def beam_search(model, inputs=None, batch_size=1, n_beams=2, start_id=0,
                eos_id=1, max_length=100, length_penalty=1.0, accelerate=True):
  """Returns a batch of n_beams-sequences created by beam search.

  This function uses `model` to generate outputs one position at a time, with
  access to inputs for the current position and all preceding positions. The
  new output becomes the next position's input, and this loop repeats until
  either the model outputs the `eos_id` value or the output sequence reaches
  `max_length` items -- but keeping n_beams top beams.

  Args:
    model: A layer object (subclass of `trax.layers.Layer`) created in
        `'predict'` mode and initialized from trained weights. The model
        must have a structure that allows it to run as autoregressive
        one-sample-at-a-time predictor (e.g., `trax.models.TransformerLM`).
    inputs: Sequence of symbols the model sees as input the first time it
        generates an output. If None, the model must generate the first output
        with no input to guide it.
    batch_size: Number of sequences to generate in parallel as a batch.
    n_beams: How many beams to consider at the same time.
    start_id: The start symbol (ID/integer) for the autoregressive process,
        or array of shape (`batch_size`, 1) of such integers.
    eos_id: The end-of-sequence symbol (ID/integer) for the autoregressive
        process.
    max_length: Maximum length for generated sequences.
    length_penalty: Factor alpha in calculating the length penalty for beams.
    accelerate: If True, create an accelerated version of `model` and use it
        for generating outputs.

  Returns:
    Tensor of integers with shape (`batch_size`, n_beams, output_length) with
    a batch of output sequences. output_length is the maximum length of the
    output sequences, where each sequence can be no longer than `max_length`.
  """
  del eos_id, length_penalty  # TODO(lukaszkaiser): add length penalty, eos
  assert batch_size == 1, 'Batch size > 1 not supported yet'
  if inputs is not None and inputs.shape[0] != batch_size:
    raise ValueError(f'Inputs batch size ({inputs.shape[0]}) does not match '
                     f'batch_size arg ({batch_size}.')

  fast_model = tl.Accelerate(model) if accelerate else model
  if np.isscalar(start_id):
    start_symbol = np.full((batch_size, 1), start_id, dtype=np.int32)
  else:
    start_symbol = start_id
  if model.n_in == 1 and inputs is not None:
    current_symbols = np.concatenate([start_symbol, inputs], axis=1)
  else:
    current_symbols = start_symbol

  beams = [current_symbols for _ in range(n_beams)]
  results = [([], 0.0) for _ in range(n_beams)]
  states = [fast_model.state for _ in range(n_beams)]
  top_k = [None] * n_beams
  counter = 0
  while counter < max_length:
    counter += 1
    # Run the model on all beams, collect states and top_k for each beam.
    for beam_id in range(n_beams if counter > 1 else 1):
      fast_model.state = states[beam_id]
      if model.n_in > 1 and inputs is not None:
        logits = fast_model((inputs, beams[beam_id]))[0]
      else:
        logits = fast_model(beams[beam_id])
      logits = tl.log_softmax(logits[:, -1, :])
      states[beam_id] = fast_model.state
      top_k[beam_id] = fastmath.top_k(logits, k=n_beams)

    # Select new beams.
    cur_values = []  # will hold triples (sum-of-logprobs, beam-id, symbol)
    for beam_id in range(n_beams if counter > 1 else 1):
      for k in range(n_beams):
        values, symbols = top_k[beam_id]
        value, symbol = values[:, k], symbols[:, k]
        cur_values.append((results[beam_id][1] + value, beam_id, symbol))
    cur_values.sort(key=lambda x: -x[0][0])  # x[0][0] as batch_size=1
    # Collect top beams to the new states and results.
    new_results, new_states, new_beams = [], [], []
    for (value, beam_id, symbol) in cur_values[:n_beams]:
      new_results.append((results[beam_id][0] + [symbol], value))
      new_states.append(states[beam_id])  # copy?
      new_beams.append(symbol[:, None])
    results, states, beams = new_results, new_states, new_beams

  return [(np.stack(r, axis=-1), v) for (r, v) in results]
Returns a batch of n_beams-sequences created by beam search.

  This function uses `model` to generate outputs one position at a time, with
  access to inputs for the current position and all preceding positions. The
  new output becomes the next position's input, and this loop repeats until
  either the model outputs the `eos_id` value or the output sequence reaches
  `max_length` items -- but keeping n_beams top beams.

  Args:
    model: A layer object (subclass of `trax.layers.Layer`) created in
        `'predict'` mode and initialized from trained weights. The model
        must have a structure that allows it to run as autoregressive
        one-sample-at-a-time predictor (e.g., `trax.models.TransformerLM`).
    inputs: Sequence of symbols the model sees as input the first time it
        generates an output. If None, the model must generate the first output
        with no input to guide it.
    batch_size: Number of sequences to generate in parallel as a batch.
    n_beams: How many beams to consider at the same time.
    start_id: The start symbol (ID/integer) for the autoregressive process,
        or array of shape (`batch_size`, 1) of such integers.
    eos_id: The end-of-sequence symbol (ID/integer) for the autoregressive
        process.
    max_length: Maximum length for generated sequences.
    length_penalty: Factor alpha in calculating the length penalty for beams.
    accelerate: If True, create an accelerated version of `model` and use it
        for generating outputs.

  Returns:
    Tensor of integers with shape (`batch_size`, n_beams, output_length) with
    a batch of output sequences. output_length is the maximum length of the
    output sequences, where each sequence can be no longer than `max_length`.
  
trax/supervised/decoding.py