code: def initialize_model_with_pytree(
      *,
      model_def: nn.Module,
      input_spec: PyTree,
      config: ml_collections.ConfigDict,
      rngs: Union[jnp.ndarray, Mapping[str, jnp.ndarray]],
      unpack_input: bool = True,
      **model_kwargs,
  ) -> Tuple[PyTree, PyTree, int, Optional[float]]:
      """Initializes parameters and model state with a pytree input_spec.
  
      This is an extension of the above initialize_model function where we can put
      pytree `input_spec`. We keep the original function for backward compatibility.
      If the root type of `input_spec` is `Sequence`, each element is fed to the
      model as position arguments whereas they are fed as keyword arguments if the
      root type is `dict`.
  
      Args:
        model_def: Definition of a model.
        input_spec: A PyTree whose leaves are (shape, dtype) pairs specifying the
          shape and dtype of the inputs. If unspecified the dtype is float32.
        config: Configurations of the initialization.
        rngs: Jax rng keys.
        unpack_input: Unpack the pytree when feeding it to the model.
        **model_kwargs: Kwargs passed to flax model initialization.
  
      Returns:
        Initial params, Init model_state, number of trainable_params, and gflops.
      """
      batch_size = (
          (config.batch_size // jax.device_count())
          if config.get("batch_size")
          else None
      )
  
      def check_leaf_spec(spec: Sequence[PyTree]) -> bool:
          return (
              len(spec) == 2
              and isinstance(spec[0], collections.Sequence)
              and all(isinstance(i, int) for i in spec[0])
              and isinstance(spec[1], jnp.dtype)
          ) or (all(isinstance(i, int) for i in spec[0]))
  
      def create_dummy_input(spec: PyTree) -> PyTree:
          if isinstance(spec, dict):
              return {k: create_dummy_input(v) for k, v in spec.items()}
          elif isinstance(spec, collections.Sequence):
              if check_leaf_spec(spec):
                  in_st = (
                      debug_utils.input_spec_to_jax_shape_dtype_struct(
                          spec, batch_size=batch_size
                      )
                  )
                  return jnp.zeros(in_st.shape, in_st.dtype)
              else:
                  return tuple(
                      create_dummy_input(child) for child in spec
                  )
          elif spec is None:
              return None
          else:
              raise NotImplementedError(
                  "Unsupported spec type.", type(spec)
              )
  
      dummy_input = create_dummy_input(input_spec)
  
      # We want all parameters to be created in host RAM, not on any device, they'll
      # be sent there later as needed, otherwise we already encountered two
      # situations where we allocate them twice.
      @functools.partial(jax.jit, backend="cpu")
      def _initialize_model(rngs):
          """Initialization function to be jitted."""
          # If dummy_input is a dict, we feed inputs as keyword arguments, otherwise
          # feed as position arguments.
          if isinstance(dummy_input, dict) and unpack_input:
              init_model_state, init_params = flax.core.pop(
                  flax.core.freeze(
                      model_def.init(
                          rngs,
                          **dummy_input,
                          train=False,
                          debug=False,
                          **model_kwargs,
                      )
                  ),
                  "params",
              )
          elif (
              isinstance(dummy_input, collections.Sequence)
              and unpack_input
          ):
              init_model_state, init_params = flax.core.pop(
                  flax.core.freeze(
                      model_def.init(
                          rngs,
                          *dummy_input,
                          train=False,
                          debug=False,
                          **model_kwargs,
                      )
                  ),
                  "params",
              )
          else:
              init_model_state, init_params = flax.core.pop(
                  flax.core.freeze(
                      model_def.init(
                          rngs,
                          dummy_input,
                          train=False,
                          debug=False,
                          **model_kwargs,
                      )
                  ),
                  "params",
              )
          # Set bias in the head to low value, such that loss is small initially.
          if config.get("init_head_bias", None) is not None:
              init_params = flax.core.unfreeze(init_params)
              init_params[
                  "output_projection"
              ] = optimizers.tree_map_with_names(
                  lambda p: jnp.full_like(p, config.init_head_bias),
                  init_params["output_projection"],
                  match_name_fn=lambda name: "bias" in name,
              )
              init_params = flax.core.freeze(init_params)
          return init_params, init_model_state
  
      if not isinstance(rngs, dict):
          rngs = {"params": rngs}
      init_params, init_model_state = _initialize_model(rngs)
      # Pop out params rng:
      rngs.pop("params")
  
      # Count number of trainable parameters:
      num_trainable_params = debug_utils.log_param_shapes(init_params)
  
      # Count gflops:
      count_flops = config.get(
          "count_flops",
          ml_collections.ConfigDict({"count_flops": True}),
      )
      if count_flops:
          variables = {"params": init_params, **init_model_state}
          flops = debug_utils.compute_flops_with_pytree(
              flax_model_apply_fn=functools.partial(
                  model_def.apply,
                  variables,
                  train=False,
                  debug=False,
                  rngs=rngs,
                  **model_kwargs,
              ),
              input_spec=count_flops.get("input_spec", input_spec),
              unpack_input=unpack_input,
              fuse_multiply_add=count_flops.get(
                  "fuse_multiply_add", True
              ),
          )
          gflops = flops / (10**9)
      else:
          gflops = None
  
      return init_params, init_model_state, num_trainable_params, gflops
  
imports: import collections.abc
  import copy
  import functools
  import os
  import re
  import time
  from typing import Any, Callable, Dict, Mapping, Optional, Sequence, Tuple, Union
  from absl import logging
  from clu import metric_writers
  import flax
  from flax import jax_utils
  from flax import struct
  import flax.linen
  from flax.training import checkpoints
  import jax
  import jax.numpy
  import ml_collections
  import numpy
  import optax
  from scenic.common_lib import debug_utils
  from scenic.dataset_lib import dataset_utils
  from scenic.dataset_lib import datasets
  from scenic.train_lib import optimizers
  from tensorflow.io import gfile
label_desc: Use image node_id 2 for calling a global function with example usage: initialize_model_with_pytree() and returns: init_params,  init_model_state,  num_trainable_params,  gflops, unknown, init_params,  init_model_state, unknown, jnp, tuple, None