r""" Computes auxiliary load balancing loss as in Switch Transformer - implemented in Pytorch. See Switch Transformer (https://arxiv.org/abs/

Process a single sample: extract logprobs, compress, and write to disk.

Compute the KL divergence between a dense set of predictions and a sparse set of target logits. See `sparse_kl_div` for details.

Compute the Total Variation Distance (TVD) between dense student predictions and sparse teacher targets. See `sparse_tvd_div` for details.