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Wei_Dai comments on Approximating Solomonoff Induction - Less Wrong Discussion
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This is an interesting way to view neural networks. After seeing your post, I happened to come across Jürgen Schmidhuber's AMA, where he gave a similar but less detailed explanation about how "RNN-based CM system of 1990 may be viewed as a limited, downscaled, sub-optimal, but at least computationally feasible approximation of AIXI".