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import torch
from torch import nn
from ...nets.attention_model.context import AutoContext
from ...nets.attention_model.dynamic_embedding import AutoDynamicEmbedding
from ...nets.attention_model.multi_head_attention import (
AttentionScore,
MultiHeadAttention,
)
class Decoder(nn.Module):
r"""
The decoder of the Attention Model.
.. math::
\{\log(\pmb{p}_t)\},\pi = \mathrm{Decoder}(s, \pmb{h})
First of all, precompute the keys and values for the embedding :math:`\pmb{h}`:
.. math::
\pmb{k}, \pmb{v}, \pmb{k}^\prime = W^K\pmb{h}, W^V\pmb{h}, W^{K^\prime}\pmb{h}
and the projection of the graph embedding:
.. math::
W_{gc}\bar{\pmb{h}} \quad \text{ for } \bar{\pmb{h}} = \frac{1}{N}\sum\nolimits_i \pmb{h}_i.
Then, the decoder iterates the decoding process autoregressively.
In each decoding step, we perform multiple attentions to get the logits for each node.
.. math::
\begin{aligned}
\pmb{h}_{(c)} &= [\bar{\pmb{h}}, \text{Context}(s,\pmb{h})] \\
q & = W^Q \pmb{h}_{(c)} = W_{gc}\bar{\pmb{h}} + W_{sc}\text{Context}(s,\pmb{h}) \\
q_{gl} &= \mathrm{MultiHeadAttention}(q,\pmb{k},\pmb{v},\mathrm{mask}_t) \\
\pmb{p}_t &= \mathrm{Softmax}(\mathrm{AttentionScore}_{\text{clip}}(q_{gl},\pmb{k}^\prime, \mathrm{mask}_t))\\
\pi_{t} &= \mathrm{DecodingStartegy}(\pmb{p}_t) \\
\mathrm{mask}_{t+1} &= \mathrm{mask}_t.update(\pi_t).
\end{aligned}
.. note::
If there are dynamic node features specified by :mod:`.dynamic_embedding` ,
the keys and values projections are updated in each decoding step by
.. math::
\begin{aligned}
\pmb{k}_{\text{dynamic}}, \pmb{v}_{\text{dynamic}}, \pmb{k}^\prime_{\text{dynamic}} &= \mathrm{DynamicEmbedding}(s)\\
\pmb{k} &= \pmb{k} + \pmb{k}_{\text{dynamic}}\\
\pmb{v} &= \pmb{v} +\pmb{v}_{\text{dynamic}} \\
\pmb{k}^\prime &= \pmb{k}^\prime +\pmb{k}^\prime_{\text{dynamic}}.
\end{aligned}
.. seealso::
* The :math:`\text{Context}` is defined in the :mod:`.context` module.
* The :math:`\text{AttentionScore}` is defined by the :class:`.AttentionScore` class.
* The :math:`\text{MultiHeadAttention}` is defined by the :class:`.MultiHeadAttention` class.
Args:
embedding_dim : the dimension of the embedded inputs
step_context_dim : the dimension of the context :math:`\text{Context}(\pmb{x})`
n_heads: number of heads in the :math:`\mathrm{MultiHeadAttention}`
problem: an object defining the state and the mask updating rule of the problem
tanh_clipping : the clipping scale of the pointer (attention layer before output)
Inputs: input, embeddings
* **input** : dict of inputs, for example ``{'loc': tensor, 'depot': tensor, 'demand': tensor}`` for CVRP.
