Efficient softmax approximation as described in Efficient softmax approximation for GPUs by Edouard Grave, Armand Joulin, Moustapha Cissé, David Grangier, and Hervé Jégou

## Usage

```
nn_adaptive_log_softmax_with_loss(
in_features,
n_classes,
cutoffs,
div_value = 4,
head_bias = FALSE
)
```

## Arguments

- in_features
(int): Number of features in the input tensor

- n_classes
(int): Number of classes in the dataset

- cutoffs
(Sequence): Cutoffs used to assign targets to their buckets

- div_value
(float, optional): value used as an exponent to compute sizes of the clusters. Default: 4.0

- head_bias
(bool, optional): If

`True`

, adds a bias term to the 'head' of the adaptive softmax. Default:`False`

## Value

`NamedTuple`

with `output`

and `loss`

fields:

**output**is a Tensor of size`N`

containing computed target log probabilities for each example**loss**is a Scalar representing the computed negative log likelihood loss

## Details

Adaptive softmax is an approximate strategy for training models with large output spaces. It is most effective when the label distribution is highly imbalanced, for example in natural language modelling, where the word frequency distribution approximately follows the Zipf's law.

Adaptive softmax partitions the labels into several clusters, according to their frequency. These clusters may contain different number of targets each.

Additionally, clusters containing less frequent labels assign lower dimensional embeddings to those labels, which speeds up the computation. For each minibatch, only clusters for which at least one target is present are evaluated.

The idea is that the clusters which are accessed frequently (like the first one, containing most frequent labels), should also be cheap to compute -- that is, contain a small number of assigned labels. We highly recommend taking a look at the original paper for more details.

`cutoffs`

should be an ordered Sequence of integers sorted in the increasing order. It controls number of clusters and the partitioning of targets into clusters. For example setting`cutoffs = c(10, 100, 1000)`

means that first`10`

targets will be assigned to the 'head' of the adaptive softmax, targets`11, 12, ..., 100`

will be assigned to the first cluster, and targets`101, 102, ..., 1000`

will be assigned to the second cluster, while targets`1001, 1002, ..., n_classes - 1`

will be assigned to the last, third cluster.`div_value`

is used to compute the size of each additional cluster, which is given as \(\left\lfloor\frac{\mbox{in\_features}}{\mbox{div\_value}^{idx}}\right\rfloor\), where \(idx\) is the cluster index (with clusters for less frequent words having larger indices, and indices starting from \(1\)).`head_bias`

if set to True, adds a bias term to the 'head' of the adaptive softmax. See paper for details. Set to False in the official implementation.

## Note

This module returns a `NamedTuple`

with `output`

and `loss`

fields. See further documentation for details.

To compute log-probabilities for all classes, the `log_prob`

method can be used.