Multiclass hinge losses for TensorFlow.

Tested with TensorFlow 2.4.1 and 2.5.0.

This package implements the following losses in the permutation-equivariant relative-margin (PERM) loss framework (more on this at the very end):

1. Weston-Watkins hinge. Reference.
2. Crammer-Singer hinge. Reference.
3. Duchi-Ruan-Khosravi hinge. Referred to as the family-wise loss and the adversarial zero-one loss.
4. Cross entropy.

There are examples in the jupyter_notebooks directory.

The notebook 02_linear_WWSVM_in_TensorFlow.ipynb shows how to use TensorFlow to train linear multiclass SVMs.

The notebook 03_comparing_cross_entropy_implementations.ipynb compares our implementation of the cross entropy with the standard TensorFlow's implementation. (They are probably the same).

Fictitiously asked questions, since this repository may still be unknown.

By THE cross entropy, I am referring to tf.keras.losses.CategoricalCrossentropy(from_logits=True). This is based on absolute margins. I will call this the absolute margin CE in contrast to our PERM CE.

So the answer is probably yes. For shallow models, they are equivalent. See jupyter_notebooks/03_comparing_cross_entropy_implementations.ipynb for a demonstration. It can be proved that relative and absolute margin cross entropies result in the same optimization trajectories for convex models.

However, the PERM CE is strictly convex while the absolute margin CE is not. Whether this leads to any differences when training deep models is, the jury is still out.

Since the multiclass hinges (DKR, WW, and CS) losses are implemented in the PERM loss framework, it's handy to implement the cross entropy also in this framework. It makes for easy apple-to-apple comparison. However, in the future, it may be useful to implement the absolute margin versions of these losses as well.

See jupyter_notebooks/01_introduction_to_PERM_losses.ipynb.