Have you ever looked at your thumb and admire how smart is your thumb? The protein molecules in your body can perform computation hundreds of times faster than a cluster of computers. There are three short stories that I want to tell. Tensor networks are tools that can be used to solve a wide class of data intensive problems in machine learning, physics, and signals processing. The basic idea is to turn a long vector or a large matrix into a tensor, then draw some cute diagrams. Each such diagram actually represents a formidable equation.
Another story here is Optimization beyond Grandma’s Lagrange Multiplier. The term Compressed Sensing means recovering a long vector by making a small number of measurements. Until a few years ago, to do compressed sensing, you need a matrix to satisfy RIP (restricted isometry property). What if your matrix does not satisfy RIP, but you have a good toolbox for solving optimization problems? For the third story, you will have to hear it at the talk.

Most of this talk will be accessible to graduate students in mathematics.

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