Department of

October 2020 November 2020 December 2020 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 1 2 3 4 5 6 7 1 2 3 4 5 4 5 6 7 8 9 10 8 9 10 11 12 13 14 6 7 8 9 10 11 12 11 12 13 14 15 16 17 15 16 17 18 19 20 21 13 14 15 16 17 18 19 18 19 20 21 22 23 24 22 23 24 25 26 27 28 20 21 22 23 24 25 26 25 26 27 28 29 30 31 29 30 27 28 29 30 31

Tuesday, November 3, 2020

**Abstract:** The scattering transform is a mathematical framework for understanding convolutional neural networks (CNNs) introduced by S. Mallat. Similar to more traditional CNNs, the scattering transform is a deep, feed-forward network featuring an alternating cascade of convolutions and nonlinearities. However, it differs by using predesigned, wavelet filters rather than filters that are learned from training data. This leads to a network that provably has desirable invariance and stability properties. In addition to preforming well on standard machine learning tasks such as image recognition. The scattering transform can also be used to extract statistical information about stochastic processes with stationary increments. The expected scattering moments are a novel form of nonparametric statistics which can be used to distinguish random textures with identical power spectrums. I will present Mallat's original construction as well as several novel variations designed for structured data such as graphs. In particular, I will discuss the use of one of the more recent construction to distinguish between different types of randomly generated graphs.