wehub-resource-sync
889 lines
37 KiB
Python
889 lines
37 KiB
Python
"""
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.. _model-transformer:
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Transformer as a Graph Neural Network
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======================================
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**Author**: Zihao Ye, Jinjing Zhou, Qipeng Guo, Quan Gan, Zheng Zhang
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.. warning::
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The tutorial aims at gaining insights into the paper, with code as a mean
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of explanation. The implementation thus is NOT optimized for running
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efficiency. For recommended implementation, please refer to the `official
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examples <https://github.com/dmlc/dgl/tree/master/examples>`_.
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"""
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################################################################################################
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# In this tutorial, you learn about a simplified implementation of the Transformer model.
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# You can see highlights of the most important design points. For instance, there is
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# only single-head attention. The complete code can be found
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# `here <https://github.com/dmlc/dgl/tree/master/examples/pytorch/transformer>`__.
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#
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# The overall structure is similar to the one from the research papaer `Annotated
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# Transformer <http://nlp.seas.harvard.edu/2018/04/03/attention.html>`__.
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#
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# The Transformer model, as a replacement of CNN/RNN architecture for
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# sequence modeling, was introduced in the research paper: `Attention is All
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# You Need <https://arxiv.org/pdf/1706.03762.pdf>`__. It improved the
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# state of the art for machine translation as well as natural language
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# inference task
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# (`GPT <https://s3-us-west-2.amazonaws.com/openai-assets/research-covers/language-unsupervised/language_understanding_paper.pdf>`__).
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# Recent work on pre-training Transformer with large scale corpus
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# (`BERT <https://arxiv.org/pdf/1810.04805.pdf>`__) supports that it is
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# capable of learning high-quality semantic representation.
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#
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# The interesting part of Transformer is its extensive employment of
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# attention. The classic use of attention comes from machine translation
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# model, where the output token attends to all input tokens.
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#
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# Transformer additionally applies *self-attention* in both decoder and
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# encoder. This process forces words relate to each other to combine
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# together, irrespective of their positions in the sequence. This is
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# different from RNN-based model, where words (in the source sentence) are
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# combined along the chain, which is thought to be too constrained.
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#
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# Attention layer of Transformer
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# ------------------------------
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#
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# In the attention layer of Transformer, for each node the module learns to
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# assign weights on its in-coming edges. For node pair :math:`(i, j)`
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# (from :math:`i` to :math:`j`) with node
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# :math:`x_i, x_j \in \mathbb{R}^n`, the score of their connection is
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# defined as follows:
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#
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# .. math::
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#
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#
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# q_j = W_q\cdot x_j \\
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# k_i = W_k\cdot x_i\\
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# v_i = W_v\cdot x_i\\
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# \textrm{score} = q_j^T k_i
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#
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# where :math:`W_q, W_k, W_v \in \mathbb{R}^{n\times d_k}` map the
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# representations :math:`x` to “query”, “key”, and “value” space
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# respectively.
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#
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# There are other possibilities to implement the score function. The dot
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# product measures the similarity of a given query :math:`q_j` and a key
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# :math:`k_i`: if :math:`j` needs the information stored in :math:`i`, the
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# query vector at position :math:`j` (:math:`q_j`) is supposed to be close
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# to key vector at position :math:`i` (:math:`k_i`).
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#
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# The score is then used to compute the sum of the incoming values,
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# normalized over the weights of edges, stored in :math:`\textrm{wv}`.
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# Then apply an affine layer to :math:`\textrm{wv}` to get the output
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# :math:`o`:
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#
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# .. math::
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#
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#
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# w_{ji} = \frac{\exp\{\textrm{score}_{ji} \}}{\sum\limits_{(k, i)\in E}\exp\{\textrm{score}_{ki} \}} \\
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# \textrm{wv}_i = \sum_{(k, i)\in E} w_{ki} v_k \\
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# o = W_o\cdot \textrm{wv} \\
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#
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# Multi-head attention layer
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~
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#
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# In Transformer, attention is *multi-headed*. A head is very much like a
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# channel in a convolutional network. The multi-head attention consists of
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# multiple attention heads, in which each head refers to a single
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# attention module. :math:`\textrm{wv}^{(i)}` for all the heads are
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# concatenated and mapped to output :math:`o` with an affine layer:
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#
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# .. math::
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#
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#
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# o = W_o \cdot \textrm{concat}\left(\left[\textrm{wv}^{(0)}, \textrm{wv}^{(1)}, \cdots, \textrm{wv}^{(h)}\right]\right)
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#
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# The code below wraps necessary components for multi-head attention, and
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# provides two interfaces.
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#
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# - ``get`` maps state ‘x’, to query, key and value, which is required by
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# following steps(\ ``propagate_attention``).
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# - ``get_o`` maps the updated value after attention to the output
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# :math:`o` for post-processing.
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#
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# .. code::
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#
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# class MultiHeadAttention(nn.Module):
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# "Multi-Head Attention"
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# def __init__(self, h, dim_model):
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# "h: number of heads; dim_model: hidden dimension"
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# super(MultiHeadAttention, self).__init__()
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# self.d_k = dim_model // h
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# self.h = h
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# # W_q, W_k, W_v, W_o
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# self.linears = clones(nn.Linear(dim_model, dim_model), 4)
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#
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# def get(self, x, fields='qkv'):
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# "Return a dict of queries / keys / values."
