def multihead_encdec_attention_incremental(query_antecedent, wq, wo, k, v, mask, name="multihead_attention"): """Incremental attention over encoder (one decode step). In order to use only one variable containing the four weight matrices packed together, we insist that the query and memory antecedents have the same dimensionality (io_channels) and that the keys and values have the same dimensionality (kv_channels). memory_dims is a subset of query_dims Args: query_antecedent: a mtf.Tensor with shape query_dims + [io_channels] wq: a mtf.Tensor with shape [heads, io_channels, kv_channels] wo: a mtf.Tensor with shape [heads, io_channels, kv_channels] k: memory_dims + [heads, memory_length, kv_channels] v: memory_dims + [heads, memory_length, kv_channels] mask: mask Tensor (see attention_mask()) name: an optional string. Returns: A mtf.Tensor with shape [batch, qlen, io_channels] """ heads, _, kv_channels = k.shape.dims[-3:] query_dims = query_antecedent.shape.dims[:-1] with tf.variable_scope(name, default_name="multihead_attention"): q = mtf.einsum( [query_antecedent, wq], mtf.Shape(query_dims + [heads, kv_channels])) o = dot_product_attention(q, k, v, mask) return mtf.einsum([o, wo], query_antecedent.shape)
def masked_local_attention_1d_incremental(x, prev_k, prev_v, step_num, master_dtype=None, slice_dtype=None, params=None, name=None): """Incremental local self-attention (one decode step). Incremental version of masked_local_attention_1d() Args: x: a mtf.Tensor with shape [batch..., io_channels] prev_k: mtf.Tensor with shape [batch..., heads, window_length, kv_channels] prev_v: mtf.Tensor with shape [batch..., heads, window_length, kv_channels] step_num: mtf Scalar with dtype tf.int32 master_dtype: a tf.dtype (deprecated) slice_dtype: a tf.dtype (deprecated) params: a quadruple of Tensors (see multihead_attention_params()) name: an optional string. Returns: y: A mtf.Tensor with shape [batch..., io_channels] new_k: mtf.Tensor with shape [batch..., heads, window_length, kv_channels] new_v: mtf.Tensor with shape [batch..., heads, window_length, kv_channels] Raises: ValueError: if the dimensions do not match. """ batch_dims = x.shape.dims[:-1] io_channels = x.shape.dims[-1] heads, window_length, kv_channels = prev_k.shape.dims[-3:] with tf.variable_scope(name, default_name="masked_local_attention_1d"): if params is None: wq, wk, wv, wo = multihead_attention_vars( x.mesh, heads, io_channels, kv_channels, master_dtype, slice_dtype, x.dtype) else: wq, wk, wv, wo = params q = mtf.einsum([x, wq], mtf.Shape(batch_dims + [heads, kv_channels])) k = mtf.einsum([x, wk], mtf.Shape(batch_dims + [heads, kv_channels])) v = mtf.einsum([x, wv], mtf.Shape(batch_dims + [heads, kv_channels])) current_position = mtf.equal( mtf.range(x.mesh, window_length, dtype=tf.int32), mtf.mod(step_num, window_length.size)) k = mtf.where(current_position, k, prev_k, output_shape=prev_k.shape) v = mtf.where(current_position, v, prev_v, output_shape=prev_v.shape) o = dot_product_attention(q, k, v, mask=None) y = mtf.einsum([o, wo], x.shape) return y, k, v
def dense(x, output_dim, reduced_dims=None, expert_dims=None, use_bias=True, activation=None, master_dtype=tf.float32, slice_dtype=tf.float32, variable_dtype=None, name=None): """Dense layer doing (kernel*x + bias) computation. Args: x: a mtf.Tensor of shape [..., reduced_dims]. output_dim: a mtf.Dimension reduced_dims: an optional list of mtf.Dimensions of x to be reduced. If omitted, we reduce the last dimension. expert_dims: an optional list of mtf.Dimension which represent different experts. Different experts get different weights. use_bias: a boolean, whether to add bias. activation: an optional function from mtf.Tensor to mtf.Tensor master_dtype: a tf.dtype (deprecated - use variable_dtype) slice_dtype: a tf.dtype (deprecated - use variable_dtype) variable_dtype: a mtf.VariableDType name: a string. variable scope. Returns: a mtf.Tensor of shape [..., output_dim]. """ if variable_dtype is None: variable_dtype = mtf.VariableDType(master_dtype, slice_dtype, x.dtype) if expert_dims is None: expert_dims = [] if reduced_dims is None: reduced_dims = x.shape.dims[-1:] w_shape = mtf.Shape(expert_dims + reduced_dims + [output_dim]) output_shape = mtf.Shape( [d for d in x.shape.dims if d not in reduced_dims] + [output_dim]) with tf.variable_scope(name, default_name="dense"): stddev = mtf.list_product(d.size for d in reduced_dims) ** -0.5 w = mtf.get_variable( x.mesh, "kernel", w_shape, initializer=tf.random_normal_initializer(stddev=stddev), dtype=variable_dtype) w = mtf.cast(w, x.dtype) y = mtf.einsum([x, w], output_shape) if use_bias: b = mtf.get_variable( x.mesh, "bias", mtf.Shape(expert_dims + [output_dim]), initializer=tf.zeros_initializer(), dtype=variable_dtype) y += b if activation is not None: y = activation(y) return y
def dot_product_attention(q, k, v, mask, dropout=0.0, dropout_broadcast_dims=None, extra_logit=None): """Dot-product attention. Args: q: Tensor with shape [...., length_q, depth_k]. Typically leading dimensions are [batch, heads]. k: Tensor with shape [..., length_kv, depth_k]. Leading dimensions must match with q. v: Tensor with shape [..., length_kv, depth_v] Leading dimensions must match with q. mask: mask Tensor (see attention_mask()) dropout: a float. dropout_broadcast_dims: an optional list of mtf.Dimension extra_logit: an optional scalar or tensor Returns: Tensor with shape [..., length_q, depth_v]. """ length_kv = k.shape.dims[-2] logits_shape = mtf.Shape(q.shape.dims[:-1] + [length_kv]) logits = mtf.einsum([q, k], logits_shape) if mask is not None: logits += mask weights = mtf.softmax(logits, length_kv, extra_logit=extra_logit) if dropout != 0.0: weights = mtf.dropout( weights, 1.0 - dropout, noise_shape=weights.shape - dropout_broadcast_dims) depth_v = v.shape.dims[-1] outputs_shape = mtf.Shape(q.shape.dims[:-1] + [depth_v]) outputs = mtf.einsum([weights, v], outputs_shape) return outputs
def inner_loop(i, alive_seq, alive_log_probs, finished_seq, finished_scores, finished_flags, *states): """Inner beam search loop. There are three groups of tensors, alive, finished, and topk. The alive group contains information about the current alive sequences The topk group contains information about alive + topk current decoded words the finished group contains information about finished sentences, that is, the ones that have decoded to <EOS>. These are what we return. The general beam search algorithm is as follows: While we haven't terminated (pls look at termination condition) 1. Grow the current alive to get beam*2 topk sequences 2. Among the topk, keep the top beam_size ones that haven't reached EOS into alive 3. Among the topk, keep the top beam_size ones have reached EOS into finished Repeat To make things simple with using fixed size tensors, we will end up inserting unfinished sequences into finished in the beginning. To stop that we add -ve INF to the score of the unfinished sequence so that when a true finished sequence does appear, it will have a higher score than all the unfinished ones. Args: i: loop index alive_seq: Topk sequences decoded so far [batch_size, beam_size, i+1] alive_log_probs: probabilities of the beams. [batch_size, beam_size] finished_seq: Current finished sequences. [batch_size, beam_size, i+1] finished_scores: scores for each of these sequences. [batch_size, beam_size] finished_flags: finished bools for each of these sequences. [batch_size, beam_size] *states: mtf Tensors Returns: Tuple of (Incremented loop index New alive sequences, Log probs of the alive sequences, New finished sequences, Scores of the new finished sequences, Flags indicating which sequence in finished as reached EOS, dict of final decoding states) """ states = [ mtf.replace_dimensions(state, batch_and_beam_dim, [batch_dim, beam_dim]) for state in states ] # Each inner loop, we carry out three steps: # 1. Get the current topk items. # 2. Extract the ones that have finished and haven't finished # 3. Recompute the contents of finished based on