Yin-Yang Dataset

This deep learning dataset was developed for research on biologically plausible error-backpropagation and deep learning in spiking neural networks. It serves as an alternative to e.g. the MNIST dataset providing the following advantages:

Very clear gap between the accuracies reached by a linear classifier/shallow network, a deep neural network and a deep network with frozen lower weights
Smaller and therefore faster to train
Symmetric input design allows successful training of neuron models without intrinsic bias

For more information see:

The Yin-Yang dataset; L. Kriener, J. Göltz, M. A. Petrovici; https://doi.org/10.1145/3517343.3517380 (https://arxiv.org/abs/2102.08211)

Structure

As shown in the image below each data sample consists of 4 values (x1, y1, x2, y2) where x2 and y2 are generated by a mirrored axis. This symmetry is helpful when training neuron models without intrinsic bias.

Each data sample is classified into one of the three classes yin (blue), yang (orange) and dot (green). All classes have approximately the same amount of samples.

Data generation

In order to produce a balanced dataset, the data is generated with rejection sampling:

draw random integer between 0 and 2, this is the desired class c of the next sample that will be generated
draw x1 and y1 value and calculate the corresponding x2 and y2
check if the drawn sample is of class c
- if yes: keep sample
- if no: draw new x1 and y1 and check again
repeat until chosen number of samples are produced

The equations for the calclulation of the Yin-Yang shape are inspired by: https://link.springer.com/content/pdf/10.1007/11564126_19.pdf (Appendix A).

Usage

This dataset is designed to make use of the PyTorch dataset and dataloader architecture, but (with some minor changes) it can also be used in any other deep learning framework.

PyTorch

A detailed example is shown in example.ipynb.

Initializing the dataset:

from dataset import YinYangDataset

dataset_train = YinYangDataset(size=5000, seed=42)
dataset_validation = YinYangDataset(size=1000, seed=41)
dataset_test = YinYangDataset(size=1000, seed=40)

Note: It is very important to give different seeds for trainings-, validation- and test set, as the data is generated randomly using rejection sampling. Therefore giving the same seed value will result in having the same samples in the different datasets!

Setting up PyTorch Dataloaders:

from torch.utils.data import DataLoader

batchsize_train = 20
batchsize_eval = len(dataset_test)

train_loader = DataLoader(dataset_train, batch_size=batchsize_train, shuffle=True)
val_loader = DataLoader(dataset_validation, batch_size=batchsize_eval, shuffle=True)
test_loader = DataLoader(dataset_test, batch_size=batchsize_eval, shuffle=False)

Other deep learning frameworks

Even though this dataset is designed for PyTorch, the following easy code changes make it useable in any deep learning framework:

In dataset.py delete line 2

from torch.utils.data.dataset import Dataset

and replace in line 5

class YinYangDataset(Dataset):

class YinYangDataset(object):

The dataset can now be loaded as shown above. The data can be iterated over, saved to file or imported in other frameworks.

Reference results

These references are generated with the same settings for network layout and training (hidden layer of 30 neurons for the ANN, batchsize of 20, learning rate of 0.01, adam optimizer, 300 epochs for the ANN as well as the shallow network) as in example.ipynb. The training was repeated 20 times with randomly chosen weight initializations. The accuracies are given as mean and standard devaition over the 20 runs. For more details see https://doi.org/10.1145/3517343.3517380 (https://arxiv.org/abs/2102.08211).

Network	Test accuracy [%]
ANN (4-30-3)	97.6 +- 1.5
ANN (4-30-3) frozen lower weights	85.5 +- 5.8
Shallow network	63.8 +- 1.0

Usage in publications

Up until now this dataset has been used in the following publications:

Fast and deep: energy-efficient neuromorphic learning with first-spike times; J. Göltz∗, L. Kriener∗, A. Baumbach, S. Billaudelle, O. Breitwieser, B. Cramer, D. Dold, A. F. Kungl, W. Senn, J. Schemmel, K. Meier, M. A. Petrovici; https://www.nature.com/articles/s42256-021-00388-x (https://arxiv.org/abs/1912.11443)
EventProp: Backpropagation for Exact Gradients in Spiking Neural Networks; T. Wunderlich and C. Pehle; https://www.nature.com/articles/s41598-021-91786-z (https://arxiv.org/abs/2009.08378)
A scalable approach to modeling on accelerated neuromorphic hardware; E. Müller, E. Arnold, O. Breitwieser, M. Czierlinski, A. Emmel, J. Kaiser, C. Mauch, S. Schmitt, P. Spilger, R. Stock, Y. Stradmann, J. Weis, A. Baumbach, S. Billaudelle, B. Cramer, F. Ebert, J. Göltz, J. Ilmberger, V. Karasenko, M. Kleider, A. Leibfried, C. Pehle, J. Schemmel; https://www.frontiersin.org/articles/10.3389/fnins.2022.884128/full
Exact gradient computation for spiking neural networks through forward propagation; J. H. Lee, S. Haghighatshoar, A. Karbasi; https://proceedings.mlr.press/v206/lee23b.html (https://arxiv.org/abs/2210.15415)
Learning efficient backprojections across cortical hierarchies in real time; K. Max, L. Kriener, G. P. García, T. Nowotny, W. Senn, M. A. Petrovici; https://arxiv.org/abs/2212.10249
hxtorch.snn: Machine-learning-inspired Spiking Neural Network Modeling on BrainScaleS-2; P. Spilger, E. Arnold, L. Blessing, C. Mauch, C. Pehle, E. Müller, J. Schemmel; https://dl.acm.org/doi/abs/10.1145/3584954.3584993
Safe semi-supervised learning for pattern classification; J. Ma, G. Yu, W. Xiong, X. Zhu; https://doi.org/10.1016/j.engappai.2023.106021
Event-based Backpropagation for Analog Neuromorphic Hardware; C. Pehle, L. Blessing, E. Arnold, E. Müller, J. Schemmel; https://arxiv.org/abs/2302.07141

If you would like to use this dataset in a publication feel free to do so and please contact me so that this list can be updated (or update it yourself via a pull request).

The data used in the publication "Fast and deep: energy-efficient neuromorphic learning with first-spike times" is also uploaded as .npy files in publication_data/.

lkriener/yin_yang_data_set