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# batch_size = x.shape[0]
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# ret = {}
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# if 'q' in fields:
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# ret['q'] = self.linears[0](x).view(batch_size, self.h, self.d_k)
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# if 'k' in fields:
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# ret['k'] = self.linears[1](x).view(batch_size, self.h, self.d_k)
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# if 'v' in fields:
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# ret['v'] = self.linears[2](x).view(batch_size, self.h, self.d_k)
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# return ret
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#
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# def get_o(self, x):
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# "get output of the multi-head attention"
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# batch_size = x.shape[0]
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# return self.linears[3](x.view(batch_size, -1))
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#
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#
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# How DGL implements Transformer with a graph neural network
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# ----------------------------------------------------------
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#
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# You get a different perspective of Transformer by treating the
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# attention as edges in a graph and adopt message passing on the edges to
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# induce the appropriate processing.
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#
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# Graph structure
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# ~~~~~~~~~~~~~~~
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#
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# Construct the graph by mapping tokens of the source and target
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# sentence to nodes. The complete Transformer graph is made up of three
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# subgraphs:
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#
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# **Source language graph**. This is a complete graph, each
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# token :math:`s_i` can attend to any other token :math:`s_j` (including
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# self-loops). |image0|
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# **Target language graph**. The graph is
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# half-complete, in that :math:`t_i` attends only to :math:`t_j` if
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# :math:`i > j` (an output token can not depend on future words). |image1|
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# **Cross-language graph**. This is a bi-partitie graph, where there is
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# an edge from every source token :math:`s_i` to every target token
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# :math:`t_j`, meaning every target token can attend on source tokens.
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# |image2|
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#
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# The full picture looks like this: |image3|
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#
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# Pre-build the graphs in dataset preparation stage.
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#
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# Message passing
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# ~~~~~~~~~~~~~~~
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#
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# Once you define the graph structure, move on to defining the
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# computation for message passing.
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#
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# Assuming that you have already computed all the queries :math:`q_i`, keys
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# :math:`k_i` and values :math:`v_i`. For each node :math:`i` (no matter
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# whether it is a source token or target token), you can decompose the
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# attention computation into two steps:
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#
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# 1. **Message computation:** Compute attention score
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# :math:`\mathrm{score}_{ij}` between :math:`i` and all nodes :math:`j`
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# to be attended over, by taking the scaled-dot product between
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# :math:`q_i` and :math:`k_j`. The message sent from :math:`j` to
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# :math:`i` will consist of the score :math:`\mathrm{score}_{ij}` and
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# the value :math:`v_j`.
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# 2. **Message aggregation:** Aggregate the values :math:`v_j` from all
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# :math:`j` according to the scores :math:`\mathrm{score}_{ij}`.
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#
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# Simple implementation
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# ^^^^^^^^^^^^^^^^^^^^
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#
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# Message computation
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# '''''''''''''''''''
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#
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# Compute ``score`` and send source node’s ``v`` to destination’s mailbox
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#
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# .. code::
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#
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# def message_func(edges):
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# return {'score': ((edges.src['k'] * edges.dst['q'])
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# .sum(-1, keepdim=True)),
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# 'v': edges.src['v']}
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#
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# Message aggregation
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# '''''''''''''''''''
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#
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# Normalize over all in-edges and weighted sum to get output
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#
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# .. code::
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#
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# import torch as th
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# import torch.nn.functional as F
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#
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# def reduce_func(nodes, d_k=64):
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# v = nodes.mailbox['v']
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# att = F.softmax(nodes.mailbox['score'] / th.sqrt(d_k), 1)
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# return {'dx': (att * v).sum(1)}
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#
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# Execute on specific edges
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# '''''''''''''''''''''''''
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#
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# .. code::
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#
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# import functools.partial as partial
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# def naive_propagate_attention(self, g, eids):
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# g.send_and_recv(eids, message_func, partial(reduce_func, d_k=self.d_k))
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#
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# Speeding up with built-in functions
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# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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#
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# To speed up the message passing process, use DGL’s built-in
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# functions, including:
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#
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# - ``fn.src_mul_egdes(src_field, edges_field, out_field)`` multiplies
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# source’s attribute and edges attribute, and send the result to the
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# destination node’s mailbox keyed by ``out_field``.
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# - ``fn.copy_e(edges_field, out_field)`` copies edge’s attribute to
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# destination node’s mailbox.
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# - ``fn.sum(edges_field, out_field)`` sums up
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# edge’s attribute and sends aggregation to destination node’s mailbox.
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#
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# Here, you assemble those built-in functions into ``propagate_attention``,
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# which is also the main graph operation function in the final
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# implementation. To accelerate it, break the ``softmax`` operation into
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# the following steps. Recall that for each head there are two phases.
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#
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# 1. Compute attention score by multiply src node’s ``k`` and dst node’s
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# ``q``
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#
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# - ``g.apply_edges(src_dot_dst('k', 'q', 'score'), eids)``
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#
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# 2. Scaled Softmax over all dst nodes’ in-coming edges
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#
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# - Step 1: Exponentialize score with scale normalize constant
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#
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# - ``g.apply_edges(scaled_exp('score', np.sqrt(self.d_k)))``
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#
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# .. math:: \textrm{score}_{ij}\leftarrow\exp{\left(\frac{\textrm{score}_{ij}}{ \sqrt{d_k}}\right)}
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#
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# - Step 2: Get the “values” on associated nodes weighted by “scores”
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# on in-coming edges of each node; get the sum of “scores” on
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# in-coming edges of each node for normalization. Note that here
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# :math:`\textrm{wv}` is not normalized.
