def get_answerable_logits(self, contextual_embedding, p_mask):
"""Get the answerable logits.
Parameters
----------
contextual_embedding
Shape (batch_size, sequence_length, C)
p_mask
Shape (batch_size, sequence_length)
Mask the sequence.
0 --> Denote that the element is masked,
1 --> Denote that the element is not masked
Returns
-------
answerable_logits
Shape (batch_size, 2)
"""
# Shape (batch_size, sequence_length)
start_scores = np.squeeze(self.start_scores(contextual_embedding), -1)
start_score_weights = masked_softmax(start_scores, p_mask, axis=-1)
start_agg_feature = npx.batch_dot(np.expand_dims(start_score_weights, axis=1),
contextual_embedding)
start_agg_feature = np.squeeze(start_agg_feature, 1)
cls_feature = contextual_embedding[:, 0, :]
answerable_scores = self.answerable_scores(np.concatenate([start_agg_feature,
cls_feature], axis=-1))
answerable_logits = npx.log_softmax(answerable_scores, axis=-1)
return answerable_logits
def forward(self, A, B):
# Shape of `A`/`B`: (b`atch_size`, no. of words in sequence A/B,
# `embed_size`)
# Shape of `f_A`/`f_B`: (`batch_size`, no. of words in sequence A/B,
# `num_hiddens`)
f_A = self.f(A)
f_B = self.f(B)
# Shape of `e`: (`batch_size`, no. of words in sequence A,
# no. of words in sequence B)
e = npx.batch_dot(f_A, f_B, transpose_b=True)
# Shape of `beta`: (`batch_size`, no. of words in sequence A,
# `embed_size`), where sequence B is softly aligned with each word
# (axis 1 of `beta`) in sequence A
beta = npx.batch_dot(npx.softmax(e), B)
# Shape of `alpha`: (`batch_size`, no. of words in sequence B,
# `embed_size`), where sequence A is softly aligned with each word
# (axis 1 of `alpha`) in sequence B
alpha = npx.batch_dot(npx.softmax(e.transpose(0, 2, 1)), A)
return beta, alpha
def forward(self, queries, keys, values, valid_lens):
queries, keys = self.W_q(queries), self.W_k(keys)
# After dimension expansion, shape of `queries`: (`batch_size`, no. of
# queries, 1, `num_hiddens`) and shape of `keys`: (`batch_size`, 1,
# no. of key-value pairs, `num_hiddens`). Sum them up with
# broadcasting
features = np.expand_dims(queries, axis=2) + np.expand_dims(
keys, axis=1)
features = np.tanh(features)
# There is only one output of `self.w_v`, so we remove the last
# one-dimensional entry from the shape. Shape of `scores`:
# (`batch_size`, no. of queries, no. of key-value pairs)
scores = np.squeeze(self.w_v(features), axis=-1)
self.attention_weights = masked_softmax(scores, valid_lens)
# Shape of `values`: (`batch_size`, no. of key-value pairs, value
# dimension)
return npx.batch_dot(self.dropout(self.attention_weights), values)
def forward(self, query, key, value, valid_len=None):
d = query.shape[-1]
# Set transpose_b=True to swap the last two dimensions of key
scores = npx.batch_dot(query, key, transpose_b=True) / math.sqrt(d)
attention_weights = self.dropout(masked_softmax(scores, valid_len))
return npx.batch_dot(attention_weights, value)
def multi_head_dot_attn(query, key, value,
mask=None,
edge_scores=None,
dropout: float = 0.0,
scaled: bool = True, normalized: bool = False,
eps: float = 1E-6, query_head_units: Optional[int] = None,
layout: str = 'NKT',
use_einsum: bool = False):
"""Multihead dot product attention between the query, key, value.
scaled is False, normalized is False:
D(h_q, h_k) = <h_q, h_k>
scaled is True, normalized is False:
D(h_q, h_k) = <h_q, h_k> / sqrt(dim_q)
scaled is False, normalized is True:
D(h_q, h_k) = <h_q / ||h_q||, h_k / ||h_k||>
scaled is True, normalized is True:
D(h_q, h_k) = <h_q / ||h_q||, h_k / ||h_k||> / sqrt(dim_q)
If edge_scores is provided, we will calcualte the attention as
scores = D(h_q, h_k) + EdgeScore_{q, k}
Parameters
----------
query
Query. The shape depends on the layout
- layout is 'NKT'
Shape (batch_size, num_heads, query_length, key_dim)
- layout is 'NTK'
Shape (batch_size, query_length, num_heads, key_dim)
- layout is 'TNK'
Shape (query_length, batch_size, num_heads, key_dim)
key
Key. The shape depends on the layout
- layout is 'NKT'
Shape (batch_size, num_heads, mem_length, key_dim)
- layout is 'NTK'
Shape (batch_size, mem_length, num_heads, key_dim)
- layout is 'TNK'
Shape (mem_length, batch_size, num_heads, key_dim)
value
Value. The shape depends on the layout
- layout is 'NKT'
Shape (batch_size, num_heads, mem_length, value_dim)
- layout is 'NTK'
Shape (batch_size, mem_length, num_heads, value_dim)
- layout is 'TNK'
Shape (mem_length, batch_size, num_heads, value_dim)
mask
Mask between query and memory. Shape (batch_size, query_length, mem_length)
edge_scores
The edge attention score. Shape can be any shape that is broadcastable to
(batch_size, num_heads, query_length, mem_length)
dropout
Dropout rate
scaled
Whether to divide the attention weights by the sqrt of the query dimension.
