Learning eigenvalue decomposition

Question

How would you build a fully connected neural network that learns eigenvalue decomposition efficiently?

I wanted to build NNs that can predict certain properties about matrices which are NP-hard to compute but might require eigenvalue decomposition. However, I am not sure if hardcode-calculating eigenvalues at any specific layer would be a good idea, because I feel the need to find eigenvalues shouldn't be pre-determined at a certain layer and maybe yield issues in backpropagating errors.

Ofcourse, I may be wrong and hence, looking for some advice.

Answer 1

This smells like an XY problem. A neural network is not a good tool to use for computing the eigenvalue decomposition. Machine learning is best for problems where you have examples of input-output pairs but you don't know of a classical algorithm to solve the problem. That doesn't apply here.

If you think that the eigenvalue decomposition of a matrix might help a neural network to learn the desired output, then compute the eigenvalue decomposition via a standard algorithm and feed it in as an additional input (additional features).

That said, I feel wary about the entire direction you are sketching. If you are trying to solve a NP-hard problem, I suspect there's a good likelihood that neural nets are probably not a helpful direction. Neural nets are not magic pixie dust that can solve every problem. See, e.g., Evolving artificial neural networks for solving NP problems and https://cs.stackexchange.com/a/128555/755 and https://cs.stackexchange.com/a/130272/755.