modeling.py

import tensorflow as tf


def positional_embedding(pos_seq, inv_freq, bsz=None):
  sinusoid_inp = tf.einsum('i,j->ij', pos_seq, inv_freq)
  pos_emb = tf.concat([tf.sin(sinusoid_inp), tf.cos(sinusoid_inp)], -1)
  if bsz is not None:
    return tf.tile(pos_emb[:, None, :], [1, bsz, 1])
  else:
    return pos_emb[:, None, :]


def positionwise_FF(inp, d_model, d_inner, dropout, kernel_initializer,
                    scope='ff', is_training=True):
  output = inp
  with tf.variable_scope(scope):
    output = tf.layers.dense(inp, d_inner, activation=tf.nn.relu,
                             kernel_initializer=kernel_initializer,
                             name='layer_1')
    output = tf.layers.dropout(output, dropout, training=is_training,
                               name='drop_1')
    output = tf.layers.dense(output, d_model,
                             kernel_initializer=kernel_initializer,
                             name='layer_2')
    output = tf.layers.dropout(output, dropout, training=is_training,
                               name='drop_2')
    output = tf.contrib.layers.layer_norm(output + inp, begin_norm_axis=-1)
  return output


def rel_shift(x):
  x_size = tf.shape(x)

  x = tf.pad(x, [[0, 0], [1, 0], [0, 0], [0, 0]])
  x = tf.reshape(x, [x_size[1] + 1, x_size[0], x_size[2], x_size[3]])
  x = tf.slice(x, [1, 0, 0, 0], [-1, -1, -1, -1])
  x = tf.reshape(x, x_size)

  return x


def rel_multihead_attn(w, r, r_w_bias, r_r_bias, attn_mask, mems, d_model,
                       n_head, d_head, dropout, dropatt, is_training,
                       kernel_initializer, scope='rel_attn'):
  scale = 1 / (d_head ** 0.5)
  with tf.variable_scope(scope):
    qlen = tf.shape(w)[0]
    rlen = tf.shape(r)[0]
    bsz = tf.shape(w)[1]

    cat = tf.concat([mems, w],
                    0) if mems is not None and mems.shape.ndims > 1 else w
    w_heads = tf.layers.dense(cat, 3 * n_head * d_head, use_bias=False,
                              kernel_initializer=kernel_initializer, name='qkv')
    r_head_k = tf.layers.dense(r, n_head * d_head, use_bias=False,
                               kernel_initializer=kernel_initializer, name='r')

    w_head_q, w_head_k, w_head_v = tf.split(w_heads, 3, -1)
    w_head_q = w_head_q[-qlen:]

    klen = tf.shape(w_head_k)[0]

    w_head_q = tf.reshape(w_head_q, [qlen, bsz, n_head, d_head])
    w_head_k = tf.reshape(w_head_k, [klen, bsz, n_head, d_head])
    w_head_v = tf.reshape(w_head_v, [klen, bsz, n_head, d_head])

    r_head_k = tf.reshape(r_head_k, [rlen, n_head, d_head])

    rw_head_q = w_head_q + r_w_bias
    rr_head_q = w_head_q + r_r_bias

    AC = tf.einsum('ibnd,jbnd->ijbn', rw_head_q, w_head_k)
    BD = tf.einsum('ibnd,jnd->ijbn', rr_head_q, r_head_k)
    BD = rel_shift(BD)

    attn_score = (AC + BD) * scale
    attn_mask_t = attn_mask[:, :, None, None]
    attn_score = attn_score * (1 - attn_mask_t) - 1e30 * attn_mask_t

    attn_prob = tf.nn.softmax(attn_score, 1)
    attn_prob = tf.layers.dropout(attn_prob, dropatt, training=is_training)

    attn_vec = tf.einsum('ijbn,jbnd->ibnd', attn_prob, w_head_v)
    size_t = tf.shape(attn_vec)
    attn_vec = tf.reshape(attn_vec, [size_t[0], size_t[1], n_head * d_head])

