code: def contract_tensor_tree(
      tensor_tree, sum_dims, cache=None, ring=None
  ):
      """
      Contract out ``sum_dims`` in a tree of tensors via message passing.
      This partially contracts out plate dimensions.
  
      This function should be deterministic and free of side effects.
  
      :param OrderedDict tensor_tree: a dictionary mapping ordinals to lists of
          tensors. An ordinal is a frozenset of ``CondIndepStack`` frames.
      :param set sum_dims: the complete set of sum-contractions dimensions
          (indexed from the right). This is needed to distinguish sum-contraction
          dimensions from product-contraction dimensions.
      :param dict cache: an optional :func:`~opt_einsum.shared_intermediates`
          cache.
      :param pyro.ops.rings.Ring ring: an optional algebraic ring defining tensor
          operations.
      :returns: A contracted version of ``tensor_tree``
      :rtype: OrderedDict
      """
      assert isinstance(tensor_tree, OrderedDict)
      assert isinstance(sum_dims, set)
  
      if ring is None:
          ring = LogRing(cache)
  
      ordinals = {
          term: t for t, terms in tensor_tree.items() for term in terms
      }
      all_terms = [
          term for terms in tensor_tree.values() for term in terms
      ]
      contracted_tree = OrderedDict()
  
      # Split this tensor tree into connected components.
      for terms, dims in _partition_terms(ring, all_terms, sum_dims):
          component = OrderedDict()
          for term in terms:
              component.setdefault(ordinals[term], []).append(term)
  
          # Contract this connected component down to a single tensor.
          ordinal, term = _contract_component(
              ring, component, dims, set()
          )
          contracted_tree.setdefault(ordinal, []).append(term)
  
      return contracted_tree
  
imports: import itertools
  import warnings
  from collections import OrderedDict, defaultdict
  import opt_einsum
  import torch
  from opt_einsum import shared_intermediates
  from pyro.ops.rings import BACKEND_TO_RING, LogRing
  from pyro.util import ignore_jit_warnings
label_desc: Use image node_id 5 for calling a global function with example usage: contract_tensor_tree(tensor_tree, sum_dims, cache, ring) and returns: contracted_tree