313 lines
12 KiB
Python
313 lines
12 KiB
Python
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from collections import namedtuple
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import torch
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from torch import Tensor
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from typing import List, Sequence
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from . import Sequential, ModuleList, Linear
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from .module import Module
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from ..functional import log_softmax
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__all__ = ['AdaptiveLogSoftmaxWithLoss']
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_ASMoutput = namedtuple('_ASMoutput', ['output', 'loss'])
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class AdaptiveLogSoftmaxWithLoss(Module):
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r"""Efficient softmax approximation.
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As described in
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`Efficient softmax approximation for GPUs by Edouard Grave, Armand Joulin,
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Moustapha Cissé, David Grangier, and Hervé Jégou
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<https://arxiv.org/abs/1609.04309>`__.
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Adaptive softmax is an approximate strategy for training models with large
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output spaces. It is most effective when the label distribution is highly
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imbalanced, for example in natural language modelling, where the word
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frequency distribution approximately follows the `Zipf's law`_.
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Adaptive softmax partitions the labels into several clusters, according to
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their frequency. These clusters may contain different number of targets
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each.
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Additionally, clusters containing less frequent labels assign lower
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dimensional embeddings to those labels, which speeds up the computation.
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For each minibatch, only clusters for which at least one target is
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present are evaluated.
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The idea is that the clusters which are accessed frequently
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(like the first one, containing most frequent labels), should also be cheap
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to compute -- that is, contain a small number of assigned labels.
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We highly recommend taking a look at the original paper for more details.
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* :attr:`cutoffs` should be an ordered Sequence of integers sorted
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in the increasing order.
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It controls number of clusters and the partitioning of targets into
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clusters. For example setting ``cutoffs = [10, 100, 1000]``
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means that first `10` targets will be assigned
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to the 'head' of the adaptive softmax, targets `11, 12, ..., 100` will be
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assigned to the first cluster, and targets `101, 102, ..., 1000` will be
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assigned to the second cluster, while targets
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`1001, 1002, ..., n_classes - 1` will be assigned
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to the last, third cluster.
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* :attr:`div_value` is used to compute the size of each additional cluster,
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which is given as
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:math:`\left\lfloor\frac{\texttt{in\_features}}{\texttt{div\_value}^{idx}}\right\rfloor`,
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where :math:`idx` is the cluster index (with clusters
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for less frequent words having larger indices,
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and indices starting from :math:`1`).
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* :attr:`head_bias` if set to True, adds a bias term to the 'head' of the
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adaptive softmax. See paper for details. Set to False in the official
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implementation.
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.. warning::
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Labels passed as inputs to this module should be sorted according to
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their frequency. This means that the most frequent label should be
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represented by the index `0`, and the least frequent
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label should be represented by the index `n_classes - 1`.
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.. note::
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This module returns a ``NamedTuple`` with ``output``
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and ``loss`` fields. See further documentation for details.
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.. note::
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To compute log-probabilities for all classes, the ``log_prob``
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method can be used.
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Args:
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in_features (int): Number of features in the input tensor
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n_classes (int): Number of classes in the dataset
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cutoffs (Sequence): Cutoffs used to assign targets to their buckets
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div_value (float, optional): value used as an exponent to compute sizes
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of the clusters. Default: 4.0
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head_bias (bool, optional): If ``True``, adds a bias term to the 'head' of the
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adaptive softmax. Default: ``False``
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Returns:
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``NamedTuple`` with ``output`` and ``loss`` fields:
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* **output** is a Tensor of size ``N`` containing computed target
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log probabilities for each example
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* **loss** is a Scalar representing the computed negative
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log likelihood loss
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Shape:
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- input: :math:`(N, \texttt{in\_features})` or :math:`(\texttt{in\_features})`
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- target: :math:`(N)` or :math:`()` where each value satisfies :math:`0 <= \texttt{target[i]} <= \texttt{n\_classes}`
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- output1: :math:`(N)` or :math:`()`
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- output2: ``Scalar``
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.. _Zipf's law: https://en.wikipedia.org/wiki/Zipf%27s_law
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"""
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in_features: int
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n_classes: int
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cutoffs: List[int]
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div_value: float
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head_bias: bool
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head: Linear
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tail: ModuleList
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def __init__(
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self,
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in_features: int,
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n_classes: int,
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cutoffs: Sequence[int],
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div_value: float = 4.,
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head_bias: bool = False,
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device=None,
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dtype=None
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) -> None:
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factory_kwargs = {'device': device, 'dtype': dtype}
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super().__init__()
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cutoffs = list(cutoffs)
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if (len(cutoffs) == 0):
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raise ValueError("cutoffs should be a sequence of length larger than 0")
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if (cutoffs != sorted(cutoffs)) \
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or (min(cutoffs) <= 0) \
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or (max(cutoffs) > (n_classes - 1)) \
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or (len(set(cutoffs)) != len(cutoffs)) \
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or any(int(c) != c for c in cutoffs):
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raise ValueError("cutoffs should be a sequence of unique, positive "
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"integers sorted in an increasing order, where "
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"each value is between 1 and n_classes-1")
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self.in_features = in_features
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self.n_classes = n_classes
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self.cutoffs = cutoffs + [n_classes]
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self.div_value = div_value
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self.head_bias = head_bias
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self.shortlist_size = self.cutoffs[0]
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self.n_clusters = len(self.cutoffs) - 1
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self.head_size = self.shortlist_size + self.n_clusters
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self.head = Linear(self.in_features, self.head_size, bias=self.head_bias,
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**factory_kwargs)
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self.tail = ModuleList()
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for i in range(self.n_clusters):
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hsz = int(self.in_features // (self.div_value ** (i + 1)))
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osz = self.cutoffs[i + 1] - self.cutoffs[i]
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projection = Sequential(
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Linear(self.in_features, hsz, bias=False, **factory_kwargs),
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Linear(hsz, osz, bias=False, **factory_kwargs),
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)
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self.tail.append(projection)
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def reset_parameters(self) -> None:
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self.head.reset_parameters()
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for i2h, h2o in self.tail:
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i2h.reset_parameters()
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h2o.reset_parameters()
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def forward(self, input_: Tensor, target_: Tensor) -> _ASMoutput:
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targ_dim = target_.dim()
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if targ_dim == 1:
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if input_.size(0) != target_.size(0):
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raise RuntimeError('Input and target should have the same size '
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'in the batch dimension.')