    attn_out = tf.layers.dense(attn_vec, d_model, use_bias=False,
                               kernel_initializer=kernel_initializer, name='o')
    attn_out = tf.layers.dropout(attn_out, dropout, training=is_training)

    output = tf.contrib.layers.layer_norm(attn_out + w, begin_norm_axis=-1)
  return output


def embedding_lookup(lookup_table, x, use_tpu=True):
  if use_tpu:
    n_token = tf.shape(lookup_table)[0]
    one_hot_idx = tf.one_hot(x, n_token)
    if one_hot_idx.shape.ndims == 2:
      return tf.einsum('nd,in->id', lookup_table, one_hot_idx)
    else:
      return tf.einsum('nd,ibn->ibd', lookup_table, one_hot_idx)
  else:
    return tf.nn.embedding_lookup(lookup_table, x)


def mask_adaptive_embedding_lookup(x, n_token, d_embed, d_proj, cutoffs, initializer,
                                   proj_initializer, div_val=1,
                                   proj_same_dim=True,
                                   scope='adaptive_embed', **kwargs):
  emb_scale = d_proj ** 0.5
  with tf.variable_scope(scope):
    if div_val == 1:
      lookup_table = tf.get_variable('lookup_table', [n_token, d_embed],
                                     initializer=initializer)
      y = embedding_lookup(lookup_table, x, use_tpu=False)
      if d_proj != d_embed:
        proj_W = tf.get_variable('proj_W', [d_embed, d_proj],
                                 initializer=proj_initializer)
        y = tf.einsum('ibe,ed->ibd', y, proj_W)
      else:
        proj_W = None
      ret_params = [lookup_table, proj_W]
    else:
      tables, projs = [], []
      cutoff_ends = [0] + cutoffs + [n_token]
      x_size = tf.shape(x)
      y = tf.zeros([x_size[0], x_size[1], d_proj])
      for i in range(len(cutoff_ends) - 1):
        with tf.variable_scope('cutoff_{}'.format(i)):
          l_idx, r_idx = cutoff_ends[i], cutoff_ends[i + 1]
          mask = (x >= l_idx) & (x < r_idx)
          cur_x = tf.boolean_mask(x, mask) - l_idx
          cur_d_embed = d_embed // (div_val ** i)
          lookup_table = tf.get_variable('lookup_table',
                                         [r_idx - l_idx, cur_d_embed],
                                         initializer=initializer)
          cur_y = embedding_lookup(lookup_table, cur_x, use_tpu=False)
          if d_proj == cur_d_embed and not proj_same_dim:
            proj_W = None
          else:
            proj_W = tf.get_variable('proj_W', [cur_d_embed, d_proj],
                                     initializer=proj_initializer)
            cur_y = tf.einsum('id,de->ie', cur_y, proj_W)
          mask_idx = tf.to_int64(tf.where(mask))
          y += tf.scatter_nd(mask_idx, cur_y, tf.to_int64(tf.shape(y)))
          tables.append(lookup_table)
          projs.append(proj_W)
      ret_params = [tables, projs]

