code: def _improve_assignment(
      assignment: jnp.ndarray, state: Dict[str, jnp.ndarray]
  ) -> jnp.ndarray:
      """Improves an assignment by backtracking the augmented path using state.
  
      Args:
        assignment: A bool [b, n, m] array, where each element of the inner matrix
          represents whether the worker has been matched to the job. This may be a
          partial assignment.
        state: Represents the outcome of running an augmenting path search on the
        graph given the assignment.
  
      Returns:
        A new assignment array of the same shape and type as assignment, where the
        assignment has been updated using the augmented path found.
      """
      b, n, m = assignment.shape
  
      # We store the current job id and iteratively backtrack using jobs_from_worker
      # and workers_from_job until we reach an unassigned worker. We flip all the
      # assignments on this path to discover a better overall assignment.
  
      # Note: The indices in state are 1-indexed, where 0 represents that the
      # worker / job cannot be reached.
  
      # Obtain initial job indices based on new_jobs.
      curr_job_idx = jnp.argmax(state["new_jobs"], axis=1)
  
      # Track whether an example is actively being backtracked. Since we are
      # operating on a batch, not all examples in the batch may be active.
      simple_gather = jax.vmap(
          lambda x, idx: x[idx], in_axes=[0, 0], out_axes=0
      )
      active = simple_gather(state["new_jobs"], curr_job_idx)
      batch_range = jnp.arange(0, b, dtype=jnp.int32)
  
      # Flip matrix tracks which assignments we need to flip - corresponding to the
      # augmenting path taken. We use an integer array here so that we can use
      # array_scatter_nd_add to update the array, and then cast it back to bool
      # after the loop.
      flip_matrix = jnp.zeros((b, n, m), dtype=jnp.int32)
  
      def _has_active_backtracks(arg):
          """Check if there are still active workers."""
          _, active, _ = arg
          return jnp.any(active)
  
      dimension_numbers = jax.lax.ScatterDimensionNumbers(
          update_window_dims=(),
          inserted_window_dims=(0, 1, 2),
          scatter_dims_to_operand_dims=(0, 1, 2),
      )
  
      def _backtrack_one_step(arg):
          """Take one step in backtracking."""
          flip_matrix, active, curr_job_idx = arg
          # Discover the worker that the job originated from, note that this worker
          # must exist by construction.
          curr_worker_idx = (
              simple_gather(state["jobs_from_worker"], curr_job_idx) - 1
          )
          curr_worker_idx = jnp.maximum(curr_worker_idx, 0)
          update_indices = jnp.stack(
              [batch_range, curr_worker_idx, curr_job_idx], axis=1
          )
          update_indices = jnp.maximum(update_indices, 0)
          flip_matrix = jax.lax.scatter_add(
              flip_matrix,
              update_indices,
              active.astype(jnp.int32),
              dimension_numbers,
              unique_indices=True,
          )
  
          # Discover the (potential) job that the worker originated from.
          curr_job_idx = (
              simple_gather(state["workers_from_job"], curr_worker_idx)
              - 1
          )
  
          # Note that jobs may not be active, and we track that here (before
          # adjusting indices so that they are all >= 0 for gather).
          active = jnp.logical_and(active, curr_job_idx >= 0)
          curr_job_idx = jnp.maximum(curr_job_idx, 0)
          update_indices = jnp.stack(
              [batch_range, curr_worker_idx, curr_job_idx], axis=1
          )
          update_indices = jnp.maximum(update_indices, 0)
          flip_matrix = jax.lax.scatter_add(
              flip_matrix,
              update_indices,
              active.astype(jnp.int32),
              dimension_numbers,
              unique_indices=True,
          )
  
          return flip_matrix, active, curr_job_idx
  
      flip_matrix, _, _ = jax.lax.while_loop(
          _has_active_backtracks,
          _backtrack_one_step,
          (flip_matrix, active, curr_job_idx),
      )
  
      assignment = jnp.logical_xor(assignment, flip_matrix > 0)
      return assignment
  
file_path: scenic/scenic/model_lib/matchers/hungarian_cover.py
imports: from typing import Tuple, Optional, Dict
  import jax
  import jax.numpy
label_desc: Use image node_id 4 for calling a global function with example usage: _improve_assignment(assignment, state) and returns: assignment, jnp, flip_matrix,  active,  curr_job_idx