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.
Astronomy! (Greig, Ting, and Kaurov 2022; S. (程思浩). Cheng et al. 2020) Via Yuan-Sen Ting.
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.
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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