@conference {677817,
	title = {Encoding Involutory Invariance in Neural Networks},
	booktitle = {IJCNN at IEEE World Congress on Computational Intelligence},
	year = {2022},
	abstract = {
	In certain situations, Neural Networks (NN) are trained upon data that obey underlying physical symmetries. However, it is not guaranteed that NNs will obey the underlying\&nbsp;symmetry unless embedded in the network structure. In this work, we explore a special kind of symmetry where functions are invariant with respect to involutory linear/affine transformations up to parity\&nbsp;p\&nbsp;=\&nbsp;{\textpm}1. We develop mathe- matical theorems and propose NN architectures that ensure invariance and universal approximation properties. Numerical experiments indicate that the proposed mod- els outperform baseline networks while respecting the imposed symmetry. An adaption of our technique to convolutional NN classification tasks for datasets with inherent horizontal/vertical reflection symmetry has also been proposed.

},
	url = {https://arxiv.org/pdf/2106.12891.pdf},
	author = {Anwesh Bhattacharya and Marios Mattheakis and Pavlos Protopapas}
}
