code: def _fbo_with_layer_and_opt(
      layer, optimizer, n_devices, stats_name=None, adasum=False
  ):
      """Create the fbo function for a given layer and optimizer."""
  
      def fbo(
          inputs, weights, grads, state, slots, opt_params, rng, step
      ):
          """FBO of the layer."""
  
          # We need a layer pure_fn but only for inputs and weights.
          def pure_fn_without_state_and_rng(x, w):
              return layer.pure_fn(x, w, state, rng)
  
          # Calculate the vector-Jacobian product of the reduced pure fn.
          activations, vjp_fn, new_state = fastmath.vjp(
              pure_fn_without_state_and_rng,
              inputs,
              weights,
              has_aux=True,
          )
  
          # In the loss layer, set gradients to 1 with the dtype of activations=loss.
          if grads is None and stats_name is not None:
              grads = jnp.ones((), dtype=activations.dtype)
  
          # The vjp function returns gradients with respect to inputs and weights.
          grads_inputs, grads_weights = vjp_fn(grads)
  
          # For non-trainable layers, return the calculated arguments.
          if _is_empty_tuple(weights):
              stats = {}
              if stats_name is not None:
                  stats[stats_name] = activations
              return weights, new_state, slots, grads_inputs, stats
  
          # In multi-device setting, average gradients from multiple devices.
          if n_devices > 1:
              grads_weights = _average_multidevice_gradients(
                  grads_weights, adasum=adasum
              )
  
          # Run the optimizer.
          new_weights, new_slots, stats = optimizer.tree_update(
              step,
              grads_weights,
              weights,
              slots,
              opt_params,
              store_slots=False,
          )
          if stats_name is not None:
              stats[stats_name] = activations
          return new_weights, new_state, new_slots, grads_inputs, stats
  
      return fbo
  
imports: from concurrent import futures
  import functools
  import os
  import time
  from absl import logging
  import jax
  import numpy
  import psutil
  from trax import fastmath
  from trax import layers
  from trax.fastmath import numpy
  from trax.layers import base
  from trax.layers import combinators
label_desc: Use image node_id 4 for calling a global function with example usage: _fbo_with_layer_and_opt(layer, optimizer, n_devices, stats_name, adasum) and returns: fbo, new_weights,  new_state,  new_slots,  grads_inputs,  stats, layer, weights,  new_state,  slots,  grads_inputs,  stats