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#
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# - ``msg: fn.u_mul_e('v', 'score', 'v'), reduce: fn.sum('v', 'wv')``
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#
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# .. math:: \textrm{wv}_j=\sum_{i=1}^{N} \textrm{score}_{ij} \cdot v_i
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#
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# - ``msg: fn.copy_e('score', 'score'), reduce: fn.sum('score', 'z')``
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#
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# .. math:: \textrm{z}_j=\sum_{i=1}^{N} \textrm{score}_{ij}
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#
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# The normalization of :math:`\textrm{wv}` is left to post processing.
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#
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# .. code::
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#
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# def src_dot_dst(src_field, dst_field, out_field):
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# def func(edges):
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# return {out_field: (edges.src[src_field] * edges.dst[dst_field]).sum(-1, keepdim=True)}
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#
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# return func
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#
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# def scaled_exp(field, scale_constant):
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# def func(edges):
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# # clamp for softmax numerical stability
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# return {field: th.exp((edges.data[field] / scale_constant).clamp(-5, 5))}
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#
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# return func
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#
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#
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# def propagate_attention(self, g, eids):
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# # Compute attention score
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# g.apply_edges(src_dot_dst('k', 'q', 'score'), eids)
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# g.apply_edges(scaled_exp('score', np.sqrt(self.d_k)))
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# # Update node state
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# g.send_and_recv(eids,
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# [fn.u_mul_e('v', 'score', 'v'), fn.copy_e('score', 'score')],
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# [fn.sum('v', 'wv'), fn.sum('score', 'z')])
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#
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# Preprocessing and postprocessing
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# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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#
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# In Transformer, data needs to be pre- and post-processed before and
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# after the ``propagate_attention`` function.
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#
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# **Preprocessing** The preprocessing function ``pre_func`` first
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# normalizes the node representations and then map them to a set of
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# queries, keys and values, using self-attention as an example:
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#
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# .. math::
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#
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#
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# x \leftarrow \textrm{LayerNorm}(x) \\
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# [q, k, v] \leftarrow [W_q, W_k, W_v ]\cdot x
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#
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# **Postprocessing** The postprocessing function ``post_funcs`` completes
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# the whole computation correspond to one layer of the transformer: 1.
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# Normalize :math:`\textrm{wv}` and get the output of Multi-Head Attention
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# Layer :math:`o`.
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#
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# .. math::
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#
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#
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# \textrm{wv} \leftarrow \frac{\textrm{wv}}{z} \\
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# o \leftarrow W_o\cdot \textrm{wv} + b_o
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#
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# add residual connection:
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#
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# .. math::
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#
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#
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# x \leftarrow x + o
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#
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# 2. Applying a two layer position-wise feed forward layer on :math:`x`
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# then add residual connection:
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#
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# .. math::
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#
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#
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# x \leftarrow x + \textrm{LayerNorm}(\textrm{FFN}(x))
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#
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# where :math:`\textrm{FFN}` refers to the feed forward function.
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#
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# .. code::
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#
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# class Encoder(nn.Module):
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# def __init__(self, layer, N):
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# super(Encoder, self).__init__()
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# self.N = N
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# self.layers = clones(layer, N)
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# self.norm = LayerNorm(layer.size)
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#
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# def pre_func(self, i, fields='qkv'):
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# layer = self.layers[i]
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# def func(nodes):
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# x = nodes.data['x']
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# norm_x = layer.sublayer[0].norm(x)
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# return layer.self_attn.get(norm_x, fields=fields)
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# return func
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#
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# def post_func(self, i):
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# layer = self.layers[i]
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# def func(nodes):
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# x, wv, z = nodes.data['x'], nodes.data['wv'], nodes.data['z']
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# o = layer.self_attn.get_o(wv / z)
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# x = x + layer.sublayer[0].dropout(o)
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# x = layer.sublayer[1](x, layer.feed_forward)
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# return {'x': x if i < self.N - 1 else self.norm(x)}
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# return func
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#
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# class Decoder(nn.Module):
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# def __init__(self, layer, N):
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# super(Decoder, self).__init__()
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# self.N = N
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# self.layers = clones(layer, N)
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# self.norm = LayerNorm(layer.size)
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#
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# def pre_func(self, i, fields='qkv', l=0):
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# layer = self.layers[i]
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# def func(nodes):
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# x = nodes.data['x']
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# if fields == 'kv':
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# norm_x = x # In enc-dec attention, x has already been normalized.
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# else:
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# norm_x = layer.sublayer[l].norm(x)
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# return layer.self_attn.get(norm_x, fields)
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# return func
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#
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# def post_func(self, i, l=0):
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# layer = self.layers[i]
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# def func(nodes):
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# x, wv, z = nodes.data['x'], nodes.data['wv'], nodes.data['z']
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# o = layer.self_attn.get_o(wv / z)
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# x = x + layer.sublayer[l].dropout(o)
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# if l == 1:
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# x = layer.sublayer[2](x, layer.feed_forward)
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# return {'x': x if i < self.N - 1 else self.norm(x)}
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# return func
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#
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# This completes all procedures of one layer of encoder and decoder in
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# Transformer.