  y *= emb_scale
  return y, ret_params


def mul_adaptive_embedding_lookup(x, n_token, d_embed, d_proj, cutoffs, initializer,
                                  proj_initializer, div_val=1, perms=None,
                                  proj_same_dim=True,
                                  scope='adaptive_embed'):
  """
  perms: If None, first compute W = W1 x W2 (projection for each bin),
      and then compute X x W (embedding lookup). If not None,
      use bin-based embedding lookup with max_bin_size defined by
      the shape of perms.
  """
  emb_scale = d_proj ** 0.5
  with tf.variable_scope(scope):
    if div_val == 1:
      lookup_table = tf.get_variable('lookup_table', [n_token, d_embed],
                                     initializer=initializer)
      y = embedding_lookup(lookup_table, x)
      if d_proj != d_embed:
        proj_W = tf.get_variable('proj_W', [d_embed, d_proj],
                                 initializer=proj_initializer)
        y = tf.einsum('ibe,ed->ibd', y, proj_W)
      else:
        proj_W = None
      ret_params = [lookup_table, proj_W]
    else:
      tables, projs = [], []
      cutoff_ends = [0] + cutoffs + [n_token]
      x_size = tf.shape(x)
      if perms is None:
        cat_lookup = []
      else:
        cat_lookup = tf.zeros([x_size[0], x_size[1], d_proj])
      for i in range(len(cutoff_ends) - 1):
        with tf.variable_scope('cutoff_{}'.format(i)):
          l_idx, r_idx = cutoff_ends[i], cutoff_ends[i + 1]
          cur_d_embed = d_embed // (div_val ** i)
          lookup_table = tf.get_variable('lookup_table',
                                         [r_idx - l_idx, cur_d_embed],
                                         initializer=initializer)
          if cur_d_embed == d_proj and not proj_same_dim:
            proj_W = None
          else:
            proj_W = tf.get_variable('proj_W', [cur_d_embed, d_proj],
                                   initializer=proj_initializer)
          if perms is None:
            cat_lookup.append(tf.einsum('ie,ed->id', lookup_table, proj_W))
          else:
            # speed up the computation of the first bin
            # also save some meory
            if i == 0:
              cur_y = embedding_lookup(lookup_table, tf.minimum(x, r_idx - 1))
              if proj_W is not None:
                cur_y = tf.einsum('ibe,ed->ibd', cur_y, proj_W)
              cur_y *= perms[i][:, :, None]
              cat_lookup += cur_y
            else:
              cur_x = tf.einsum('ib,ibk->k', tf.to_float(x - l_idx), perms[i])
              cur_x = tf.to_int32(cur_x)
              cur_y = embedding_lookup(lookup_table, cur_x)
              if proj_W is not None:
                cur_y = tf.einsum('ke,ed->kd', cur_y, proj_W)
              cat_lookup += tf.einsum('kd,ibk->ibd', cur_y, perms[i])
          tables.append(lookup_table)
          projs.append(proj_W)
      if perms is None:
        cat_lookup = tf.concat(cat_lookup, 0)
        y = embedding_lookup(cat_lookup, x)
      else:
        y = cat_lookup
      ret_params = [tables, projs]

  y *= emb_scale
  return y, ret_params


def mask_adaptive_logsoftmax(hidden, target, n_token, d_embed, d_proj, cutoffs,
                             params, tie_projs,
                             initializer=None, proj_initializer=None,
                             div_val=1, scope='adaptive_softmax',
                             proj_same_dim=True,
                             return_mean=True, **kwargs):
  def _logit(x, W, b, proj):
    y = x
    if proj is not None:
      y = tf.einsum('ibd,ed->ibe', y, proj)
    return tf.einsum('ibd,nd->ibn', y, W) + b

  params_W, params_projs = params[0], params[1]

  def _gather_logprob(logprob, target):
    lp_size = tf.shape(logprob)
    r = tf.range(lp_size[0])
    idx = tf.stack([r, target], 1)
    return tf.gather_nd(logprob, idx)

  with tf.variable_scope(scope):
    if len(cutoffs) == 0:
      softmax_b = tf.get_variable('bias', [n_token],
                                  initializer=tf.zeros_initializer())
      output = _logit(hidden, params_W, softmax_b, params_projs)
      nll = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=target,
                                                           logits=output)
    else:
      cutoff_ends = [0] + cutoffs + [n_token]
      nll = tf.zeros_like(target, dtype=tf.float32)
      for i in range(len(cutoff_ends) - 1):
        with tf.variable_scope('cutoff_{}'.format(i)):
          l_idx, r_idx = cutoff_ends[i], cutoff_ends[i + 1]
          mask = (target >= l_idx) & (target < r_idx)
          mask_idx = tf.where(mask)
          cur_target = tf.boolean_mask(target, mask) - l_idx
          cur_d_embed = d_embed // (div_val ** i)