* **embeddings**: [batch, graph_size, embedding_dim]
Outputs: log_ps, pi
* **log_ps**: [batch, graph_size, T]
* **pi**: [batch, T]
"""
def __init__(self, embedding_dim, step_context_dim, n_heads, problem, tanh_clipping):
super(Decoder, self).__init__()
# For each node we compute (glimpse key, glimpse value, logit key) so 3 * embedding_dim
self.project_node_embeddings = nn.Linear(embedding_dim, 3 * embedding_dim, bias=False)
self.project_fixed_context = nn.Linear(embedding_dim, embedding_dim, bias=False)
self.project_step_context = nn.Linear(step_context_dim, embedding_dim, bias=False)
self.context = AutoContext(problem.NAME, {"context_dim": step_context_dim})
self.dynamic_embedding = AutoDynamicEmbedding(
problem.NAME, {"embedding_dim": embedding_dim}
)
self.glimpse = MultiHeadAttention(embedding_dim=embedding_dim, n_heads=n_heads)
self.pointer = AttentionScore(use_tanh=True, C=tanh_clipping)
self.decode_type = None
self.problem = problem
def forward(self, input, embeddings):
outputs = []
sequences = []
state = self.problem.make_state(input)
# Compute keys, values for the glimpse and keys for the logits once as they can be reused in every step
cached_embeddings = self._precompute(embeddings)
# Perform decoding steps
while not (state.all_finished()):
log_p, mask = self.advance(cached_embeddings, state)
# Select the indices of the next nodes in the sequences, result (batch_size) long
# Squeeze out steps dimension
action = self.decode(log_p.exp(), mask)
state = state.update(action)
# Collect output of step
outputs.append(log_p)
sequences.append(action)
# Collected lists, return Tensor
return torch.stack(outputs, 1), torch.stack(sequences, 1)
def set_decode_type(self, decode_type):
r"""
Currently support
.. code-block:: python
["greedy", "sampling"]
"""
self.decode_type = decode_type
def decode(self, probs, mask):
r"""
Execute the decoding strategy specified by ``self.decode_type``.
Inputs:
* **probs**: [batch_size, graph_size]
* **mask** (bool): [batch_size, graph_size]
Outputs:
* **idxs** (int): index of action chosen. [batch_size]
"""
assert (probs == probs).all(), "Probs should not contain any nans"
if self.decode_type == "greedy":
_, selected = probs.max(1)
assert not mask.gather(
1, selected.unsqueeze(-1)
).data.any(), "Decode greedy: infeasible action has maximum probability"
elif self.decode_type == "sampling":
selected = probs.multinomial(1).squeeze(1)
# Check if sampling went OK, can go wrong due to bug on GPU
# See https://discuss.pytorch.org/t/bad-behavior-of-multinomial-function/10232
while mask.gather(1, selected.unsqueeze(-1)).data.any():
print("Sampled bad values, resampling!")
selected = probs.multinomial(1).squeeze(1)
else:
assert False, "Unknown decode type"
return selected
def _precompute(self, embeddings):
# The fixed context projection of the graph embedding is calculated only once for efficiency
graph_embed = embeddings.mean(1)
# fixed context = (batch_size, 1, embed_dim) to make broadcastable with parallel timesteps
graph_context = self.project_fixed_context(graph_embed).unsqueeze(-2)
# The projection of the node embeddings for the attention is calculated once up front
glimpse_key, glimpse_val, logit_key = self.project_node_embeddings(embeddings).chunk(
3, dim=-1
)
cache = (
embeddings,
graph_context,
glimpse_key,
glimpse_val,
logit_key,
) # single head for the final logit
return cache
def advance(self, cached_embeddings, state):
node_embeddings, graph_context, glimpse_K, glimpse_V, logit_K = cached_embeddings
# Compute context node embedding: [graph embedding| prev node| problem-state-context]
# [batch, 1, context dim]
context = self.context(node_embeddings, state)
step_context = self.project_step_context(context) # [batch, 1, embed_dim]
query = graph_context + step_context # [batch, 1, embed_dim]
glimpse_key_dynamic, glimpse_val_dynamic, logit_key_dynamic = self.dynamic_embedding(state)
glimpse_K = glimpse_K + glimpse_key_dynamic
glimpse_V = glimpse_V + glimpse_val_dynamic
logit_K = logit_K + logit_key_dynamic
# Compute the mask
mask = state.get_mask()
# Compute logits (unnormalized log_p)
logits, glimpse = self.calc_logits(query, glimpse_K, glimpse_V, logit_K, mask)
return logits, glimpse
def calc_logits(self, query, glimpse_K, glimpse_V, logit_K, mask):
# Compute glimpse with multi-head-attention.
# Then use glimpse as a query to compute logits for each node
# [batch, 1, embed dim]
glimpse = self.glimpse(query, glimpse_K, glimpse_V, mask)
logits = self.pointer(glimpse, logit_K, mask)
return logits, glimpse
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