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#
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# .. note::
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#
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# The sublayer connection part is little bit different from the
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# original paper. However, this implementation is the same as `The Annotated
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# Transformer <http://nlp.seas.harvard.edu/2018/04/03/attention.html>`__
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# and
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# `OpenNMT <https://github.com/OpenNMT/OpenNMT-py/blob/cd29c1dbfb35f4a2701ff52a1bf4e5bdcf02802e/onmt/encoders/transformer.py>`__.
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#
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# Main class of Transformer graph
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# -------------------------------
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#
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# The processing flow of Transformer can be seen as a 2-stage
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# message-passing within the complete graph (adding pre- and post-
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# processing appropriately): 1) self-attention in encoder, 2)
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# self-attention in decoder followed by cross-attention between encoder
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# and decoder, as shown below. |image4|
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#
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# .. code:: python
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#
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# class Transformer(nn.Module):
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# def __init__(self, encoder, decoder, src_embed, tgt_embed, pos_enc, generator, h, d_k):
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# super(Transformer, self).__init__()
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# self.encoder, self.decoder = encoder, decoder
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# self.src_embed, self.tgt_embed = src_embed, tgt_embed
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# self.pos_enc = pos_enc
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# self.generator = generator
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# self.h, self.d_k = h, d_k
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#
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# def propagate_attention(self, g, eids):
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# # Compute attention score
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# g.apply_edges(src_dot_dst('k', 'q', 'score'), eids)
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# g.apply_edges(scaled_exp('score', np.sqrt(self.d_k)))
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# # Send weighted values to target nodes
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# g.send_and_recv(eids,
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# [fn.u_mul_e('v', 'score', 'v'), fn.copy_e('score', 'score')],
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# [fn.sum('v', 'wv'), fn.sum('score', 'z')])
