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18.What is a convolution?

19.Image recognition Cornell Lab of Ornithology, Merlin bird identification app (see Van Horn et al. 2015)

20.Some classic CNNs

21.Convolutional filters: cross-correlation in 2 dimensions

22.Visualizing neurons in a network https://distill.pub/2017/feature-visualization/ Visualization by optimizing image to maximize activation at particular neurons/layers. How does this work?

23.Notes from previous lecture: sawtooth Sawtooth function The sawtooth function with 2 n pieces can be expressed succinctly with ~3n neurons (Telgarsky 2015) and depth ~2n. The naive shallow implementation takes exponentially more neurons.

24.Not entirely true Betsch et al 2004

25.Not entirely true Betsch et al 2004

26.Linear regions in ReLU nets Hanin & Rolnick (2019) Initialization Epoch 1 Epoch 20

27.Visual processing in the brain

28.Insights of U-Net “Up-convolution” Fixes the problem of s hrinking images with CNNs One example of how to make “fully convolutional” nets: pixels to pixels “Up-convolution” is just upsampling, then convolution Allows for refinement of the upsample by learned weights Goes along with decreasing the number of feature channels Not the same as “de-convolution”. Connections across the “U” in the architecture

29.Graph convolution For a full intro: https://tkipf.github.io/graph-convolutional-networks/ Basic idea: A convolution for matrices is a “local” combination of entries in the matrix Can do the same thing for a graph Here, “local” is whatever nodes a node is adjacent to Just the tip of an iceberg… Used in learning stuff about molecules, citations, social networks, etc.