def _beam_search(
        self,
        input_ids: None,
        max_length: Optional[int] = None,
        pad_token_id: Optional[int] = None,
        eos_token_id: Optional[int] = None,
        length_penalty: Optional[float] = None,
        early_stopping: Optional[Union[bool, str]] = None,
        logits_processor: Optional[FlaxLogitsProcessorList] = None,
        trace: bool = True,
        params: Optional[Dict[str, jnp.ndarray]] = None,
        num_return_sequences: Optional[int] = None,
        model_kwargs: Optional[Dict[str, jnp.ndarray]] = None,
    ):
        """
        This beam search function is heavily inspired by Flax's official example:
        https://github.com/google/flax/blob/main/examples/wmt/decode.py
        """

        def flatten_beam_dim(tensor):
            """Flattens the first two dimensions of a non-scalar array."""
            # ignore scalars (e.g. cache index)
            if tensor.ndim == 0:
                return tensor
            return tensor.reshape((tensor.shape[0] * tensor.shape[1],) + tensor.shape[2:])

        def unflatten_beam_dim(tensor, batch_size, num_beams):
            """Unflattens the first, flat batch*beam dimension of a non-scalar array."""
            # ignore scalars (e.g. cache index)
            if tensor.ndim == 0:
                return tensor
            return tensor.reshape((batch_size, num_beams) + tensor.shape[1:])

        def gather_beams(nested, beam_indices, batch_size, new_num_beams):
            """
            Gathers the beam slices indexed by beam_indices into new beam array.
            """
            batch_indices = jnp.reshape(
                jnp.arange(batch_size * new_num_beams) // new_num_beams, (batch_size, new_num_beams)
            )

            def gather_fn(tensor):
                # ignore scalars (e.g. cache index)
                if tensor.ndim == 0:
                    return tensor
                else:
                    return tensor[batch_indices, beam_indices]

            return jax.tree_util.tree_map(gather_fn, nested)

        # init values
        max_length = max_length if max_length is not None else self.generation_config.max_length
        pad_token_id = pad_token_id if pad_token_id is not None else self.generation_config.pad_token_id
        eos_token_id = eos_token_id if eos_token_id is not None else self.generation_config.eos_token_id
        length_penalty = length_penalty if length_penalty is not None else self.generation_config.length_penalty
        early_stopping = early_stopping if early_stopping is not None else self.generation_config.early_stopping
        num_return_sequences = (
            num_return_sequences if num_return_sequences is not None else self.generation_config.num_return_sequences
        )

        batch_size, num_beams, cur_len = input_ids.shape

        eos_token_id = jnp.array(eos_token_id, dtype=jnp.int32 if eos_token_id is not None else None)
        pad_token_id = jnp.array(pad_token_id, dtype=jnp.int32)
        cur_len = jnp.array(cur_len)

        # per batch,beam-item holding current token in loop.
        sequences = jnp.full((batch_size, num_beams, max_length), pad_token_id, dtype=jnp.int32)
        running_sequences = jnp.full((batch_size, num_beams, max_length), pad_token_id, dtype=jnp.int32)
        running_sequences = lax.dynamic_update_slice(sequences, input_ids, (0, 0, 0))

        # per batch,beam-item state bit indicating if sentence has finished.
        is_sent_finished = jnp.zeros((batch_size, num_beams), dtype=jnp.bool_)

        # per batch,beam-item score, logprobs
        running_scores = jnp.tile(jnp.array([0.0] + [np.array(-1.0e7)] * (num_beams - 1)), [batch_size, 1])
        scores = jnp.ones((batch_size, num_beams)) * np.array(-1.0e7)

        # For Seq2Seq generation, we only need to use the decoder instead of the whole model in generation loop
        # and pass it the `encoder_outputs`, which are part of the `model_kwargs`.
        model = self.decode if self.config.is_encoder_decoder else self

        # flatten beam dim
        if "encoder_outputs" in model_kwargs:
            model_kwargs["encoder_outputs"]["last_hidden_state"] = flatten_beam_dim(
                model_kwargs["encoder_outputs"]["last_hidden_state"]
            )
        for kwarg in ["attention_mask", "decoder_attention_mask"]:
            if kwarg in model_kwargs:
                model_kwargs[kwarg] = flatten_beam_dim(model_kwargs[kwarg])

        # initialize model specific kwargs
        model_kwargs = self.prepare_inputs_for_generation(flatten_beam_dim(input_ids), max_length, **model_kwargs)

        # initialize state
        state = BeamSearchState(
            cur_len=cur_len,
            running_sequences=running_sequences,
            running_scores=running_scores,
            sequences=sequences,
            scores=scores,
            is_sent_finished=is_sent_finished,
            model_kwargs=model_kwargs,
        )

        def beam_search_cond_fn(state):
            """beam search state termination condition fn."""

