code: def _accelerate_update_fn(
      forward_and_backward_fn,
      optimizer,
      n_devices,
      accelerate=True,
      adasum=False,
  ):
      """Accelerates the given forward_and_backward_fn function."""
      if n_devices == 1:
  
          def single_device_update_fn(
              weights_and_slots, step, opt_params, batch, state, rng
          ):
              step = jnp.array(
                  step, dtype=jnp.int32
              )  # Needed in TFNP backend.
              weights, slots = weights_and_slots
              (loss, state), gradients = forward_and_backward_fn(
                  batch, weights, state, rng
              )
              weights, slots, stats = optimizer.tree_update(
                  step,
                  gradients,
                  weights,
                  slots,
                  opt_params,
                  store_slots=False,
              )
              stats["loss"] = loss
              return (weights, slots), state, stats
  
          if accelerate:
              # TODO(afrozm): Find out the status of buffer donation on GPUs, then do
              #  donate_argnums=(0,).
              single_device_update_fn = fastmath.jit(
                  single_device_update_fn
              )
          return single_device_update_fn
  
      # More than one device (core), i.e. all of TPU configurations etc.
      assert n_devices > 1, f"{n_devices} should be greater than 1."
  
      @functools.partial(
          fastmath.pmap, axis_name="batch", donate_argnums=(0,)
      )
      def _multi_device_update_fn(
          weights_and_slots, step, opt_params, batch, state, rng
      ):
          # All tensors should have the first dimension = n_devices.
          weights, slots = weights_and_slots
          (loss, state), gradients = forward_and_backward_fn(
              batch, weights, state, rng
          )
          gradients = _average_multidevice_gradients(
              gradients, adasum=adasum
          )
          weights, slots, stats = optimizer.tree_update(
              step,
              gradients,
              weights,
              slots,
              opt_params,
              store_slots=False,
          )
          stats["loss"] = loss
          return (weights, slots), state, stats
  
      def multi_device_update_fn(
          weights_and_slots, step, opt_params, batch, state, rng
      ):
          # Need to replicate step to n_devices leading dimension.
          return _multi_device_update_fn(
              weights_and_slots,
              jnp.repeat(step, n_devices),
              opt_params,
              batch,
              state,
              rng,
          )
  
      return multi_device_update_fn
  
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 3 for calling a global function with example usage: _accelerate_update_fn(forward_and_backward_fn, optimizer, n_devices, accelerate, adasum) and returns: multi_device_update_fn, single_device_update_fn, weights,  slots,  state,  stats, _multi_device_update_fn, weights,  slots,  state,  stats