求以十为单位的变长三维矩阵的和或平均值

Question

我要做一个3d张量的平均值，其中第一个维度表示批处理的大小，第二个维度表示批处理中句子的最大长度（时间轴），最后一个维度表示嵌入维度。熟悉lstm的人可以通过tf.nn.emebedding_lookup获得

例如：

Assume I have 3 sentences
[ [i, love, you,], [i, don't, love, you,], [i, always, love, you, so, much ]]

这里batch_size = 3，max_length = 6（第三句话）并假设embedding dimension = 100。一般情况下，我们会把前两个句子填充起来，以匹配最大长度。现在，我需要平均每个单词的单词嵌入量。但是，如果我使用tf.减少总额这两个向量会考虑到第一个错误的句子。在tensorflow中有没有一种有效的方法可以做到这一点。在

Answer 1

方法如下。这有点复杂，但效果很好。在

一些函数是从https://github.com/tensorflow/tensorflow/blob/master/tensorflow/python/ops/rnn.py得到的。我建议执行与上述代码相同的导入。主要代码如下

def _dynamic_average_loop(inputs,
                  initial_state,
                  parallel_iterations,
                  swap_memory,
                  sequence_length=None,
                  dtype=None):

        state = initial_state
        assert isinstance(parallel_iterations, int), "parallel_iterations must be int"
        flat_input = nest.flatten(inputs)
        embedding_dimension = tf.shape(inputs)[2]
        flat_output_size = [embedding_dimension]

        # Construct an initial output
        input_shape = array_ops.shape(flat_input[0])
        time_steps = input_shape[0]
        batch_size = _best_effort_input_batch_size(flat_input)

        inputs_got_shape = tuple(input_.get_shape().with_rank_at_least(3)
                               for input_ in flat_input)

        const_time_steps, const_batch_size = inputs_got_shape[0].as_list()[:2]

        for shape in inputs_got_shape:
            if not shape[2:].is_fully_defined():
              raise ValueError(
                  "Input size (depth of inputs) must be accessible via shape inference,"
                  " but saw value None.")
            got_time_steps = shape[0].value
            got_batch_size = shape[1].value
            if const_time_steps != got_time_steps:
              raise ValueError(
                  "Time steps is not the same for all the elements in the input in a "
                  "batch.")
            if const_batch_size != got_batch_size:
              raise ValueError(
        "Batch_size is not the same for all the elements in the input.")
        # Prepare dynamic conditional copying of state & output
        def _create_zero_arrays(size):
            size = _concat(batch_size, size)
            return array_ops.zeros(
                array_ops.stack(size), _infer_state_dtype(dtype, state))

        flat_zero_output = tuple(_create_zero_arrays(output)
                               for output in flat_output_size)
        zero_output = nest.pack_sequence_as(structure=embedding_dimension,
                                          flat_sequence=flat_zero_output)

        if sequence_length is not None:
            min_sequence_length = math_ops.reduce_min(sequence_length)
            max_sequence_length = math_ops.reduce_max(sequence_length)
        else:
            max_sequence_length = time_steps

        time = array_ops.constant(0, dtype=dtypes.int32, name="time")

        with ops.name_scope("dynamic_rnn") as scope:
            base_name = scope

        def _create_ta(name, element_shape, dtype):
            return tensor_array_ops.TensorArray(dtype=dtype,
                                                size=time_steps,
                                                element_shape=element_shape,
                                                tensor_array_name=base_name + name)

        in_graph_mode = not context.executing_eagerly()
        if in_graph_mode:
            output_ta = tuple(
                _create_ta(
                    "output_%d" % i,
                    element_shape=(tensor_shape.TensorShape([const_batch_size])
                                   .concatenate(
                                       _maybe_tensor_shape_from_tensor(out_size))),
                    dtype=_infer_state_dtype(dtype, state))
                for i, out_size in enumerate(flat_output_size))
            input_ta = tuple(
                _create_ta(
                    "input_%d" % i,
                    element_shape=flat_input_i.shape[1:],
                    dtype=flat_input_i.dtype)
                for i, flat_input_i in enumerate(flat_input))
            input_ta = tuple(ta.unstack(input_)
                             for ta, input_ in zip(input_ta, flat_input))
        else:
            output_ta = tuple([0 for _ in range(time_steps.numpy())]
                              for i in range(len(flat_output_size)))
            input_ta = flat_input


        def tf_average(A, B):

            return A+B 


        def _time_step(time, output_ta_t, state):

            input_t = tuple(ta.read(time) for ta in input_ta)
            # Restore some shape information
            for input_, shape in zip(input_t, inputs_got_shape):
                input_.set_shape(shape[1:])

            input_t = nest.pack_sequence_as(structure=inputs, flat_sequence=input_t)

            flat_state = nest.flatten(state)
            flat_zero_output = nest.flatten(zero_output)

            # Vector describing which batch entries are finished.
            copy_cond = time >= sequence_length



            def _copy_one_through(output, new_output):
                # Otherwise propagate the old or the new value.
                with ops.colocate_with(new_output):
                    return array_ops.where(copy_cond, output, new_output)

            the_average = tf_average(input_t, state)
            the_average_updated = _copy_one_through(zero_output, the_average)
            the_average_last_state = _copy_one_through(state, the_average)

            for output, flat_output in zip([the_average_updated], flat_zero_output):
                output.set_shape(flat_output.get_shape())

            final_output = nest.pack_sequence_as(structure=zero_output, flat_sequence=[the_average_updated])
            output_ta_t = tuple(ta.write(time, out) for ta, out in zip(output_ta_t, [final_output]))
            return (time + 1, output_ta_t, the_average_last_state)


        if in_graph_mode:
            # Make sure that we run at least 1 step, if necessary, to ensure
            # the TensorArrays pick up the dynamic shape.
            loop_bound = math_ops.minimum(
                time_steps, math_ops.maximum(1, max_sequence_length))
        else:
        # Using max_sequence_length isn't currently supported in the Eager branch.
            loop_bound = time_steps