scores. (top2k_seq, top2k_log_probs, top2k_scores, top2k_finished, new_states, first_selector) = grow_topk(i, alive_seq, alive_log_probs, states) with tf.variable_scope("grow_alive"): alive_seq, alive_log_probs, _, second_selector = grow_alive( top2k_seq, top2k_scores, top2k_log_probs, top2k_finished) with tf.variable_scope("grow_finished"): finished_seq, finished_scores, finished_flags, _ = grow_finished( finished_seq, finished_scores, finished_flags, top2k_seq, top2k_scores, top2k_finished) old_beam_dim = mtf.Dimension("old_beam", beam_dim.size) selector = mtf.einsum([ mtf.rename_dimension(first_selector, beam_dim.name, old_beam_dim.name), second_selector ], output_shape=[batch_dim, old_beam_dim, beam_dim]) gathered_states = [] if use_tpu and layout is not None and mesh_shape is not None: # This hack combines the beam dimension with some of the batch dimension. # It makes gathering faster on TPU. # # Instead of multiplying by a [beam, beam] selector matrix, we instead # multiply by a [minor_batch*beam, minor_batch*beam] selector matrix. # This is theoretically more FLOPs, but it brings the matrix size closer # to the magic optimal value of 128. # # TODO(noam): file a bug with the XLA team to do this automatically major_batch_size = mtf.tensor_dim_to_mesh_dim_size( layout, mesh_shape, batch_dim) major_batch = mtf.Dimension(batch_dim.name, major_batch_size) minor_batch = mtf.Dimension("minor_batch", batch_dim.size // major_batch.size) old_minor_batch = mtf.Dimension("old_minor_batch", minor_batch.size) old_combined = mtf.Dimension("old_combined", minor_batch.size * beam_dim.size) combined = mtf.Dimension("new_combined", old_combined.size) same_minor_batch = mtf.to_float( mtf.equal(mtf.range(mesh, old_minor_batch, tf.float32), mtf.range(mesh, minor_batch, tf.float32))) selector = mtf.reshape( selector, [major_batch, minor_batch, old_beam_dim, beam_dim]) selector = mtf.einsum([selector, same_minor_batch], output_shape=[ major_batch, old_minor_batch, old_beam_dim, minor_batch, beam_dim ], reduced_dims=[]) selector = mtf.reshape(selector, [major_batch, old_combined, combined]) for state in new_states: s = mtf.replace_dimensions(state, [batch_dim, beam_dim], [major_batch, old_combined]) s = mtf.einsum([s, mtf.cast(selector, state.dtype)], reduced_dims=[old_combined], output_shape=mtf.replace_dimensions( state.shape, [batch_dim, beam_dim], [major_batch, combined])) gathered_states.append( mtf.replace_dimensions(s, [major_batch, combined], batch_and_beam_dim)) else: for state in new_states: state = mtf.einsum([ mtf.rename_dimension(state, beam_dim.name, old_beam_dim.name), mtf.cast(selector, state.dtype) ], reduced_dims=[old_beam_dim], output_shape=state.shape) state = mtf.replace_dimensions(state, [batch_dim, beam_dim], batch_and_beam_dim) gathered_states.append(state) return (i + 1, alive_seq, alive_log_probs, finished_seq, finished_scores, finished_flags) + tuple(gathered_states)
def multihead_self_attention_incremental(query_antecedent, prev_k, prev_v, step_num, master_dtype, slice_dtype, name="multihead_attention"): """Incremental self-attention (one decode step). In order to use only one variable containing the four weight matrices packed together, we insist that the query and memory antecedents have the same dimensionality (io_channels) and that the keys and values have the same dimensionality (kv_channels). Args: query_antecedent: a mtf.Tensor with shape [batch..., io_channels] prev_k: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels] prev_v: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels] step_num: mtf Scalar with dtype tf.int32 master_dtype: a tf.dtype slice_dtype: a tf.dtype name: an optional string. Returns: y: A mtf.Tensor with shape [batch..., io_channels] new_k: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels] new_v: mtf.Tensor with shape [batch..., heads, memory_length, kv_channels] Raises: ValueError: if the dimensions do not match. """ batch_dims = query_antecedent.shape.dims[:-1] io_channels = query_antecedent.shape.dims[-1] heads, memory_length, kv_channels = prev_k.shape.dims[-3:] with tf.variable_scope(name, default_name="multihead_attention"): wq, wk, wv, wo = multihead_attention_vars( query_antecedent.mesh, heads, io_channels, kv_channels, master_dtype, slice_dtype, query_antecedent.dtype) memory_antecedent = query_antecedent q = mtf.einsum( [query_antecedent, wq], mtf.Shape(batch_dims + [heads, kv_channels])) k = mtf.einsum( [memory_antecedent, wk], mtf.Shape(batch_dims + [heads, kv_channels])) v = mtf.einsum( [memory_antecedent, wv], mtf.Shape(batch_dims + [heads, kv_channels])) k = prev_k + mtf.multiply( k, mtf.one_hot(step_num, memory_length, dtype=prev_k.dtype), output_shape=prev_k.shape) v = prev_v + mtf.multiply( v, mtf.one_hot(step_num, memory_length, dtype=prev_v.dtype), output_shape=prev_v.shape) mask = mtf.cast( mtf.greater(mtf.range( query_antecedent.mesh, memory_length, dtype=tf.int32), step_num), q.dtype) * -1e9 o = dot_product_attention(q, k, v, mask) y = mtf.einsum([o, wo], query_antecedent.shape) return y, k, v
def multihead_attention(query_antecedent, memory_antecedent, mask, kv_channels, heads, dropout=0.0, dropout_broadcast_dims=None, master_dtype=tf.float32, slice_dtype=tf.float32, name="multihead_attention"): """Multihead scaled-dot-product attention with input/output transformations. In order to use only one variable containing the four weight matrices packed together, we insist that the query and memory antecedents have the same dimensionality (io_channels) and that the keys and values have the same dimensionality (kv_channels). Args: query_antecedent: a mtf.Tensor with shape [<batch_dims>, query_length, io_channels] memory_antecedent: a mtf.Tensor with shape [batch, memory_length, io_channels] (optional) mask: mask Tensor (see attention_mask()) kv_channels: a mtf.Dimension (the size of the key and value vectors) heads: a mtf.Dimension (the number of heads) dropout: a floating point value dropout_broadcast_dims: an optional list of mtf.Dimension master_dtype: a tf.dtype slice_dtype: a tf.dtype name: an optional string. Returns: A mtf.Tensor with shape [batch, query_length, io_channels] Raises: ValueError: if the dimensions do not match. """ batch_dims = query_antecedent.shape.dims[:-2] query_length, io_channels = query_antecedent.shape.dims[-2:] with tf.variable_scope(name, default_name="multihead_attention", values=[query_antecedent, memory_antecedent]): wq, wk, wv, wo = multihead_attention_vars( query_antecedent.mesh, heads, io_channels, kv_channels, master_dtype, slice_dtype, query_antecedent.dtype) if memory_antecedent is None: memory_antecedent = rename_length_to_memory_length( query_antecedent, query_length.name) memory_batch_dims = memory_antecedent.shape.dims[:-2] memory_length, memory_channels = memory_antecedent.shape.dims[-2:] if memory_batch_dims != batch_dims: raise ValueError("memory batch must equal query batch") if memory_channels != io_channels: raise ValueError("memory channels must equal query channels") q = mtf.einsum( [query_antecedent, wq], mtf.Shape(batch_dims + [heads, query_length, kv_channels])) k = mtf.einsum( [memory_antecedent, wk], mtf.Shape(batch_dims + [heads, memory_length, kv_channels])) v = mtf.einsum( [memory_antecedent, wv], mtf.Shape(batch_dims + [heads, memory_length, kv_channels])) o = dot_product_attention( q, k, v, mask, dropout, dropout_broadcast_dims) return mtf.einsum( [o, wo], mtf.Shape(batch_dims + [query_length, io_channels]))
