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This article suggests that deep learning is not designed to produce the universal algorithm and cannot be used to create such a complex systems.

First of all it requires huge amounts of computing power, time and effort to train the algorithm the right way and adding extra layers doesn't really help to solve complex problems which cannot be easily predicted.

Secondly some tasks are extremely difficult or impossible to solve using DNN, like solving a math equations, predicting pseudo-random lists, fluid mechanics, guessing encryption algorithms, or decompiling unknown formats, because there is no simple mapping between input and output.

So I'm asking, are there any alternative learning algorithms as powerful as deep architectures for general purpose problem solving? Which can solve more variety of problems, than "deep" architectures cannot?

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Have you read the book The Master Algorithm: by Pedro Domingos?

He discusses the present day machine learning algorithms... Their strengths, weaknesses and applications...

  • Deep Neural Network
  • Genetic Algorithm
  • Bayesian Network
  • Support Vector Machine
  • Inverse Deduction

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Deep learning is actually pretty useful (relative to other techniques) precisely when there is no simple mapping between input and output, and features from the raw input need to be aggregated and combined in complex ways by successive layers to form the output.

As I pointed out in my answer to the AI SE decompilation question, there is recent DL research which takes a natural language description as input and generates program text as output. Despite working in this general research area, I was personally surprised by this - the problem is significantly harder than the 'AI math' link you provide above.

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