hmatrix-backprop

hmatrix operations lifted for backprop, along with orphan instances of Backprop.

Meant to act as a drop-in replacement to the API of Numeric.LinearAlgebra.Static. Just change your imports, and your functions are automatically backpropagatable. Useful types are all re-exported.

Formulas for gradients come from the following papers:

• https://people.maths.ox.ac.uk/gilesm/files/NA-08-01.pdf
• http://www.dtic.mil/dtic/tr/fulltext/u2/624426.pdf
• http://www.cs.cmu.edu/~zkolter/course/15-884/linalg-review.pdf
• https://arxiv.org/abs/1602.07527

Some functions are not yet implemented! See module documentation for details. PR's definitely appreciated :)

Tests

Currently numeric tests are implemented as property tests using hedgehog, but it is possible that the answers might differ from the true values by an amount undetectable by property tests.

All functions currently are tested except for the higher-order functions.

They are tested by "nudging" components of inputs and checking if the change in the function outputs match what is expected from the backpropagated gradient.

TODO

1. Now that new backprop no longer requires Num, we can lift normal hmatrix operations as well.
2. Statically sized convolutions. Should probably add this to hmatrix instead first, though.