Gradient descent on a non-Euclidean surface

Is the salesman travelling on foot or on an airplane? This article describes an experiment to develop a version of the elastic net algorithm that works on spherical surfaces. I needed it for a computational neuroscience problem, but for those who are mainly interested in machine learning, it also serves a simple and intuitive demonstration of using gradient descent on non-Euclidian surfaces. The Tensorflow source code is available on GitHub. I also made a youtube video showing the algorithm in action.
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