          if div_val == 1:
            cur_W = params_W[l_idx: r_idx]
          else:
            cur_W = params_W[i]
          cur_b = tf.get_variable('b', [r_idx - l_idx],
                                  initializer=tf.zeros_initializer())
          if tie_projs[i]:
            if div_val == 1:
              cur_proj = params_projs
            else:
              cur_proj = params_projs[i]
          else:
            if (div_val == 1 or not proj_same_dim) and d_proj == cur_d_embed:
              cur_proj = None
            else:
              cur_proj = tf.get_variable('proj', [cur_d_embed, d_proj],
                                         initializer=proj_initializer)
          if i == 0:
            cluster_W = tf.get_variable('cluster_W', [len(cutoffs), d_embed],
                                        initializer=tf.zeros_initializer())
            cluster_b = tf.get_variable('cluster_b', [len(cutoffs)],
                                        initializer=tf.zeros_initializer())
            cur_W = tf.concat([cur_W, cluster_W], 0)
            cur_b = tf.concat([cur_b, cluster_b], 0)

            head_logit = _logit(hidden, cur_W, cur_b, cur_proj)
            head_logprob = tf.nn.log_softmax(head_logit)
            cur_head_logprob = tf.boolean_mask(head_logprob, mask)
            cur_logprob = _gather_logprob(cur_head_logprob, cur_target)
          else:
            cur_head_logprob = tf.boolean_mask(head_logprob, mask)
            cur_hidden = tf.boolean_mask(hidden, mask)
            tail_logit = tf.squeeze(_logit(
                cur_hidden[None], cur_W, cur_b, cur_proj), 0)
            tail_logprob = tf.nn.log_softmax(tail_logit)
            cur_logprob = (cur_head_logprob[:, cutoff_ends[1] + i - 1] +
                           _gather_logprob(tail_logprob, cur_target))
          nll += tf.scatter_nd(mask_idx, -cur_logprob,
                                 tf.to_int64(tf.shape(nll)))
  if return_mean:
    nll = tf.reduce_mean(nll)
  return nll


def mul_adaptive_logsoftmax(hidden, target, n_token, d_embed, d_proj, cutoffs,
                            params, tie_projs,
                            initializer=None, proj_initializer=None,
                            div_val=1, perms=None, proj_same_dim=True,
                            scope='adaptive_softmax',
                            **kwargs):
  def _logit(x, W, b, proj):
    y = x
    if x.shape.ndims == 3:
      if proj is not None:
        y = tf.einsum('ibd,ed->ibe', y, proj)
      return tf.einsum('ibd,nd->ibn', y, W) + b
    else:
      if proj is not None:
        y = tf.einsum('id,ed->ie', y, proj)
      return tf.einsum('id,nd->in', y, W) + b

  params_W, params_projs = params[0], params[1]

  with tf.variable_scope(scope):
    if len(cutoffs) == 0:
      softmax_b = tf.get_variable('bias', [n_token],
                                  initializer=tf.zeros_initializer())
      output = _logit(hidden, params_W, softmax_b, params_projs)
      nll = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=target,
                                                           logits=output)
      nll = tf.reduce_mean(nll)
    else:
      total_loss, total_cnt = 0, 0
      cutoff_ends = [0] + cutoffs + [n_token]
      for i in range(len(cutoff_ends) - 1):
        with tf.variable_scope('cutoff_{}'.format(i)):
          l_idx, r_idx = cutoff_ends[i], cutoff_ends[i + 1]

          cur_d_embed = d_embed // (div_val ** i)