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#
|
||
# def update_graph(self, g, eids, pre_pairs, post_pairs):
|
||
# "Update the node states and edge states of the graph."
|
||
#
|
||
# # Pre-compute queries and key-value pairs.
|
||
# for pre_func, nids in pre_pairs:
|
||
# g.apply_nodes(pre_func, nids)
|
||
# self.propagate_attention(g, eids)
|
||
# # Further calculation after attention mechanism
|
||
# for post_func, nids in post_pairs:
|
||
# g.apply_nodes(post_func, nids)
|
||
#
|
||
# def forward(self, graph):
|
||
# g = graph.g
|
||
# nids, eids = graph.nids, graph.eids
|
||
#
|
||
# # Word Embedding and Position Embedding
|
||
# src_embed, src_pos = self.src_embed(graph.src[0]), self.pos_enc(graph.src[1])
|
||
# tgt_embed, tgt_pos = self.tgt_embed(graph.tgt[0]), self.pos_enc(graph.tgt[1])
|
||
# g.nodes[nids['enc']].data['x'] = self.pos_enc.dropout(src_embed + src_pos)
|
||
# g.nodes[nids['dec']].data['x'] = self.pos_enc.dropout(tgt_embed + tgt_pos)
|
||
#
|
||
# for i in range(self.encoder.N):
|
||
# # Step 1: Encoder Self-attention
|
||
# pre_func = self.encoder.pre_func(i, 'qkv')
|
||
# post_func = self.encoder.post_func(i)
|
||
# nodes, edges = nids['enc'], eids['ee']
|
||
# self.update_graph(g, edges, [(pre_func, nodes)], [(post_func, nodes)])
|
||
#
|
||
# for i in range(self.decoder.N):
|
||
# # Step 2: Dncoder Self-attention
|
||
# pre_func = self.decoder.pre_func(i, 'qkv')
|
||
# post_func = self.decoder.post_func(i)
|
||
# nodes, edges = nids['dec'], eids['dd']
|
||
# self.update_graph(g, edges, [(pre_func, nodes)], [(post_func, nodes)])
|
||
# # Step 3: Encoder-Decoder attention
|
||
# pre_q = self.decoder.pre_func(i, 'q', 1)
|
||
# pre_kv = self.decoder.pre_func(i, 'kv', 1)
|
||
# post_func = self.decoder.post_func(i, 1)
|
||
# nodes_e, nodes_d, edges = nids['enc'], nids['dec'], eids['ed']
|
||
# self.update_graph(g, edges, [(pre_q, nodes_d), (pre_kv, nodes_e)], [(post_func, nodes_d)])
|
||
#
|
||
# return self.generator(g.ndata['x'][nids['dec']])
|
||
#
|
||
#
|
||
# .. note::
|
||
#
|
||
# By calling ``update_graph`` function, you can create your own
|
||
# Transformer on any subgraphs with nearly the same code. This
|
||
# flexibility enables us to discover new, sparse structures (c.f. local attention
|
||
# mentioned `here <https://arxiv.org/pdf/1508.04025.pdf>`__). Note in this
|
||
# implementation you don't use mask or padding, which makes the logic
|
||
# more clear and saves memory. The trade-off is that the implementation is
|
||
# slower.
|
||
#
|
||
# Training
|
||
# --------
|
||
#
|
||
# This tutorial does not cover several other techniques such as Label
|
||
# Smoothing and Noam Optimizations mentioned in the original paper. For
|
||
# detailed description about these modules, read `The
|
||
# Annotated
|
||
# Transformer <http://nlp.seas.harvard.edu/2018/04/03/attention.html>`__
|
||
# written by Harvard NLP team.
|
||
#
|
||
# Task and the dataset
|
||
# ~~~~~~~~~~~~~~~~~~~~
|
||
#
|
||
# The Transformer is a general framework for a variety of NLP tasks. This tutorial focuses
|
||
# on the sequence to sequence learning: it’s a typical case to illustrate how it works.
|
||
#
|
||
# As for the dataset, there are two example tasks: copy and sort, together
|
||
# with two real-world translation tasks: multi30k en-de task and wmt14
|
||
# en-de task.
|
||
#
|
||
# - **copy dataset**: copy input sequences to output. (train/valid/test:
|
||
# 9000, 1000, 1000)
|
||
# - **sort dataset**: sort input sequences as output. (train/valid/test:
|
||
# 9000, 1000, 1000)
|
||
# - **Multi30k en-de**, translate sentences from En to De.
|
||
# (train/valid/test: 29000, 1000, 1000)
|
||
# - **WMT14 en-de**, translate sentences from En to De.
|
||
# (Train/Valid/Test: 4500966/3000/3003)
|
||
#
|
||
# .. note::
|
||
# Training with wmt14 requires multi-GPU support and is not available. Contributions are welcome!
|
||
#
|
||
# Graph building
|
||
# ~~~~~~~~~~~~~~
|
||
#
|
||
# **Batching** This is similar to the way you handle Tree-LSTM. Build a graph pool in
|
||
# advance, including all possible combination of input lengths and output
|
||
# lengths. Then for each sample in a batch, call ``dgl.batch`` to batch
|
||
# graphs of their sizes together in to a single large graph.
|
||
#
|
||
# You can wrap the process of creating graph pool and building
|
||
# BatchedGraph in ``dataset.GraphPool`` and
|
||
# ``dataset.TranslationDataset``.
|
||
#
|
||
# .. code:: python
|
||
#
|
||
# graph_pool = GraphPool()
|
||
#
|
||
# data_iter = dataset(graph_pool, mode='train', batch_size=1, devices=devices)
|
||
# for graph in data_iter:
|
||
# print(graph.nids['enc']) # encoder node ids
|
||
# print(graph.nids['dec']) # decoder node ids
|
||
# print(graph.eids['ee']) # encoder-encoder edge ids
|
||
# print(graph.eids['ed']) # encoder-decoder edge ids
|
||
# print(graph.eids['dd']) # decoder-decoder edge ids
|
||
# print(graph.src[0]) # Input word index list
|
||
# print(graph.src[1]) # Input positions
|
||
# print(graph.tgt[0]) # Output word index list
|
||
# print(graph.tgt[1]) # Ouptut positions
|
||
# break
|
||
#
|
||
# Output:
|
||
#
|
||
# .. code::
|
||
#
|