            # 1. is less than max length?
            not_max_length_yet = state.cur_len < max_length

            # 2. can the new beams still improve?
            # early_stopping == False -> apply heuristic = always get the best score from `cur_len`. See the discussion
            # below for more details.
            # https://github.com/huggingface/transformers/pull/20901#issuecomment-1369845565
            # early_stopping == "never" -> compute the best score from max_length or cur_len, depending on the sign of
            #   length_penalty. Positive length_penalty favors longer sequences, thus we use max_length there.
            if early_stopping == "never" and length_penalty > 0.0:
                best_running_score = state.running_scores[:, :1] / (max_length**length_penalty)
            else:
                best_running_score = state.running_scores[:, :1] / (state.cur_len**length_penalty)
            worst_finished_score = jnp.where(
                state.is_sent_finished, jnp.min(state.scores, axis=1, keepdims=True), np.array(-1.0e7)
            )
            improvement_still_possible = jnp.any(best_running_score > worst_finished_score)

            # 3. is there still a beam that has not finished?
            still_open_beam = ~(jnp.all(state.is_sent_finished) & (early_stopping is True))

            return not_max_length_yet & still_open_beam & improvement_still_possible

        def beam_search_body_fn(state, input_ids_length=1):
            """beam search state update fn."""
            # 1. Forward current tokens
            # Collect the current position slice along length to feed the fast
            # autoregressive decoder model.  Flatten the beam dimension into batch
            # dimension for feeding into the model.
            # unflatten beam dimension
            # Unflatten beam dimension in attention cache arrays
            input_token = flatten_beam_dim(
                lax.dynamic_slice(
                    state.running_sequences,
                    (0, 0, state.cur_len - input_ids_length),
                    (batch_size, num_beams, input_ids_length),
                )
            )
            model_outputs = model(input_token, params=params, **state.model_kwargs)

            logits = unflatten_beam_dim(model_outputs.logits[:, -1], batch_size, num_beams)
            cache = jax.tree_util.tree_map(
                lambda tensor: unflatten_beam_dim(tensor, batch_size, num_beams), model_outputs.past_key_values
            )

            # adapt logits for FlaxMarianMTModel
            logits = self._adapt_logits_for_beam_search(logits)

            # 2. Compute log probs
            # get log probabilities from logits,
            # process logits with processors (*e.g.* min_length, ...), and
            # add new logprobs to existing running logprobs scores.
            log_probs = jax.nn.log_softmax(logits)
            log_probs = logits_processor(
                flatten_beam_dim(running_sequences), flatten_beam_dim(log_probs), state.cur_len
            )
            log_probs = unflatten_beam_dim(log_probs, batch_size, num_beams)
            log_probs = log_probs + jnp.expand_dims(state.running_scores, axis=2)
            vocab_size = log_probs.shape[2]
            log_probs = log_probs.reshape((batch_size, num_beams * vocab_size))

            # 3. Retrieve top-K
            # Each item in batch has num_beams * vocab_size candidate sequences.
            # For each item, get the top 2*k candidates with the highest log-
            # probabilities. We gather the top 2*K beams here so that even if the best
            # K sequences reach EOS simultaneously, we have another K sequences
            # remaining to continue the live beam search.
            # Gather the top 2*K scores from _all_ beams.
            # Gather 2*k top beams.
            # Recover the beam index by floor division.
            # Recover token id by modulo division and expand Id array for broadcasting.
            # Update sequences for the 2*K top-k new sequences.
            beams_to_keep = 2 * num_beams
            topk_log_probs, topk_indices = lax.top_k(log_probs, k=beams_to_keep)
            topk_beam_indices = topk_indices // vocab_size
            topk_running_sequences = gather_beams(
                state.running_sequences, topk_beam_indices, batch_size, beams_to_keep
            )
            topk_ids = jnp.expand_dims(topk_indices % vocab_size, axis=2)
            topk_sequences = lax.dynamic_update_slice(topk_running_sequences, topk_ids, (0, 0, state.cur_len))