          if div_val == 1:
            cur_W = params_W[l_idx: r_idx]
          else:
            cur_W = params_W[i]
          cur_b = tf.get_variable('b', [r_idx - l_idx],
                                  initializer=tf.zeros_initializer())
          if tie_projs[i]:
            if div_val == 1:
              cur_proj = params_projs
            else:
              cur_proj = params_projs[i]
          else:
            if (div_val == 1 or not proj_same_dim) and d_proj == cur_d_embed:
              cur_proj = None
            else:
              cur_proj = tf.get_variable('proj', [cur_d_embed, d_proj],
                                         initializer=proj_initializer)

          if i == 0:
            cluster_W = tf.get_variable('cluster_W', [len(cutoffs), d_embed],
                                        initializer=tf.zeros_initializer())
            cluster_b = tf.get_variable('cluster_b', [len(cutoffs)],
                                        initializer=tf.zeros_initializer())
            cur_W = tf.concat([cur_W, cluster_W], 0)
            cur_b = tf.concat([cur_b, cluster_b], 0)

            head_logit = _logit(hidden, cur_W, cur_b, cur_proj)

            head_target = kwargs.get("head_target")
            head_nll = tf.nn.sparse_softmax_cross_entropy_with_logits(
                labels=head_target,
                logits=head_logit)

            masked_loss = head_nll * perms[i]
            total_loss += tf.reduce_sum(masked_loss)
            total_cnt += tf.reduce_sum(perms[i])

            # head_logprob = tf.nn.log_softmax(head_logit)

            # final_logprob = head_logprob * perms[i][:, :, None]
            # final_target = tf.one_hot(target, tf.shape(head_logprob)[2])
            # total_loss -= tf.einsum('ibn,ibn->', final_logprob, final_target)
            # total_cnt += tf.reduce_sum(perms[i])
          else:
            cur_head_nll = tf.einsum('ib,ibk->k', head_nll, perms[i])

            cur_hidden = tf.einsum('ibd,ibk->kd', hidden, perms[i])
            tail_logit = _logit(cur_hidden, cur_W, cur_b, cur_proj)

            tail_target = tf.einsum('ib,ibk->k', tf.to_float(target - l_idx),
                                    perms[i])
            tail_nll = tf.nn.sparse_softmax_cross_entropy_with_logits(
                labels=tf.to_int32(tail_target),
                logits=tail_logit)

            sum_nll = cur_head_nll + tail_nll
            mask = tf.reduce_sum(perms[i], [0, 1])

            masked_loss = sum_nll * mask
            total_loss += tf.reduce_sum(masked_loss)
            total_cnt += tf.reduce_sum(mask)

      nll = total_loss / total_cnt

  return nll


def _create_mask(qlen, mlen, same_length=False):
  attn_mask = tf.ones([qlen, qlen])
  mask_u = tf.matrix_band_part(attn_mask, 0, -1)
  mask_dia = tf.matrix_band_part(attn_mask, 0, 0)
  attn_mask_pad = tf.zeros([qlen, mlen])
  ret = tf.concat([attn_mask_pad, mask_u - mask_dia], 1)
  if same_length:
    mask_l = tf.matrix_band_part(attn_mask, -1, 0)
    ret = tf.concat([ret[:, :qlen] + mask_l - mask_dia, ret[:, qlen:]], 1)
  return ret

def _cache_mem(curr_out, prev_mem, mem_len=None):
  if mem_len is None or prev_mem is None:
    new_mem = curr_out
  elif mem_len == 0:
    return prev_mem
  else:
    new_mem = tf.concat([prev_mem, curr_out], 0)[- mem_len:]

  return tf.stop_gradient(new_mem)