def local_2d_self_attention_spatial_blocks(query_antecedent, kv_channels, heads, memory_h_dim=None, memory_w_dim=None, mask_right=False, master_dtype=tf.float32, slice_dtype=tf.float32, name=None): """Attention to the source position and a neighborhood to the left or right. The sequence is divided into blocks of length block_size. Attention for a given query position can only see memory positions less than or equal to the query position, in the corresponding block and the previous block. Args: query_antecedent: a mtf.Tensor with shape [batch, num_h_blocks, num_w_blocks, h_dim, w_dim, io_channels] must have the same size as query_length, but a different name. kv_channels: a mtf.Dimension (the size of the key and value vectors) heads: a mtf.Dimension (the number of heads) memory_h_dim: mtf Dimension, for the memory height block. memory_w_dim: mtf Dimension, for the memory width block. mask_right: bool, flag specifying whether we mask out attention to the right for the decoder. master_dtype: a tf.dtype slice_dtype: a tf.dtype name: an optional string. Returns: a Tensor of shape [batch, num_h_blocks, num_w_blocks, h_dim, w_dim, io_channels] Raises: ValueError: if channels or depth don't match. """ with tf.variable_scope( name, default_name="multihead_attention", values=[query_antecedent]): h_dim, w_dim, io_channels = query_antecedent.shape.dims[-3:] batch, num_h_blocks, num_w_blocks = query_antecedent.shape.dims[:3] wq, wk, wv, wo = multihead_attention_vars( query_antecedent.mesh, heads, io_channels, kv_channels, master_dtype, slice_dtype, query_antecedent.dtype) # Rename dimensions for the memory height and width. memory_antecedent = mtf.rename_dimension(query_antecedent, h_dim.name, "memory_" + h_dim.name) memory_antecedent = mtf.rename_dimension(memory_antecedent, w_dim.name, "memory_" + w_dim.name) memory_h_dim, memory_w_dim = memory_antecedent.shape.dims[-3:-1] # Call einsum over the query and memory to get query q, keys k and values v. q = mtf.einsum([query_antecedent, wq], mtf.Shape([ batch, heads, num_h_blocks, num_w_blocks, h_dim, w_dim, kv_channels ])) k = mtf.einsum([memory_antecedent, wk], mtf.Shape([batch, heads, num_h_blocks, num_w_blocks, memory_h_dim, memory_w_dim, kv_channels])) v = mtf.einsum([memory_antecedent, wv], mtf.Shape([batch, heads, num_h_blocks, num_w_blocks, memory_h_dim, memory_w_dim, kv_channels])) # Halo exchange for memory blocks. k, v = local_2d_halo_exchange(k, v, num_h_blocks, memory_h_dim, num_w_blocks, memory_w_dim, mask_right) # Calculate the causal mask to avoid peeking into the future. We compute # this once and reuse it for all blocks since the block_size is known. mask = None if mask_right: mask = attention_bias_local_2d_block(query_antecedent.mesh, h_dim, w_dim, memory_h_dim, memory_w_dim) output = dot_product_attention(q, k, v, mask=mask) return mtf.einsum( [output, wo], mtf.Shape( [batch, num_h_blocks, num_w_blocks, h_dim, w_dim, io_channels]))
def masked_local_attention_1d(x, kv_channels, heads, window_size=128, master_dtype=tf.float32, slice_dtype=tf.float32, length_per_split=None, return_kv=None, params=None, name=None): """Attention to the source position and a neighborhood to the left of it. Attention for a given query position p can only see memory positions in the range (p - window_size, p]. Args: x: a mtf.Tensor with shape batch_dims + [length, io_channels] kv_channels: a mtf.Dimension (the size of the key and value vectors) heads: a mtf.Dimension (the number of heads) window_size: an integer master_dtype: a tf.dtype (deprecated - use params arg) slice_dtype: a tf.dtype (deprecated - use params arg) length_per_split: an optional integer indicating the part of the length dimension per processor. You can omit if the length dimension is not split. return_kv: an optional list onto which to append the computed k and v. params: an optional quadruple of Tensors (see multihead_attention_params()) name: an optional string. Returns: a Tensor with the same shape as x Raises: ValueError: if channels or depth don't match. """ with tf.variable_scope( name, default_name="masked_local_attention_1d", values=[x]): batch_dims = x.shape.dims[:-2] length, io_channels = x.shape.dims[-2:] if params is None: wq, wk, wv, wo = multihead_attention_vars( x.mesh, heads, io_channels, kv_channels, master_dtype, slice_dtype, x.dtype) else: wq, wk, wv, wo = params # Get query q, keys k and values v. qkv_shape = mtf.Shape(batch_dims + [heads, length, kv_channels]) q = mtf.einsum([x, wq], qkv_shape) k = mtf.einsum([x, wk], qkv_shape) v = mtf.einsum([x, wv], qkv_shape) if