Generalize bilinear filler to for N-D multilinear filler

[christianpayer]

This branch changes the bilinear filler (#2213) to support an arbitrary number of dimensions. Also, different scaling factors for each dimension are supported. I changed the name of the filler from "bilinear" to "linear", as it suits better for its multi-dimensional functionality.

The usage of this filler is the same as before (see comments, or #2213). Tests are not included, but I plan to write some using python scikit-image.

[shelhamer]

While there is no reason this filler should be limited to 4-D, as it is now, this breaks backward compatibility as-is since there are existing definitions that make use of bilinear. See our upgrade proto code for an idea of how to automatically upgrade old definitions -- this is our practice for schema changes.

See #2213 for some earlier discussion of the naming. linear doesn't feel quite right since that could be nearly anything, although bilinear is admittedly over specific. Perhaps interp would do? The combination of a linear layer like Convolution and an interp filler might be clear enough.

Thoughts @longjon?

[longjon]

In the usual interpolation sense (i.e., as a function of coordinates), linear is not correct; bilinear functions are nonlinear functions which are separately linear in each of their arguments. interp is too generic, as there are non-bilinear interpolation methods (e.g., biquadratic or bicubic) which can be implemented using fillers and convolutions.

The generalization of bilinear is multilinear. Perhaps these could be accepted as synonyms.

[christianpayer]

Thanks for your suggestions. I agree that linear is not the best name and that multilinear is much better.
If you agree to use multilinear I will change it and adapt the code for upgrade proto.

[seanbell]

Shouldn't this be CHECK_GE, if you want to test the condition "at least 3"?

[christianpayer]

You are right, thanks for pointing that out. I will change it. I never tested the code for 1d inputs, but it should work, too.

[shelhamer]

@christianpayer I second multilinear, so if you agree then go ahead with the new name.
Once done, please squash your commits into a new commit with a message that reflects the new filler (in particular the new name and generality of dimensions). Thanks!

[christianpayer]

@shelhamer Thanks for the comments. I changed the name to multilinear, squashed the commit and changed the commit message.
I did not edit upgrade_proto.cpp, as I am not sure, where/how to change the code there. As far as I can see an upgrade of a filler name has not been done before. Do you want me to implement something like

bool NetNeedsWeightFillerUpgrade(const NetParameter& net_param);
void UpgradeNetWeightFiller(NetParameter* net_param);

in upgrade_proto.hpp/cpp?

[shelhamer]

@christianpayer adding the check NetNeedsWeightFIllerUpgrade() and update UpgradeNetWeightFiller() is the idea. You'll need to be a bit familiar with the C++ interface to protobuf, but hopefully the existing methods can be a guide. Here's a quick sketch to illustrate key pieces:

for (int i = 0; i < net_param->layer_size(); ++i) {
      if (net_param->layer(i).has_convolution_param()) {
          FillerParameter* filler_param = net_param->mutable_layer(i)->mutable_convolution_param()->mutable_filler_parameter();
          if (filler_param.type() == "bilinear") {
              filler_param->set_type("multilinear");
          }
      }
}

Care to take a stab at it and we'll go from there?

[christianpayer]

@shelhamer Thanks for the code snippet. I just implemented upgrade_proto for weight fillers and hope that this is what you had in mind.

[christianpayer]

Please do not merge this PR, as I implemented in the meantime a more general interpolation filler, that allows linear/cubic/lanczos interpolation and rewrites most of the code of this PR.
Next week I will create a new PR with this more general filler.

[christianpayer]

Closed in favour of #4198.