def transformer(dec_inp, target, mems, n_token, n_layer, d_model, d_embed,
                n_head, d_head, d_inner, dropout, dropatt,
                initializer, is_training, proj_initializer=None,
                mem_len=None, cutoffs=[], div_val=1, tie_projs=[],
                same_length=False, clamp_len=-1, use_tpu=True,
                input_perms=None, target_perms=None, head_target=None,
                untie_r=False, proj_same_dim=True,
                scope='transformer'):
  """
  cutoffs: a list of python int. Cutoffs for adaptive softmax.
  tie_projs: a list of python bools. Whether to tie the projections.
  use_tpu: if True, use one_hot in embedding lookup and bin-based implementation
        of adaptive softmax.
  perms: a list of tensors. Each tensor should of size [len, bsz, bin_size].
        Only used in the adaptive setting.
  """
  new_mems = []
  with tf.variable_scope(scope):
    if untie_r:
      r_w_bias = tf.get_variable('r_w_bias', [n_layer, n_head, d_head],
                               initializer=initializer)
      r_r_bias = tf.get_variable('r_r_bias', [n_layer, n_head, d_head],
                                 initializer=initializer)
    else:
      r_w_bias = tf.get_variable('r_w_bias', [n_head, d_head],
                                 initializer=initializer)
      r_r_bias = tf.get_variable('r_r_bias', [n_head, d_head],
                                 initializer=initializer)

    qlen = tf.shape(dec_inp)[0]
    mlen = tf.shape(mems[0])[0] if mems is not None else 0
    klen = mlen + qlen

    if proj_initializer is None:
      proj_initializer = initializer
    lookup_fn = (mul_adaptive_embedding_lookup if use_tpu else
                 mask_adaptive_embedding_lookup)
    embeddings, shared_params = lookup_fn(
        x=dec_inp,
        n_token=n_token,
        d_embed=d_embed,
        d_proj=d_model,
        cutoffs=cutoffs,
        initializer=initializer,
        proj_initializer=proj_initializer,
        div_val= div_val,
        perms=input_perms,
        proj_same_dim=proj_same_dim)

    attn_mask = _create_mask(qlen, mlen, same_length)

    pos_seq = tf.range(klen - 1, -1, -1.0)
    if clamp_len > 0:
      pos_seq = tf.minimum(pos_seq, clamp_len)
    inv_freq = 1 / (10000 ** (tf.range(0, d_model, 2.0) / d_model))
    pos_emb = positional_embedding(pos_seq, inv_freq)

    output = tf.layers.dropout(embeddings, dropout, training=is_training)
    pos_emb = tf.layers.dropout(pos_emb, dropout, training=is_training)

    if mems is None:
      mems = [None] * n_layer

    for i in range(n_layer):
      # cache new mems
      new_mems.append(_cache_mem(output, mems[i], mem_len))

      with tf.variable_scope('layer_{}'.format(i)):
        output = rel_multihead_attn(
            w=output,
            r=pos_emb,
            r_w_bias=r_w_bias if not untie_r else r_w_bias[i],
            r_r_bias=r_r_bias if not untie_r else r_r_bias[i],
            attn_mask=attn_mask,
            mems=mems[i],
            d_model=d_model,
            n_head=n_head,
            d_head=d_head,
            dropout=dropout,
            dropatt=dropatt,
            is_training=is_training,
            kernel_initializer=initializer)
        output = positionwise_FF(
            inp=output,
            d_model=d_model,
            d_inner=d_inner,
            dropout=dropout,
            kernel_initializer=initializer,
            is_training=is_training)

    output = tf.layers.dropout(output, dropout, training=is_training)

    logsoftmax_fn = (mul_adaptive_logsoftmax if use_tpu else
                     mask_adaptive_logsoftmax)
    loss = logsoftmax_fn(
        hidden=output,
        target=target,
        n_token=n_token,
        d_embed=d_embed,
        d_proj=d_model,
        cutoffs=cutoffs,
        params=shared_params,
        tie_projs=tie_projs,
        initializer=initializer,
        proj_initializer=proj_initializer,
        div_val=div_val,
        perms=target_perms,
        head_target=head_target,
        proj_same_dim=proj_same_dim)
    return loss, new_mems