return_kv is not None: return_kv.extend([k, v]) # Choose a suitable block size. # We choose the greatest divisor of length_per_split less than or equal # to max(window_size, 128) if length_per_split is None: length_per_split = length.size block_length = max(window_size, 128) while length_per_split % block_length != 0: block_length -= 1 query_block_length = mtf.Dimension("query_block_length", block_length) memory_block_length = mtf.Dimension("memory_block_length", block_length) # The num_blocks dimension gets the same name as the length dimension, # so it will be split in the same way. num_blocks = mtf.Dimension(length.name, length.size // block_length) q_shape = batch_dims + [heads, num_blocks, query_block_length, kv_channels] kv_shape = batch_dims + [ heads, num_blocks, memory_block_length, kv_channels] q = mtf.reshape(q, q_shape) k = mtf.reshape(k, kv_shape) v = mtf.reshape(v, kv_shape) # augment the keys and values for each block with keys and values for # the previous window_size timesteps. k = mtf.left_halo_exchange(k, num_blocks, memory_block_length, window_size) v = mtf.left_halo_exchange(v, num_blocks, memory_block_length, window_size) padded_memory_block_length = mtf.Dimension( "memory_block_length", window_size + block_length) mpos = mtf.range(x.mesh, padded_memory_block_length, tf.float32) qpos = mtf.range(x.mesh, query_block_length, tf.float32) + window_size # prevent looking forward mask = mtf.cast(mtf.greater(mpos, qpos), x.dtype) * -1e9 # prevent looking >=block_length timesteps backward mask += mtf.cast(mtf.less_equal(mpos, qpos - block_length), x.dtype) * -1e9 # Note: The first window_size-1 positions can see back into pre-time # where all the keys and values are zero. We could mask this out, but we # don't. o = dot_product_attention(q, k, v, mask=mask) o = mtf.reshape(o, batch_dims + [heads, length, kv_channels]) return mtf.einsum([o, wo], mtf.Shape(batch_dims + [length, io_channels]))
def multihead_self_attention_memory_compressed(x, mask_right, compression_factor, kv_channels, heads, dropout=0.0, dropout_broadcast_dims=None, master_dtype=tf.float32, slice_dtype=tf.float32, name="multihead_attention"): """Memory-compressed self-attention. The memory is first average-pooled (strided) to make it shorter by a factor of compression_factor. Args: x: a mtf.Tensor with shape [<batch_dims>, query_length, io_channels] mask_right: a boolean compression_factor: an integer kv_channels: a mtf.Dimension (the size of the key and value vectors) heads: a mtf.Dimension (the number of heads) dropout: a floating point value dropout_broadcast_dims: an optional list of mtf.Dimension master_dtype: a tf.dtype slice_dtype: a tf.dtype name: an optional string. Returns: A mtf.Tensor with shape [batch, query_length, io_channels] Raises: ValueError: if the dimensions do not match. """ batch_dims = x.shape.dims[:-2] length, io_channels = x.shape.dims[-2:] with tf.variable_scope(name, default_name="compressed_attention", values=[x]): wq, wk, wv, wo = multihead_attention_vars( x.mesh, heads, io_channels, kv_channels, master_dtype, slice_dtype, x.dtype) memory_antecedent = compress_mean(x, length, compression_factor) memory_antecedent = rename_length_to_memory_length(memory_antecedent) memory_length = memory_antecedent.shape.dims[-2] q = mtf.einsum( [x, wq], mtf.Shape(batch_dims + [heads, length, kv_channels])) k = mtf.einsum( [memory_antecedent, wk], mtf.Shape(batch_dims + [heads, memory_length, kv_channels])) v = mtf.einsum( [memory_antecedent, wv], mtf.Shape(batch_dims + [heads, memory_length, kv_channels])) if mask_right: query_pos = mtf.range(x.mesh, length, dtype=tf.int32) memory_pos = ( mtf.range(x.mesh, memory_length, dtype=tf.int32) * compression_factor + (compression_factor - 1)) mask = mtf.cast(mtf.greater(memory_pos, query_pos), x.dtype) * -1e9 else: mask = None o = dot_product_attention( q, k, v, mask, dropout, dropout_broadcast_dims, extra_logit=0.0) return mtf.einsum( [o, wo], mtf.Shape(batch_dims + [length, io_channels]))