||
# tensor([0, 1, 2, 3, 4, 5, 6, 7, 8], device='cuda:0')
|
||
# tensor([ 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], device='cuda:0')
|
||
# tensor([ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
|
||
# 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35,
|
||
# 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53,
|
||
# 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71,
|
||
# 72, 73, 74, 75, 76, 77, 78, 79, 80], device='cuda:0')
|
||
# tensor([ 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94,
|
||
# 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108,
|
||
# 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122,
|
||
# 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136,
|
||
# 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150,
|
||
# 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164,
|
||
# 165, 166, 167, 168, 169, 170], device='cuda:0')
|
||
# tensor([171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184,
|
||
# 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198,
|
||
# 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
|
||
# 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225],
|
||
# device='cuda:0')
|
||
# tensor([28, 25, 7, 26, 6, 4, 5, 9, 18], device='cuda:0')
|
||
# tensor([0, 1, 2, 3, 4, 5, 6, 7, 8], device='cuda:0')
|
||
# tensor([ 0, 28, 25, 7, 26, 6, 4, 5, 9, 18], device='cuda:0')
|
||
# tensor([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], device='cuda:0')
|
||
#
|
||
# Put it all together
|
||
# -------------------
|
||
#
|
||
# Train a one-head transformer with one layer, 128 dimension on copy
|
||
# task. Set other parameters to the default.
|
||
#
|
||
# Inference module is not included in this tutorial. It
|
||
# requires beam search. For a full implementation, see the `GitHub
|
||
# repo <https://github.com/dmlc/dgl/tree/master/examples/pytorch/transformer>`__.
|
||
#
|
||
# .. code:: python
|
||
#
|
||
# from tqdm.auto import tqdm
|
||
# import torch as th
|
||
# import numpy as np
|
||
#
|
||
# from loss import LabelSmoothing, SimpleLossCompute
|
||
# from modules import make_model
|
||
# from optims import NoamOpt
|
||
# from dgl.contrib.transformer import get_dataset, GraphPool
|
||
#
|
||
# def run_epoch(data_iter, model, loss_compute, is_train=True):
|
||
# for i, g in tqdm(enumerate(data_iter)):
|
||
# with th.set_grad_enabled(is_train):
|
||
# output = model(g)
|
||
# loss = loss_compute(output, g.tgt_y, g.n_tokens)
|
||
# print('average loss: {}'.format(loss_compute.avg_loss))
|
||
# print('accuracy: {}'.format(loss_compute.accuracy))
|
||
#
|
||
# N = 1
|
||
# batch_size = 128
|
||
# devices = ['cuda' if th.cuda.is_available() else 'cpu']
|
||
#
|
||
# dataset = get_dataset("copy")
|
||
# V = dataset.vocab_size
|
||
# criterion = LabelSmoothing(V, padding_idx=dataset.pad_id, smoothing=0.1)
|
||
# dim_model = 128
|
||
#
|
||
# # Create model
|
||
# model = make_model(V, V, N=N, dim_model=128, dim_ff=128, h=1)
|
||
#
|
||
# # Sharing weights between Encoder & Decoder
|
||
# model.src_embed.lut.weight = model.tgt_embed.lut.weight
|
||
# model.generator.proj.weight = model.tgt_embed.lut.weight
|
||
#
|
||
# model, criterion = model.to(devices[0]), criterion.to(devices[0])
|
||
# model_opt = NoamOpt(dim_model, 1, 400,
|
||
# th.optim.Adam(model.parameters(), lr=1e-3, betas=(0.9, 0.98), eps=1e-9))
|
||
# loss_compute = SimpleLossCompute
|
||
#
|
||
# att_maps = []
|
||
# for epoch in range(4):
|
||
# train_iter = dataset(graph_pool, mode='train', batch_size=batch_size, devices=devices)
|
||
# valid_iter = dataset(graph_pool, mode='valid', batch_size=batch_size, devices=devices)
|
||
# print('Epoch: {} Training...'.format(epoch))
|
||
# model.train(True)
|
||
# run_epoch(train_iter, model,
|
||
# loss_compute(criterion, model_opt), is_train=True)
|
||
# print('Epoch: {} Evaluating...'.format(epoch))
|
||
# model.att_weight_map = None
|
||
# model.eval()
|
||
# run_epoch(valid_iter, model,
|
||
# loss_compute(criterion, None), is_train=False)
|
||
# att_maps.append(model.att_weight_map)
|
||
#
|
||
# Visualization
|
||
# -------------
|
||
#
|
||
# After training, you can visualize the attention that the Transformer generates
|
||
# on copy task.
|
||
#
|
||
# .. code:: python
|
||
#
|
||
# src_seq = dataset.get_seq_by_id(VIZ_IDX, mode='valid', field='src')
|
||
# tgt_seq = dataset.get_seq_by_id(VIZ_IDX, mode='valid', field='tgt')[:-1]
|
||
# # visualize head 0 of encoder-decoder attention
|
||
# att_animation(att_maps, 'e2d', src_seq, tgt_seq, 0)
|
||
#
|
||
# |image5| from the figure you see the decoder nodes gradually learns to
|
||
# attend to corresponding nodes in input sequence, which is the expected
|
||
# behavior.
|
||
#
|
||
# Multi-head attention
|
||
# ~~~~~~~~~~~~~~~~~~~~
|
||
#
|
||
# Besides the attention of a one-head attention trained on toy task. We
|
||
# also visualize the attention scores of Encoder’s Self Attention,
|
||
# Decoder’s Self Attention and the Encoder-Decoder attention of an
|
||
# one-Layer Transformer network trained on multi-30k dataset.
|
||
#
|
||
# From the visualization you see the diversity of different heads, which is what you would
|
