A transform landing somewhere between wavelets and convnets which can encode some desirable invariances (translation, rotation), and multiple moments of a random field.
More than that I do not know.
the original authors do, though; (Bruna and Mallat 2013; Mallat 2012).
Cheng and Ménard (2021) summarises some recent research in scattering transforms .
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]
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, and Brice Ménard. 2021. “How to Quantify Fields or Textures? A Guide to the Scattering Transform.” arXiv:2112.01288 [Astro-Ph, Physics:physics]
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]