Scattering transforms



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Transforms landing somewhere between wavelets and convnets which can encode some desirable invariances (translation, rotation), and multiple moments of a random field. This is not the same thing as scattering theory in physics, although presumably if I read deep enough I will find that the scattering transforms are named for scattering theory.

More than that I do not know. The original authors do, though; (Bruna and Mallat 2013; Mallat 2012). S. Cheng and Ménard (2021) summarises some recent research in scattering transforms.

References

Bruna, Joan, and Stephane Mallat. 2013. Invariant Scattering Convolution Networks.” IEEE Transactions on Pattern Analysis and Machine Intelligence 35 (8): 1872–86.
———. 2019. Multiscale Sparse Microcanonical Models.” arXiv:1801.02013 [Math-Ph, Stat], May.
Bruna, Joan, Stéphane Mallat, Emmanuel Bacry, and Jean-François Muzy. 2015. Intermittent Process Analysis with Scattering Moments.” The Annals of Statistics 43 (1): 323–51.
Cheng, Sihao (程思浩), Yuan-Sen (丁源森) Ting, Brice Ménard, and Joan Bruna. 2020. A New Approach to Observational Cosmology Using the Scattering Transform.” Monthly Notices of the Royal Astronomical Society 499 (4): 5902–14.
Cheng, Sihao, and Brice Ménard. 2021. How to Quantify Fields or Textures? A Guide to the Scattering Transform.” arXiv:2112.01288 [Astro-Ph, Physics:physics], November.
Greig, Bradley, Yuan-Sen (丁源森) Ting, and Alexander A Kaurov. 2022. Exploring the Cosmic 21-Cm Signal from the Epoch of Reionization Using the Wavelet Scattering Transform.” Monthly Notices of the Royal Astronomical Society 513 (2): 1719–41.
Mallat, Stéphane. 2012. Group Invariant Scattering.” Communications on Pure and Applied Mathematics 65 (10): 1331–98.
Oyallon, Edouard, Eugene Belilovsky, and Sergey Zagoruyko. 2017. Scaling the Scattering Transform: Deep Hybrid Networks.” arXiv Preprint arXiv:1703.08961.
Sprechmann, Pablo, Joan Bruna, and Yann LeCun. 2014. Audio Source Separation with Discriminative Scattering Networks.” arXiv:1412.7022 [Cs], December.
Wiatowski, Thomas, Philipp Grohs, and Helmut Bölcskei. 2018. Energy Propagation in Deep Convolutional Neural Networks.” IEEE Transactions on Information Theory 64 (7): 1–1.

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