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if input_.dim() != 2:
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raise RuntimeError('1D target tensor expects 2D input tensors, '
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'but found inputs with size', input_.size())
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elif targ_dim == 0:
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if input_.dim() != 1:
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raise RuntimeError('0D target tensor expects 1D input tensors, '
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'but found inputs with size', input_.size())
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else:
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raise RuntimeError('0D or 1D target tensor expected, '
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'multi-target not supported')
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is_batched = targ_dim > 0
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input = input_ if is_batched else input_.unsqueeze(0)
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target = target_ if is_batched else target_.unsqueeze(0)
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used_rows = 0
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batch_size = target.size(0)
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output = input.new_zeros(batch_size)
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gather_inds = target.new_empty(batch_size)
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cutoff_values = [0] + self.cutoffs
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for i in range(len(cutoff_values) - 1):
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low_idx = cutoff_values[i]
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high_idx = cutoff_values[i + 1]
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target_mask = (target >= low_idx) & (target < high_idx)
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row_indices = target_mask.nonzero().squeeze()
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if row_indices.numel() == 0:
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continue
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if i == 0:
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gather_inds.index_copy_(0, row_indices, target[target_mask])
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else:
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relative_target = target[target_mask] - low_idx
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input_subset = input.index_select(0, row_indices)
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cluster_output = self.tail[i - 1](input_subset)
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cluster_index = self.shortlist_size + i - 1
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gather_inds.index_fill_(0, row_indices, cluster_index)
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cluster_logprob = log_softmax(cluster_output, dim=1)
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local_logprob = cluster_logprob.gather(1, relative_target.unsqueeze(1))
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output.index_copy_(0, row_indices, local_logprob.squeeze(1))
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used_rows += row_indices.numel()
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if used_rows != batch_size:
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raise RuntimeError(f"Target values should be in [0, {self.n_classes - 1}], "
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f"but values in range [{target.min().item()}, {target.max().item()}] "
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"were found. ")
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head_output = self.head(input)
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head_logprob = log_softmax(head_output, dim=1)
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output += head_logprob.gather(1, gather_inds.unsqueeze(1)).squeeze()
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loss = (-output).mean()
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if not is_batched:
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output = output.squeeze(0)
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return _ASMoutput(output, loss)
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def _get_full_log_prob(self, input, head_output):
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"""Given input tensor, and output of ``self.head``, compute the log of the full distribution."""
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out = input.new_empty((head_output.size(0), self.n_classes))
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head_logprob = log_softmax(head_output, dim=1)
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out[:, :self.shortlist_size] = head_logprob[:, :self.shortlist_size]
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for i, (start_idx, stop_idx) in enumerate(zip(self.cutoffs, self.cutoffs[1:])):
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cluster_output = self.tail[i](input)
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cluster_logprob = log_softmax(cluster_output, dim=1)
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output_logprob = cluster_logprob + head_logprob[:, self.shortlist_size + i].unsqueeze(1)
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out[:, start_idx:stop_idx] = output_logprob
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return out
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def log_prob(self, input: Tensor) -> Tensor:
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r"""Compute log probabilities for all :math:`\texttt{n\_classes}`.
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Args:
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input (Tensor): a minibatch of examples
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Returns:
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log-probabilities of for each class :math:`c`
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in range :math:`0 <= c <= \texttt{n\_classes}`, where :math:`\texttt{n\_classes}` is a
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parameter passed to ``AdaptiveLogSoftmaxWithLoss`` constructor.
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Shape:
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- Input: :math:`(N, \texttt{in\_features})`
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- Output: :math:`(N, \texttt{n\_classes})`
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"""
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head_output = self.head(input)
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return self._get_full_log_prob(input, head_output)
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def predict(self, input: Tensor) -> Tensor:
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r"""Return the class with the highest probability for each example in the input minibatch.
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This is equivalent to ``self.log_prob(input).argmax(dim=1)``, but is more efficient in some cases.
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Args:
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input (Tensor): a minibatch of examples
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Returns:
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output (Tensor): a class with the highest probability for each example
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Shape:
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- Input: :math:`(N, \texttt{in\_features})`
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- Output: :math:`(N)`
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"""
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head_output = self.head(input)
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output = torch.argmax(head_output, dim=1)
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not_in_shortlist = (output >= self.shortlist_size)
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all_in_shortlist = not (not_in_shortlist.any())
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if all_in_shortlist:
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return output
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elif not_in_shortlist.all():
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log_prob = self._get_full_log_prob(input, head_output)
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return torch.argmax(log_prob, dim=1)
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else:
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log_prob = self._get_full_log_prob(input[not_in_shortlist],
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head_output[not_in_shortlist])
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output[not_in_shortlist] = torch.argmax(log_prob, dim=1)
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return output
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