Clips values of multiple tensors by the ratio of the sum of their norms.

Given a tuple or list of tensors t_list, and a clipping ratio clip_norm, this operation returns a list of clipped tensors list_clipped and the global norm (global_norm) of all tensors in t_list. Optionally, if you've already computed the global norm for t_list, you can specify the global norm with use_norm.

To perform the clipping, the values t_list[i] are set to:

t_list[i] * clip_norm / max(global_norm, clip_norm)


global_norm = sqrt(sum([l2norm(t)**2 for t in t_list]))

If clip_norm > global_norm then the entries in t_list remain as they are, otherwise they're all shrunk by the global ratio.

If global_norm == infinity then the entries in t_list are all set to NaN to signal that an error occurred.

Any of the entries of t_list that are of type None are ignored.

This is the correct way to perform gradient clipping (Pascanu et al., 2012).

However, it is slower than clip_by_norm() because all the parameters must be ready before the clipping operation can be performed.