# Improving the Sample-complexity of Deep Classification Networks with Invariant Integration

### Matthias Rath, Matthias Rath, Alexandru Paul Condurache, Alexandru Paul Condurache

#### 2022

#### Abstract

Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. This makes them applicable to practically important use-cases where training data is scarce. Rather than being learned, this knowledge can be embedded by enforcing invariance to those transformations. Invariance can be imposed using group-equivariant convolutions followed by a pooling operation. For rotation-invariance, previous work investigated replacing the spatial pooling operation with invariant integration which explicitly constructs invariant representations. Invariant integration uses monomials which are selected using an iterative approach requiring expensive pre-training. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. Additionally, we replace monomials with different functions such as weighted sums, multi-layer perceptrons and self-attention, thereby streamlining the training of invariant-integration-based architectures. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets where rotation-invariant-integration-based Wide-ResNet architectures using monomials and weighted sums outperform the respective baselines in the limited sample regime. We achieve state-of-the-art results using full data on Rotated-MNIST and SVHN where rotation is a main source of intraclass variation. On STL-10 we outperform a standard and a rotation-equivariant convolutional neural network using pooling.

Download#### Paper Citation

#### in Harvard Style

Rath M. and Condurache A. (2022). **Improving the Sample-complexity of Deep Classification Networks with Invariant Integration**. In *Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2022) - Volume 5: VISAPP*; ISBN 978-989-758-555-5, SciTePress, pages 214-225. DOI: 10.5220/0010872000003124

#### in Bibtex Style

@conference{visapp22,

author={Matthias Rath and Alexandru Paul Condurache},

title={Improving the Sample-complexity of Deep Classification Networks with Invariant Integration},

booktitle={Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2022) - Volume 5: VISAPP},

year={2022},

pages={214-225},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010872000003124},

isbn={978-989-758-555-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 17th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2022) - Volume 5: VISAPP

TI - Improving the Sample-complexity of Deep Classification Networks with Invariant Integration

SN - 978-989-758-555-5

AU - Rath M.

AU - Condurache A.

PY - 2022

SP - 214

EP - 225

DO - 10.5220/0010872000003124

PB - SciTePress