            # 4. Check which sequences have ended
            # Update current sequences:
            # Did any of these sequences reach an end marker?
            # To prevent these just finished sequences from being added to the current sequences
            # set of active beam search sequences, set their log probs to a very large
            # negative value.
            did_topk_just_finished = topk_sequences[:, :, state.cur_len] == eos_token_id
            running_topk_log_probs = topk_log_probs + did_topk_just_finished * np.array(-1.0e7)
            # 5. Get running sequences scores for next
            # Determine the top k beam indices (from top 2*k beams) from log probs
            # and gather top k beams (from top 2*k beams).
            next_topk_indices = lax.top_k(running_topk_log_probs, k=num_beams)[1]
            next_running_sequences, next_running_scores = gather_beams(
                [topk_sequences, running_topk_log_probs], next_topk_indices, batch_size, num_beams
            )

            # 6. Process topk logits
            # Further process log probs:
            # - add length penalty
            # - make sure no scores can be added anymore if beam is full
            # - make sure still running sequences cannot be chosen as finalized beam
            topk_log_probs = topk_log_probs / (state.cur_len**length_penalty)
            beams_in_batch_are_full = jnp.broadcast_to(
                state.is_sent_finished.all(axis=-1, keepdims=True), did_topk_just_finished.shape
            ) & (early_stopping is True)
            add_penalty = ~did_topk_just_finished | beams_in_batch_are_full
            topk_log_probs += add_penalty * np.array(-1.0e7)

            # 7. Get scores, sequences, is sentence finished for next.
            # Combine sequences, scores, and flags along the beam dimension and compare
            # new finished sequence scores to existing finished scores and select the
            # best from the new set of beams
            merged_sequences = jnp.concatenate([state.sequences, topk_sequences], axis=1)
            merged_scores = jnp.concatenate([state.scores, topk_log_probs], axis=1)
            merged_is_sent_finished = jnp.concatenate([state.is_sent_finished, did_topk_just_finished], axis=1)
            topk_merged_indices = lax.top_k(merged_scores, k=num_beams)[1]
            next_sequences, next_scores, next_is_sent_finished = gather_beams(
                [merged_sequences, merged_scores, merged_is_sent_finished], topk_merged_indices, batch_size, num_beams
            )

            # 8. Update model kwargs.
            # Determine the top k beam indices from the original set of all beams.
            # With these, gather the top k beam-associated caches.
            next_running_indices = gather_beams(topk_beam_indices, next_topk_indices, batch_size, num_beams)
            next_cache = gather_beams(cache, next_running_indices, batch_size, num_beams)
            model_outputs["past_key_values"] = jax.tree_util.tree_map(lambda x: flatten_beam_dim(x), next_cache)
            next_model_kwargs = self.update_inputs_for_generation(model_outputs, state.model_kwargs)

            return BeamSearchState(
                cur_len=state.cur_len + 1,
                running_scores=next_running_scores,
                running_sequences=next_running_sequences,
                scores=next_scores,
                sequences=next_sequences,
                is_sent_finished=next_is_sent_finished,
                model_kwargs=next_model_kwargs,
            )

        # The very first prompt often has sequence length > 1, so run outside of `lax.while_loop` to comply with TPU
        if input_ids.shape[-1] > 1:
            state = partial(beam_search_body_fn, input_ids_length=input_ids.shape[-1])(state)

        if not trace:
            state = self._run_loop_in_debug(beam_search_cond_fn, beam_search_body_fn, state)
        else:
            state = lax.while_loop(beam_search_cond_fn, beam_search_body_fn, state)

        # Account for the edge-case where there are no finished sequences for a
        # particular batch item. If so, return running sequences for that batch item.
        none_finished = jnp.any(state.is_sent_finished, axis=1)
        sequences = jnp.where(none_finished[:, None, None], state.sequences, state.running_sequences)
        scores = jnp.where(none_finished[:, None], state.scores, state.running_scores)

        # Take best beams for each batch (the score is sorted in descending order)
        sequences = flatten_beam_dim(sequences[:, :num_return_sequences, :])
        scores = flatten_beam_dim(scores[:, :num_return_sequences])

        return FlaxBeamSearchOutput(sequences=sequences, scores=scores)

        This beam search function is heavily inspired by Flax's official example:
        https://github.com/google/flax/blob/main/examples/wmt/decode.py
        
dpkd/transformers/src/transformers/generation/flax_utils.py