code: def initialize_multitask_model(
      *,
      model_def: nn.Module,
      input_spec: Dict[
          str,
          Sequence[
              Union[Tuple[Tuple[int, ...], jnp.dtype], Tuple[int, ...]]
          ],
      ],
      config: ml_collections.ConfigDict,
      rngs: Union[jnp.ndarray, Mapping[str, jnp.ndarray]],
  ) -> Tuple[PyTree, PyTree, int, Optional[float]]:
      """Initializes parameters and model state.
  
      Args:
        model_def: Definition of a model.
        input_spec: A dictionary from task names to an iterable of (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.
  
      Returns:
        Initial params, Init model_state, and number of trainable_params.
      """
      batch_size = (
          (config.batch_size // jax.device_count())
          if config.get("batch_size")
          else None
      )
  
      def init_fn(model_def):
          for task, in_spec in input_spec.items():
              input_shapetype = [
                  debug_utils.input_spec_to_jax_shape_dtype_struct(
                      spec, batch_size=batch_size
                  )
                  for spec in in_spec
              ]
              dummy_input = []
              for in_st in input_shapetype:
                  dummy_input.append(
                      jnp.zeros(in_st.shape, in_st.dtype)
                  )
              model_def(
                  *dummy_input, task=task, train=False, debug=False
              )
  
      # 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."""
          init_model_state, init_params = nn.init(
              fn=init_fn, module=model_def
          )(rngs).pop("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
              and "output_projection" in init_params
          ):
              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 = 0
          for task, in_spec in input_spec.items():
              flops += debug_utils.compute_flops(
                  flax_model_apply_fn=functools.partial(
                      model_def.apply,
                      variables,
                      train=False,
                      debug=False,
                      rngs=rngs,
                      task=task,
                  ),
                  input_spec=count_flops.get("input_spec", in_spec),
                  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
  import copy
  import functools
  from typing import Any, Dict, Mapping, Optional, Sequence, Tuple, Union
  from absl import logging
  import flax
  import flax.linen
  import jax
  import jax.numpy
  import ml_collections
  import numpy
  from scenic.common_lib import debug_utils
  from scenic.train_lib_deprecated import optimizers
  from scenic.train_lib_deprecated import train_utils
label_desc: Use image node_id 1 for calling a global function with example usage: initialize_multitask_model() and returns: init_params,  init_model_state,  num_trainable_params,  gflops, init_params,  init_model_state