# Scattering transforms

March 16, 2022 — August 31, 2022

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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.

## 1 Interesting applications

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

## 2 References

Bruna, and Mallat. 2013. “Invariant Scattering Convolution Networks.”

*IEEE Transactions on Pattern Analysis and Machine Intelligence*.
———. 2019. “Multiscale Sparse Microcanonical Models.”

*arXiv:1801.02013 [Math-Ph, Stat]*.
Bruna, Mallat, Bacry, et al. 2015. “Intermittent Process Analysis with Scattering Moments.”

*The Annals of Statistics*.
Cheng, Sihao, and Ménard. 2021. “How to Quantify Fields or Textures? A Guide to the Scattering Transform.”

Cheng, Sihao (程思浩), Ting, Ménard, et al. 2020. “A New Approach to Observational Cosmology Using the Scattering Transform.”

*Monthly Notices of the Royal Astronomical Society*.
Greig, Ting, and 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*.
Mallat. 2012. “Group Invariant Scattering.”

*Communications on Pure and Applied Mathematics*.
Oyallon, Belilovsky, and Zagoruyko. 2017. “Scaling the Scattering Transform: Deep Hybrid Networks.”

*arXiv Preprint arXiv:1703.08961*.
Sprechmann, Bruna, and LeCun. 2014. “Audio Source Separation with Discriminative Scattering Networks.”

*arXiv:1412.7022 [Cs]*.
Wiatowski, Grohs, and Bölcskei. 2018. “Energy Propagation in Deep Convolutional Neural Networks.”

*IEEE Transactions on Information Theory*.