        _, output_final_ta, final_state = control_flow_ops.while_loop(
              cond=lambda time, *_: time < loop_bound,
              body=_time_step,
              loop_vars=(time, output_ta, state),
              parallel_iterations=parallel_iterations,
              maximum_iterations=time_steps,
             swap_memory=swap_memory)

        final_outputs = tuple(ta.stack() for ta in output_final_ta)
            # Restore some shape information
        for output, output_size in zip(final_outputs, flat_output_size):
            shape = _concat(
              [const_time_steps, const_batch_size], output_size, static=True)
            output.set_shape(shape)

        final_outputs = nest.pack_sequence_as(structure=embedding_dimension,
                                              flat_sequence=final_outputs)

        return final_outputs , final_state



def dynamic_average(inputs, sequence_length=None, initial_state=None,
            dtype=None, parallel_iterations=None, swap_memory=False,
            time_major=False, scope=None):

        with vs.variable_scope(scope or "rnn") as varscope:
        # Create a new scope in which the caching device is either
        # determined by the parent scope, or is set to place the cached
        # Variable using the same placement as for the rest of the RNN.
            if _should_cache():
              if varscope.caching_device is None:
                varscope.set_caching_device(lambda op: op.device)

            # By default, time_major==False and inputs are batch-major: shaped
            #   [batch, time, depth]
            # For internal calculations, we transpose to [time, batch, depth]
        flat_input = nest.flatten(inputs)
        embedding_dimension = tf.shape(inputs)[2]

        if not time_major:
          # (B,T,D) => (T,B,D)
          flat_input = [ops.convert_to_tensor(input_) for input_ in flat_input]
          flat_input = tuple(_transpose_batch_time(input_) for input_ in flat_input)

        parallel_iterations = parallel_iterations or 32
        if sequence_length is not None:
          sequence_length = math_ops.to_int32(sequence_length)
          if sequence_length.get_shape().ndims not in (None, 1):
            raise ValueError(
                "sequence_length must be a vector of length batch_size, "
                "but saw shape: %s" % sequence_length.get_shape())
          sequence_length = array_ops.identity(  # Just to find it in the graph.
              sequence_length, name="sequence_length")

        batch_size = _best_effort_input_batch_size(flat_input)

        state = tf.zeros(shape=(batch_size, embedding_dimension))

        def _assert_has_shape(x, shape):
          x_shape = array_ops.shape(x)
          packed_shape = array_ops.stack(shape)
          return control_flow_ops.Assert(
              math_ops.reduce_all(math_ops.equal(x_shape, packed_shape)),
              ["Expected shape for Tensor %s is " % x.name,
               packed_shape, " but saw shape: ", x_shape])

        if not context.executing_eagerly() and sequence_length is not None:
          # Perform some shape validation
          with ops.control_dependencies(
              [_assert_has_shape(sequence_length, [batch_size])]):
            sequence_length = array_ops.identity(
                sequence_length, name="CheckSeqLen")

        inputs = nest.pack_sequence_as(structure=inputs, flat_sequence=flat_input)

        (outputs, final_state) = _dynamic_average_loop(
            inputs,
            state,
            parallel_iterations=parallel_iterations,
            swap_memory=swap_memory,
            sequence_length=sequence_length,
    dtype=dtype)

        if not time_major:
            outputs = nest.map_structure(_transpose_batch_time, outputs)
        return outputs, final_state

这是主代码。所以要求一个3D矩阵的和，长度可变，如RNN中的，我们可以测试如下

^{pr2}$

Answer 2

一个可能的解决方案是将原始句子（没有填充的句子）的长度传递给模型。这样我们就可以计算出每个句子的正确平均嵌入量。在

在预处理阶段（生成句子时），跟踪每个句子的长度。假设您用generate_batch函数生成句子，然后：

batch = generate_batch(...)
batch_sentences = batch["sentences"] # [[i, love, you], [i, don't, love, you], ...]
batch_sentence_lengths = batch["sentence_lengths"] # [3, 4, ...]

现在，您可以将句子及其长度输入模型：

^{pr2}$

现在可以使用模型中每个句子的长度：

...
# sentence_lengths is a sequence of integers: convert it to a sequence of floats
# sentence_lengths_float.shape = sentence_lengths.shape = (batch_size, )
sentence_lengths_float = tf.cast(sentence_lengths, tf.float32)

# Compute the sum of the embeddings for each sentence.
# If sentence_embeddings.shape = (batch_size, max_sentence_length, embedding_size), then sentence_axis = 1
# embeddings_sum_for_each_sentence.shape = (batch_size, embeddings_size)
embeddings_sum_for_each_sentence = tf.reduce_sum(sentence_embeddings, axis=sentence_axis)

# tf.div(a, b) divides each element of the last dimension of a by each element of b as long as the a.shape[-1] = n and b.shape = (1, n). See broadcasting in tf.
# If a is matrix, then tf.div divides each element of a row by the corresponding element in b. But we want a column-wise division, so we need to transpose a first.
# embeddings_avg_for_each_sentence_t.shape = (embedding_size, batch_size)
embeddings_avg_for_each_sentence_t = tf.div(tf.transpose(embeddings_sum_for_each_sentence), sentence_lengths_float)

# Finally we need to tranpose the result again.
# embeddings_avg_for_each_sentence.shape = (batch_size, embedding_size)
embeddings_avg_for_each_sentence = tf.tranpose(embeddings_avg_for_each_sentence_t)
...