README.md

Relative gradient optimization of the Jacobian term in unsupervised deep learning

Reference implementation for the paper Relative gradient optimization of the Jacobian term in unsupervised deep learning

• https://arxiv.org/abs/2006.15090

A commented implementation of a training example over the MNIST dataset is found in the following notebooks (JAX and PyTorch versions):

• mnist_training.ipynb.
• mnist_training_pytorch.ipynb.

To reproduce the results reported in the paper, see below.

Requirements

Packages

To install required python packages:

pip install -r requirements.txt

Datasets

MNIST and CIFAR are automatically downloaded when needed.

To download and setup the needed UCI datasets, follow the instructions in https://github.com/gpapamak/maf#how-to-get-the-datasets and put the individual datasets folders inside experiments/storage.

Training

To train the model in the paper, run the command:

$ cd experiments
$ python train.py <args>

Here is the full list of optional arguments:

--epochs           number of epochs of training
--batch_size       size of the batches
--lr               adam: learning rate
--log_every        interval between logs
--seed             random generator seed
--dataset          one among: MNIST | CIFAR | POWER | GAS | HEPMASS | MINIBOONE | BSDS300 | TOY
--toy_name         one among: sine | moons | smile | 2spirals | checkerboard | rings | trimodal
--num_layers       define a model with `num_layers - 1` linear layers and 1 final affine layer
--nonlinearity     nonlinear activation function
--alpha            angular coefficient for the left side of RELU-type activation functions
--look_ahead       stop training if no improvement has been observed for `look_ahead` epochs
--log_dir          directory in which to save the model (ending in '/')
--bias             whether to include the bias in the linear layers or not
--trick            whether to apply the relative trick to the gradients or not
--generation       whether to perform data generation during training

Examples

To train the model over the MNIST dataset specifying a set of hyperparameters, run:

$ python train.py --dataset MNIST
                  --log_dir mnist_run1/
                  --batch_size 10
                  --lr 1e-4
                  --bias True
                  --num_layers 2

To train over the sine toy distribution:

$ python train.py --dataset TOY --toy_name sine

Evaluation

To evaluate a trained model, run:

$ cd experiments
$ python eval.py --dataset MNIST --log_dir mnist_run1/
Test set evaluation: -1375.2 +- 1.4

Results

Our model achieves the following performance for the density estimation task on the tested datasets:

POWER	GAS	HEPMASS	MINIBOONE	BSDS300	MNIST
0.065 +- 0.013	6.978 +- 0.020	-21.958 +- 0.019	-13.372 +- 0.450	151.12 +- 0.28	-1375.2 +- 1.4