.2.4)

This table considers two additional Fishr variants, reproduced with algorithm set to:

• fishr_offdiagonal for Fishr but without centering the gradient variances
• fishr_notcentered for Fishr but on the full covariance rather than only the diagonal

DomainBed

DomainBed is a PyTorch suite containing benchmark datasets and algorithms for domain generalization, as introduced in In Search of Lost Domain Generalization. Instructions below are copied and adapted from the official github.

Algorithms and hyperparameter grids

We added Fishr as a new algorithm here, and defined Fishr's hyperparameter grids here, as defined in Table 7 in Appendix D.

Datasets

We ran Fishr on following datasets:

• Rotated MNIST (Ghifary et al., 2015)
• Colored MNIST (Arjovsky et al., 2019)
• VLCS (Fang et al., 2013)
• PACS (Li et al., 2017)
• OfficeHome (Venkateswara et al., 2017)
• A TerraIncognita (Beery et al., 2018) subset
• DomainNet (Peng et al., 2019)

Launch training

Download the datasets:

python3 -m domainbed.scripts.download\
       --data_dir=/my/data/dir

Train a model for debugging:

python3 -m domainbed.scripts.train\
       --data_dir=/my/data/dir/\
       --algorithm Fishr\
       --dataset ColoredMNIST\
       --test_env 2

Launch a sweep for hyperparameter search:

python -m domainbed.scripts.sweep launch\
       --data_dir=/my/data/dir/\
       --output_dir=/my/sweep/output/path\
       --command_launcher MyLauncher
       --datasets ColoredMNIST\
       --algorithms Fishr

Here, MyLauncher is your cluster's command launcher, as implemented in command_launchers.py.

Performances inspection (Tables 3 and 4 in Section 6.B.2, Tables in Appendix G)

To view the results of your sweep:

python -m domainbed.scripts.collect_results\
       --input_dir=/my/sweep/output/path

We inspect performances using following model selection criteria, that differ in what data is used to choose the best hyper-parameters for a given model:

• OracleSelectionMethod (Oracle): A random subset from the data of the test domain.
• IIDAccuracySelectionMethod (Training): A random subset from the data of the training domains.

Critically, Fishr performs consistently better than Empirical Risk Minimization.

Model selection	Algorithm	Colored MNIST	Rotated MNIST	VLCS	PACS	OfficeHome	TerraIncognita	DomainNet	Avg
Oracle	ERM	57.8 ± 0.2	97.8 ± 0.1	77.6 ± 0.3	86.7 ± 0.3	66.4 ± 0.5	53.0 ± 0.3	41.3 ± 0.1	68.7
Oracle	Fishr	68.8 ± 1.4	97.8 ± 0.1	78.2 ± 0.2	86.9 ± 0.2	68.2 ± 0.2	53.6 ± 0.4	41.8 ± 0.2	70.8
Training	ERM	51.5 ± 0.1	98.0 ± 0.0	77.5 ± 0.4	85.5 ± 0.2	66.5 ± 0.3	46.1 ± 1.8	40.9 ± 0.1	66.6
Training	Fishr	52.0 ± 0.2	97.8 ± 0.0	77.8 ± 0.1	85.5 ± 0.4	67.8 ± 0.1	47.4 ± 1.6	41.7 ± 0.0	67.1

Conclusion

We addressed the task of out-of-distribution generalization for computer vision classification tasks. We derive a new and simple regularization - Fishr - that matches the gradient variances across domains as a proxy for matching domain-level Hessians. Our scalable strategy reaches state-of-the-art performances on the DomainBed benchmark and performs better than ERM. Our empirical experiments suggest that Fishr regularization would consistently improve a deep classifier in real-world applications when dealing with data from multiple domains. If you need help to use Fishr, please open an issue or contact alexandre.rame@lip6.fr.

Citation

If you find this code useful for your research, please consider citing our work:

@inproceedings{rame2021ishr,
    title={Fishr: Invariant Gradient Variances for Out-of-distribution Generalization},
    author={Alexandre Rame and Corentin Dancette and Matthieu Cord},
    year={2022},
    booktitle={ICML}
}