def compress_mean(x, dim, compression_factor): """Compress by taking group means. Args: x: a Tensor dim: a dimension in x.shape compression_factor: an integer Returns: a Tensor """ dims = x.shape.dims pos = dims.index(dim) compressed_dim = mtf.Dimension(dim.name, dim.size // compression_factor) compression_factor_dim = mtf.Dimension( "compression_factor", compression_factor) new_shape = ( dims[:pos] + [compressed_dim, compression_factor_dim] + dims[pos + 1:]) x = mtf.reshape(x, new_shape) x = mtf.reduce_mean(x, reduced_dim=compression_factor_dim) return x
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 grow_topk(i, alive_seq, alive_log_probs, states=None): r"""Inner beam search loop. This function takes the current alive sequences, and grows them to topk sequences where k = 2*beam. We use 2*beam because, we could have beam_size number of sequences that might hit <EOS> and there will be no alive sequences to continue. With 2*beam_size, this will not happen. This relies on the assumption the vocab size is > beam size. If this is true, we'll have at least beam_size non <EOS> extensions if we extract the next top 2*beam words. Length penalty is given by = (5+len(decode)/6) ^ -\alpha. Pls refer to https://arxiv.org/abs/1609.08144. Args: i: loop index alive_seq: Topk sequences decoded so far [batch, beam, length] alive_log_probs: probabilities of these sequences. [batch, beam] states: optional list of mtf.Tensor Returns: Tuple of (Topk sequences extended by the next word, The log probs of these sequences, The scores with length penalty of these sequences, Flags indicating which of these sequences have finished decoding, list of transformed decoding states) """ logits, new_states = logits_fn(i, alive_seq, states) batch_dim, beam_dim, vocab_dim = logits.shape.dims # Convert logits to normalized log probs candidate_log_probs = mtf.log_softmax(logits, vocab_dim) # Multiply the probabilities by the current probabilities of the beam. # (batch_size, beam_size, vocab_size) + (batch_size, beam_size, 1) log_probs = candidate_log_probs + alive_log_probs length_penalty = mtf.pow(((5. + mtf.cast(i + 1, logits.dtype)) / 6.), alpha) # scores have shape [batch, beam, vocab] curr_scores = log_probs / length_penalty # We find the top 2k sequences to make sure we get k alive sequences. # # TODO(noam): This is inefficient. We should separately compute the k # finished sequences (previously alive sequences + EOS), and the top k new # alive sequences. double_beam = mtf.Dimension("double_beam", beam_dim.size * 2) if use_tpu and layout is not None and mesh_shape is not None: # Do some partial top-k-ing first locally to avoid communication. # We reshape the logits from: # [batch, beam, vocab] to # [batch, beam, major_vocab, minor_vocab] # We first reduce (locally) across the minor_vocab dimension. This makes # the thing we need to broadcast smaller. # This also enables our shortcut of only picking the top num_prefilter # sequences per beam per major_vocab in the first pass. major_vocab_size = mtf.tensor_dim_to_mesh_dim_size( layout, mesh_shape, vocab_dim) major_vocab = mtf.Dimension(vocab_dim.name, major_vocab_size) minor_vocab = mtf.Dimension("minor_vocab", vocab_dim.size // major_vocab_size) curr_scores = mtf.reshape( curr_scores, [batch_dim, beam_dim, major_vocab, minor_vocab]) prefilter = mtf.Dimension("prefilter", num_prefilter or double_beam.size) # shape = [batch_dim, beam_dim, major_vocab, prefilter] top_scores, top_minor_vocab_ids = mtf.top_k( curr_scores, reduced_dim=minor_vocab, k_dim=prefilter) combined = mtf.Dimension( "combined", beam_dim.size * major_vocab.size * prefilter.size) top_scores = mtf.reshape(top_scores, [batch_dim, combined]) top_minor_vocab_ids = mtf.reshape(top_minor_vocab_ids, [batch_dim, combined]) # shpae = [batch_dim, double_beam] # ids are indices representing (beam, major_vocab, prefilter) top_scores, top_combined_ids = mtf.top_k(top_scores, reduced_dim=combined, k_dim=double_beam) top_minor_vocab_ids = mtf.gather( top_minor_vocab_ids, top_combined_ids, combined, output_shape=[batch_dim, double_beam]) top_beam_index = top_combined_ids // (major_vocab.size * prefilter.size) top_combined_ids -= top_beam_index * (major_vocab.size * prefilter.size) top_major_vocab_ids = top_combined_ids // prefilter.size top_combined_ids -= top_major_vocab_ids * prefilter.size top_ids = top_major_vocab_ids * minor_vocab.size + top_minor_vocab_ids else: beam_and_vocab_dim = mtf.Dimension("beam_and_vocab", beam_dim.size * vocab_dim.size) flat_shape = mtf.Shape([batch_dim, beam_and_vocab_dim]) # Flatten out (beam_size, vocab_size) probs into a list of possibilities flat_curr_scores = mtf.reshape(curr_scores, flat_shape, name="flatten_scores") top_scores, top_ids = mtf.top_k(flat_curr_scores, reduced_dim=beam_and_vocab_dim, k_dim=double_beam) # Work out what beam the top probs are in. top_beam_index = top_ids // vocab_dim.size top_ids %= vocab_dim.size # Unflatten the ids # Recovering the log probs because we will need to send them back top_log_probs = top_scores * length_penalty selector = mtf.one_hot(top_beam_index, beam_dim, dtype=tf.float32) def my_gather(tensor): return mtf.gather(tensor, top_beam_index, beam_dim, output_shape=mtf.Shape([ double_beam if d == beam_dim else d for d in tensor.shape.dims ])) # Gather up the most probable 2*beams both for the ids and finished_in_alive # bools top_seq = my_gather(alive_seq) # Append the most probable alive top_seq += top_ids * mtf.one_hot(i, length_dim, dtype=tf.int32) top_finished = mtf.equal(top_ids, eos_id) return (top_seq, top_log_probs, top_scores, top_finished, new_states, selector)
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]))