This is first proposed in "[NIPS2017] Attention is all you need."::
.. code-block:: none
score = <h_q, h_k> / sqrt(dim_q)
normalized
If turned on, the cosine distance is used, i.e::
.. code-block:: none
score = <h_q / ||h_q||, h_k / ||h_k||>
eps
The epsilon value used in L2 normalization
query_head_units
The units of each query head. If it's empty, we will estimate it via the
shape_array of the query.
layout
This stands for the layout of the attention cell. The shape of the input/output will depend
on the layout. Currently, we support 'NKT', 'NTK' and 'TNK' in which
'N' means the batch_size, 'K' means the head, and 'T' means the length dimension.
use_einsum
Whether to use einsum for the computation
Returns
-------
context_vec
- layout is 'NKT' or 'NTK'
Shape (batch_size, query_length, num_heads * value_units)
- layout is 'TNK'
Shape (query_length, batch_size, num_heads * value_units)
additional_info
scores:
Shape (batch_size, num_head, query_length, mem_length)
attn_weight:
Shape (batch_size, num_head, query_length, mem_length)
"""
# TODO(sxjscience) Profile layout
if normalized:
query = l2_normalize(query, axis=-1, eps=eps)
key = l2_normalize(key, axis=-1, eps=eps)
if scaled:
if query_head_units is None:
raise NotImplementedError('You will need to specify query_head_units!')
else:
scale = math.sqrt(query_head_units)
else:
scale = None
if layout == 'NKT':
# 1. Expand the dimension of the mask:
# (B, L_query, L_mem) --> (B, 1, L_query, L_mem)
if mask is not None:
mask = np.expand_dims(mask, axis=1).astype(np.bool)
# 2. Calculate the attention weights
# Score: (B, N, L_query, C_Q) X (B, N, L_mem, C_Q) --> (B, N, L_query, L_mem)
scores = npx.batch_dot(query, key, transpose_b=True)
if edge_scores is not None:
scores = scores + edge_scores
attn_weights = masked_softmax(scores, mask, axis=-1, temperature=scale)
attn_weights = npx.dropout(attn_weights, p=dropout)
# 3. Calculate the context vector
# (B, N, L_query, L_mem) X (B, N, L_mem, C_V) --> (B, L_query, N * C_V)
if use_einsum:
context_vec = np.einsum('bnij,bnjc->binc', attn_weights, value)
else:
context_vec = npx.batch_dot(attn_weights, value).transpose((0, 2, 1, 3))
context_vec = npx.reshape(context_vec, (-2, -2, -1))
elif layout == 'NTK':
# 1. Expand the dimension of the mask:
# (B, L_query, L_mem) --> (B, 1, L_query, L_mem)
if mask is not None:
mask = np.expand_dims(mask, axis=1).astype(np.bool)
# 2. Calculate the attention weights
# Score: (B, L_query, N, C_Q) X (B, L_mem, N, C_Q) --> (B, N, L_query, L_mem)
if use_einsum:
scores = np.einsum('binc,bjnc->bnij', query, key)
else:
scores = npx.batch_dot(np.swapaxes(query, 1, 2), np.swapaxes(key, 1, 2),
transpose_b=True)
if edge_scores is not None:
scores = scores + edge_scores
attn_weights = masked_softmax(scores, mask, axis=-1, temperature=scale)
attn_weights = npx.dropout(attn_weights, p=dropout)
# 3. Calculate the context vector
# (B, N, L_query, L_mem) X (B, L_mem, N, C_V) --> (B, L_query, N * C_V)
if use_einsum:
context_vec = np.einsum('bnij,bjnc->binc', attn_weights, value)
else:
context_vec = npx.batch_dot(attn_weights,
np.swapaxes(value, 1, 2)).transpose((0, 2, 1, 3))
context_vec = npx.reshape(context_vec, (-2, -2, -1))
elif layout == 'TNK':
# 1. Expand the dimension of the mask:
# (B, L_query, L_mem) --> (B, 1, L_query, L_mem)
if mask is not None:
mask = np.expand_dims(mask, axis=1).astype(np.bool)
