2021

Symmetry meets AI

Barenboim, Gabriela, Hirn, Johannes, Sanz, Veronica

Understand

We explore whether Neural Networks (NNs) can {\it discover} the presence of symmetries as they learn to perform a task.

For this, we train hundreds of NNs on a {\it decoy task} based on well-controlled Physics templates, where no information on symmetry is provided.
We use the output from the last hidden layer of all these NNs, projected to fewer dimensions, as the input for a symmetry classification task, and show that information on symmetry had indeed been identified by the original NN without guidance.
As an interdisciplinary application of this procedure, we identify the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van Gogh.

G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto and L. Zdeborová, “Machine learning and the physical sciences,” Rev. Mod. Phys. 91
Original
1903
Earlier work this paper cites.
S. M. Udrescu and M. Tegmark, “AI Feynman: a Physics-Inspired Method for Symbolic Regression,” Sci. Adv. 6
Original
1905
Earlier work this paper cites.
F. J. Hasert et al
1973
Earlier work this paper cites.
Canny, J., “A Computational Approach To Edge Detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6):679–698, 1986
1986
Earlier work this paper cites.

R. M. Haralick, S. R. Sternberg and X. Zhuang, “Image Analysis Using Mathematical Morphology,” in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-9, no. 4, pp. 532-550, July 1987, doi: 10.1109/TPAMI.1987.4767941
1987
Cited alongside, same era.
S. Krippendorf and M. Syvaeri, “Detecting Symmetries with Neural Networks,” [arXiv:2003.13679 [physics.comp-ph]]
Original
2003
Cited alongside, same era.
P. Locher and C. Nodine. “The perceptual value of symmetry” In Symmetry 2, pp. 475-484. Pergamon, 1989. I.C. McManus. “Symmetry and asymmetry in aesthetics and the arts.” European Review 13, no. S2 (2005): 157
2005
Cited alongside, same era.
Goodfellow, Ian J., Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. ”Generative adversarial networks.” arXiv preprint arXiv:1406.2661 (2014)
Original
2014
Cited alongside, same era.
See the tool’s webpage at https://www.fast.ai/
Cited in the paper.

He, Kaiming, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. “Deep residual learning for image recognition,” Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778. 2016
2016
Later among the works it cites.
L. N. Smith. “A disciplined approach to neural network hyper-parameters: Part 1–learning rate, batch size, momentum, and weight decay.” arXiv preprint arXiv:1803.09820 (2018)
Original
2018
Later among the works it cites.
Kingma, D. P. and Welling, M.“ An Introduction to Variational Autoencoders,” Foundations and Trends in Machine Learning: Vol. 12 (2019): No. 4, pp 307-392; doi:10.1561/2200000056
2019
Later among the works it cites.

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