||
# expect. Different heads learn different relations between word pairs.
|
||
#
|
||
# - **Encoder Self-Attention** |image6|
|
||
#
|
||
# - **Encoder-Decoder Attention** Most words in target sequence attend on
|
||
# their related words in source sequence, for example: when generating
|
||
# “See” (in De), several heads attend on “lake”; when generating
|
||
# “Eisfischerhütte”, several heads attend on “ice”. |image7|
|
||
#
|
||
# - **Decoder Self-Attention** Most words attend on their previous few
|
||
# words. |image8|
|
||
#
|
||
# Adaptive Universal Transformer
|
||
# ------------------------------
|
||
#
|
||
# A recent research paper by Google, `Universal
|
||
# Transformer <https://arxiv.org/pdf/1807.03819.pdf>`__, is an example to
|
||
# show how ``update_graph`` adapts to more complex updating rules.
|
||
#
|
||
# The Universal Transformer was proposed to address the problem that
|
||
# vanilla Transformer is not computationally universal by introducing
|
||
# recurrence in Transformer:
|
||
#
|
||
# - The basic idea of Universal Transformer is to repeatedly revise its
|
||
# representations of all symbols in the sequence with each recurrent
|
||
# step by applying a Transformer layer on the representations.
|
||
# - Compared to vanilla Transformer, Universal Transformer shares weights
|
||
# among its layers, and it does not fix the recurrence time (which
|
||
# means the number of layers in Transformer).
|
||
#
|
||
# A further optimization employs an `adaptive computation time
|
||
# (ACT) <https://arxiv.org/pdf/1603.08983.pdf>`__ mechanism to allow the
|
||
# model to dynamically adjust the number of times the representation of
|
||
# each position in a sequence is revised (refereed to as **step**
|
||
# hereafter). This model is also known as the Adaptive Universal
|
||
# Transformer (AUT).
|
||
#
|
||
# In AUT, you maintain an active nodes list. In each step :math:`t`, we
|
||
# compute a halting probability: :math:`h (0<h<1)` for all nodes in this
|
||
# list by:
|
||
#
|
||
# .. math:: h^t_i = \sigma(W_h x^t_i + b_h)
|
||
#
|
||
# then dynamically decide which nodes are still active. A node is halted
|
||
# at time :math:`T` if and only if
|
||
# :math:`\sum_{t=1}^{T-1} h_t < 1 - \varepsilon \leq \sum_{t=1}^{T}h_t`.
|
||
# Halted nodes are removed from the list. The procedure proceeds until the
|
||
# list is empty or a pre-defined maximum step is reached. From DGL’s
|
||
# perspective, this means that the “active” graph becomes sparser over
|
||
# time.
|
||
#
|
||
# The final state of a node :math:`s_i` is a weighted average of
|
||
# :math:`x_i^t` by :math:`h_i^t`:
|
||
#
|
||
# .. math:: s_i = \sum_{t=1}^{T} h_i^t\cdot x_i^t
|
||
#
|
||
# In DGL, implement an algorithm by calling
|
||
# ``update_graph`` on nodes that are still active and edges associated
|
||
# with this nodes. The following code shows the Universal Transformer
|
||
# class in DGL:
|
||
#
|
||
# .. code::
|
||
#
|
||
# class UTransformer(nn.Module):
|
||
# "Universal Transformer(https://arxiv.org/pdf/1807.03819.pdf) with ACT(https://arxiv.org/pdf/1603.08983.pdf)."
|
||
# MAX_DEPTH = 8
|
||
# thres = 0.99
|
||
# act_loss_weight = 0.01
|
||
# def __init__(self, encoder, decoder, src_embed, tgt_embed, pos_enc, time_enc, generator, h, d_k):
|
||
# super(UTransformer, self).__init__()
|
||
# self.encoder, self.decoder = encoder, decoder
|
||
# self.src_embed, self.tgt_embed = src_embed, tgt_embed
|
||
# self.pos_enc, self.time_enc = pos_enc, time_enc
|
||
# self.halt_enc = HaltingUnit(h * d_k)
|
||
# self.halt_dec = HaltingUnit(h * d_k)
|
||
# self.generator = generator
|
||
# self.h, self.d_k = h, d_k
|
||
#
|
||
# def step_forward(self, nodes):
|
||
# # add positional encoding and time encoding, increment step by one
|
||
# x = nodes.data['x']
|
||
# step = nodes.data['step']
|
||
# pos = nodes.data['pos']
|
||
# return {'x': self.pos_enc.dropout(x + self.pos_enc(pos.view(-1)) + self.time_enc(step.view(-1))),
|
||
# 'step': step + 1}
|
||
#
|
||
# def halt_and_accum(self, name, end=False):
|
||
# "field: 'enc' or 'dec'"
|
||
# halt = self.halt_enc if name == 'enc' else self.halt_dec
|
||
# thres = self.thres
|
||
# def func(nodes):
|
||
# p = halt(nodes.data['x'])
|
||
# sum_p = nodes.data['sum_p'] + p
|
||
# active = (sum_p < thres) & (1 - end)
|
||
# _continue = active.float()
|
||
# r = nodes.data['r'] * (1 - _continue) + (1 - sum_p) * _continue
|
||
# s = nodes.data['s'] + ((1 - _continue) * r + _continue * p) * nodes.data['x']
|
||
# return {'p': p, 'sum_p': sum_p, 'r': r, 's': s, 'active': active}
|
||
# return func
|
||
#
|
||
# def propagate_attention(self, g, eids):
|
||
# # Compute attention score
|
||
# g.apply_edges(src_dot_dst('k', 'q', 'score'), eids)
|
||
# g.apply_edges(scaled_exp('score', np.sqrt(self.d_k)), eids)
|
||
# # Send weighted values to target nodes
|
||
# g.send_and_recv(eids,
|
||
# [fn.u_mul_e('v', 'score', 'v'), fn.copy_e('score', 'score')],
|
||
# [fn.sum('v', 'wv'), fn.sum('score', 'z')])
|
||
#
|
||
# def update_graph(self, g, eids, pre_pairs, post_pairs):
|
||
# "Update the node states and edge states of the graph."
|
||