# 2. Calculate the attention weights
# Score: (L_query, B, N, C_Q) X (L_mem, B, N, C_Q) --> (B, N, L_query, L_mem)
# This layout structure can be implemented very efficiently because B, N are consecutive
# to each other. To have a clear picture of what's happening, we may consider the
# (i, j)th element of the output
# out[i, j, :, :] = query[:, i, j, :] X key[:, i, j, :].T, which is just one GEMM call
# We can thus implement the whole kernel via a single call of batched GEMM with stride.
if use_einsum:
scores = np.einsum('ibnc,jbnc->bnij', query, key)
else:
scores = npx.batch_dot(query.transpose((1, 2, 0, 3)),
key.transpose((1, 2, 3, 0)))
if edge_scores is not None:
scores = scores + edge_scores
attn_weights = masked_softmax(scores, mask, axis=-1, temperature=scale)
attn_weights = npx.dropout(attn_weights, p=dropout)
# 3. Calculate the context vector
# (B, N, L_query, L_mem) X (L_mem, B, N, C_V) --> (L_query, B, N * C_V)
# Again, we can implement it via a single call to batched GEMM with stride.
# Shape (B, N, L_query, C_V)
if use_einsum:
context_vec = np.einsum('bnij,jbnc->ibnc', attn_weights, value)
else:
context_vec = npx.batch_dot(attn_weights,
value.transpose((1, 2, 0, 3))).transpose((2, 0, 1, 3))
context_vec = npx.reshape(context_vec, (-2, -2, -1))
else:
raise NotImplementedError('layout="{}" is not supported! '
'We only support layout = "NKT", "NTK", and "TNK".'
.format(layout))
return context_vec, [scores, attn_weights]
def forward(self, query, key, value, valid_len=None):
d = query.shape[-1] # dimension
# Set transpose_b=True to swap the last two dimensions of key
scores = npx.batch_dot(query, key, transpose_b=True) / math.sqrt(d) # check the reference (http://www.peterbloem.nl/blog/transformers_ - Why k−−√? Imagine a vector in ℝk with values all c. Its Euclidean length is k−−√c. Therefore, we are dividing out the amount by which the increase in dimension increases the length of the average vectors.
attention_weights = self.dropout(masked_softmax(scores, valid_len))
return npx.batch_dot(attention_weights, value)
def forward(self, queries, keys, values, valid_lens=None):
d = queries.shape[-1]
# Set `transpose_b=True` to swap the last two dimensions of `keys`
scores = npx.batch_dot(queries, keys, transpose_b=True) / math.sqrt(d)
self.attention_weights = masked_softmax(scores, valid_lens)
return npx.batch_dot(self.dropout(self.attention_weights), values)
def dot_attn_score(query,
key,
scaled=True,
normalized=False,
eps=1E-6,
layout='NT'):
"""The inner function call to calculate the score used in dot-product attention.
We support multiple leading batch dimensions.
scaled is True:
D(h_q, h_k) = <h_q, h_k> / sqrt(dim_q)
normalized is True:
D(h_q, h_k) = <h_q / ||h_q||, h_k / ||h_k||>
both scaled and normalized:
D(h_q, h_k) = <h_q / ||h_q||, h_k / ||h_k||> / sqrt(dim_q)
Parameters
----------
query : symbol or ndarray
- layout is 'NT'
(B0, ..., BN, query_length, query_dim)
- layout is 'TN'
(query_length, B0, ..., BN, query_dim)
key : symbol or ndarray
- layout is 'NT'
(B0, ..., BN, key_length, key_dim)
- layout is 'TN'
(key_length, B0, ..., BN, key_dim)
scaled : bool
Whether to divide the query by the square-root of the query_dim
If True: D(h_q, h_k) = <h_q, h_k> / sqrt(dim_q)
normalized : bool
Whether to normalize the query and the key embeddings
If True: D(h_q, h_k) = <h_q / ||h_q||, h_k / ||h_k||>
eps : float
The epsilon used in the normalization
layout
The layout of the layer. Can be 'TN' or 'NT'.
Returns
-------
scores : symbol or ndarray
(B0, ..., BN, query_length, key_length)
"""
if normalized:
query = l2_normalize(query, -1, eps=eps)
key = l2_normalize(key, -1, eps=eps)
if scaled:
query_shape = npx.shape_array(query)
# TODO(sxjscience) Remove .astype(np.float32).
# Wait for https://github.com/apache/incubator-mxnet/issues/18084
query_units = query_shape[-1].astype(np.float32)
query = query / np.sqrt(query_units)
if layout == 'NT':
scores = npx.batch_dot(query, key, transpose_b=True)
else:
raise NotImplementedError(
'layout={} is not supported.'
' Currently, only layout = "NT" is implemented!'.format(layout))
return scores
