Introduction to Convolutional Neural Network (CNN/ConvNET)-insights from amateur George (Tian Zhou)

Big Thanks to Brandon’s Presentation Brandon Rohrer http://brohrer.github.io/how_convolutional _neural_networks_work.html https://brohrer.github.io/blog.html

A toy ConvNet: X’s and O’s Says whether a picture is of an X or an O CNN X or O We want to know if a given pixel is x or o. by passing the image through the black box “CNN” and CNN process it and gives a possibility of the prediction.

Convolution Kernal, Filter

Filtering: The math behind the match Line up the filter and the image patch. Multiply each image pixel by the corresponding filter pixel. Add them up. Divide by the total number of pixels in the filter. Move across

Line up the filter and the image patch. 1 x 1 = 1 Line up the filter and the image patch. Multiply each image pixel by the corresponding filter pixel. Add them up. Divide by the total number of pixels in the filter. Move across

1+1+1+1+1+1+1+1+1 9 =1

1+1−1+1+1+1−1+1+1 9 =.55 .55

Convolution: Trying every possible match

Convolution: Trying every possible match =

= = =

Convolution layer One image becomes a stack of filtered images (image feature is captured) First define three kernels and pass the image through the kernel to get a filtered picture (image feature is captured.).

Pooling Layer: Reduce the size of image Pick a window size (usually 2 or 3). Pick a stride (usually 2). Walk window across filtered images. From each window, take the maximum value. max pooling maximum

Pooling layer A stack of images becomes a stack of smaller images.

Rectified Linear Units (ReLUs) -Tuning maths A stack of images becomes a stack of images with no negative values.

Stacking Layers can be repeated several times. To achieve decent amount of “predictors” Convolution ReLU Pooling

X O 𝑥 1 𝑤 1 𝑤 2 𝑥 2 𝑤 3 𝑥 3 Σ Output Fully connected layer 𝑓(𝑥) Every value gets a vote, Vote depends on how strongly a value predicts X or O 𝑤 1 X 𝑤 2 𝑤 3 … 𝑤 12 O

X O

Fully connected layer of unknown image X .92 O .51

Putting it all together A set of pixels becomes a set of votes. .92 X O connected Fully connected Fully Convolution ReLU Convolution ReLU Pooling Convolution ReLU Pooling .51

Backpropagation .92 Error = right answer – actual answer X O CNN .51

Minimizing error For each feature pixel and voting weight, adjust it up and down a bit and see how the error changes. error weight

Decisions for CNN designers For each convolution layer, How many filter? How many pixels in each filter? For each pooling layer, What window size? What stride?

References Brandon Rohrer, http://brohrer.github.io/how_convolutional_neural_networks_work.html Gu, J., Wang, Z., Kuen, J., Ma, L., Shahroudy, A., Shuai, B., Liu, T., Wang, X., Wang, G., 2015. Recent advances in convolutional neural networks. arXiv:1512.07108. "Convolutional Neural Networks (LeNet) – DeepLearning 0.1 documentation". DeepLearning 0.1. LISA Lab. Hubel, D. and Wiesel, T. (1968). Receptive fields and functional architecture of monkey striate cortex. Journal of Physiology (London), 195, 215–243