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I've seen examples of 2d decision boundaries taking on odd shapes, like spirals, and I've always been curious just how flexible neural networks can be. To that end, I tried to get it to learn a photograph, Elon Musk's face, and it worked. It seems to be the case that decision boundaries can be arbitrarily complex, assuming a sufficiently complex model. The photo is from wikipedia.jpg). The model takes in the x and y coordinates of each pixel, and is trained to predict the grayscale value mapped to values between 0 and 1. I used a decision threshold of 0.5. I've included both the image after applying the threshold(which illustrates the decision boundary), and the grayscale that the model generated before applying the threshold. I've also included what the model thinks a continuation of the image would look like. I also made a video of the training process, one image every few epochs, but can't share it on reddit :(. Anyway, hope everyone enjoys the pictures!
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