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Dmytro Mishkin 🇺🇦

OK, let’s try to have an ML-related conversation. Any tried to train a model to solve math equations or systems of them?
How much overhead ? Any reason to use it? Original solver is not differentiable, but new one is?
E.g “Learning to Solve Hard Minimal Problems “ is faster, but less successful that Niester arxiv.org/abs/2112.03424, also requiring special formulation. Obviously one can use huge models like GPT3, but that’s impractical.

arXiv.orgLearning to Solve Hard Minimal ProblemsWe present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization problem into a minimal problem with many spurious solutions. Our approach avoids computing large numbers of spurious solutions. We design a learning strategy for selecting a starting problem-solution pair that can be numerically continued to the problem and the solution of interest. We demonstrate our approach by developing a RANSAC solver for the problem of computing the relative pose of three calibrated cameras, via a minimal relaxation using four points in each view. On average, we can solve a single problem in under 70 $μs.$ We also benchmark and study our engineering choices on the very familiar problem of computing the relative pose of two calibrated cameras, via the minimal case of five points in two views.

As a toy scale exp, it would be interesting to learn cubic eq solver with NN and SGD. Bonus question: it is easier to network to learn if we spesent the cubic equatiom coeffs, or the several (x,y) pairs?
@brohrer @francoisfleuret do you have anything similar in your DL courses?