# # Pre-compute queries and key-value pairs.
|
||
# for pre_func, nids in pre_pairs:
|
||
# g.apply_nodes(pre_func, nids)
|
||
# self.propagate_attention(g, eids)
|
||
# # Further calculation after attention mechanism
|
||
# for post_func, nids in post_pairs:
|
||
# g.apply_nodes(post_func, nids)
|
||
#
|
||
# def forward(self, graph):
|
||
# g = graph.g
|
||
# N, E = graph.n_nodes, graph.n_edges
|
||
# nids, eids = graph.nids, graph.eids
|
||
#
|
||
# # embed & pos
|
||
# g.nodes[nids['enc']].data['x'] = self.src_embed(graph.src[0])
|
||
# g.nodes[nids['dec']].data['x'] = self.tgt_embed(graph.tgt[0])
|
||
# g.nodes[nids['enc']].data['pos'] = graph.src[1]
|
||
# g.nodes[nids['dec']].data['pos'] = graph.tgt[1]
|
||
#
|
||
# # init step
|
||
# device = next(self.parameters()).device
|
||
# g.ndata['s'] = th.zeros(N, self.h * self.d_k, dtype=th.float, device=device) # accumulated state
|
||
# g.ndata['p'] = th.zeros(N, 1, dtype=th.float, device=device) # halting prob
|
||
# g.ndata['r'] = th.ones(N, 1, dtype=th.float, device=device) # remainder
|
||
# g.ndata['sum_p'] = th.zeros(N, 1, dtype=th.float, device=device) # sum of pondering values
|
||
# g.ndata['step'] = th.zeros(N, 1, dtype=th.long, device=device) # step
|
||
# g.ndata['active'] = th.ones(N, 1, dtype=th.uint8, device=device) # active
|
||
#
|
||
# for step in range(self.MAX_DEPTH):
|
||
# pre_func = self.encoder.pre_func('qkv')
|
||
# post_func = self.encoder.post_func()
|
||
# nodes = g.filter_nodes(lambda v: v.data['active'].view(-1), nids['enc'])
|
||
# if len(nodes) == 0: break
|
||
# edges = g.filter_edges(lambda e: e.dst['active'].view(-1), eids['ee'])
|
||
# end = step == self.MAX_DEPTH - 1
|
||
# self.update_graph(g, edges,
|
||
# [(self.step_forward, nodes), (pre_func, nodes)],
|
||
# [(post_func, nodes), (self.halt_and_accum('enc', end), nodes)])
|
||
#
|
||
# g.nodes[nids['enc']].data['x'] = self.encoder.norm(g.nodes[nids['enc']].data['s'])
|
||
#
|
||
# for step in range(self.MAX_DEPTH):
|
||
# pre_func = self.decoder.pre_func('qkv')
|
||
# post_func = self.decoder.post_func()
|
||
# nodes = g.filter_nodes(lambda v: v.data['active'].view(-1), nids['dec'])
|
||
# if len(nodes) == 0: break
|
||
# edges = g.filter_edges(lambda e: e.dst['active'].view(-1), eids['dd'])
|
||
# self.update_graph(g, edges,
|
||
# [(self.step_forward, nodes), (pre_func, nodes)],
|
||
# [(post_func, nodes)])
|
||
#
|
||
# pre_q = self.decoder.pre_func('q', 1)
|
||
# pre_kv = self.decoder.pre_func('kv', 1)
|
||
# post_func = self.decoder.post_func(1)
|
||
# nodes_e = nids['enc']
|
||
# edges = g.filter_edges(lambda e: e.dst['active'].view(-1), eids['ed'])
|
||
# end = step == self.MAX_DEPTH - 1
|
||
# self.update_graph(g, edges,
|
||
# [(pre_q, nodes), (pre_kv, nodes_e)],
|
||
# [(post_func, nodes), (self.halt_and_accum('dec', end), nodes)])
|
||
#
|
||
# g.nodes[nids['dec']].data['x'] = self.decoder.norm(g.nodes[nids['dec']].data['s'])
|
||
# act_loss = th.mean(g.ndata['r']) # ACT loss
|
||
#
|
||
# return self.generator(g.ndata['x'][nids['dec']]), act_loss * self.act_loss_weight
|
||
#
|
||
# Call ``filter_nodes`` and ``filter_edge`` to find nodes/edges
|
||
# that are still active:
|
||
#
|
||
# .. note::
|
||
#
|
||
# - :func:`~dgl.DGLGraph.filter_nodes` takes a predicate and a node
|
||
# ID list/tensor as input, then returns a tensor of node IDs that satisfy
|
||
# the given predicate.
|
||
# - :func:`~dgl.DGLGraph.filter_edges` takes a predicate
|
||
# and an edge ID list/tensor as input, then returns a tensor of edge IDs
|
||
# that satisfy the given predicate.
|
||
#
|
||
# For the full implementation, see the `GitHub
|
||
# repo <https://github.com/dmlc/dgl/tree/master/examples/pytorch/transformer/modules/act.py>`__.
|
||
#
|
||
# The figure below shows the effect of Adaptive Computational
|
||
# Time. Different positions of a sentence were revised different times.
|
||
#
|
||
# |image9|
|
||
#
|
||
# You can also visualize the dynamics of step distribution on nodes during the
|
||
# training of AUT on sort task(reach 99.7% accuracy), which demonstrates
|
||
# how AUT learns to reduce recurrence steps during training. |image10|
|
||
#
|
||
# .. |image0| image:: https://i.imgur.com/zV5LmTX.png
|
||
# .. |image1| image:: https://i.imgur.com/dETQMMx.png
|
||
# .. |image2| image:: https://i.imgur.com/hnGP229.png
|
||
# .. |image3| image:: https://i.imgur.com/Hj2rRGT.png
|
||
# .. |image4| image:: https://i.imgur.com/zlUpJ41.png
|
||
# .. |image5| image:: https://s1.ax1x.com/2018/12/06/F126xI.gif
|
||
# .. |image6| image:: https://i.imgur.com/HjYb7F2.png
|
||
# .. |image7| image:: https://i.imgur.com/383J5O5.png
|
||
# .. |image8| image:: https://i.imgur.com/c0UWB1V.png
|
||
# .. |image9| image:: https://s1.ax1x.com/2018/12/06/F1sGod.png
|
||
# .. |image10| image:: https://s1.ax1x.com/2018/12/06/F1r8Cq.gif
|
||
#
|
||
# .. note::
|
||
# The notebook itself is not executable due to many dependencies.
|
||
# Download `7_transformer.py <https://data.dgl.ai/tutorial/7_transformer.py>`__,
|
||
# and copy the python script to directory ``examples/pytorch/transformer``
|
||
# then run ``python 7_transformer.py`` to see how it works.
|