code: def sdpa_backward_flop_count(
      grad_out_shape, query_shape, key_shape, value_shape
  ):
      total_flops = 0
      b, h, s_q, d_q = query_shape
      _b2, _h2, s_k, _d2 = key_shape
      _b3, _h3, _s3, d_v = value_shape
      _b4, _h4, _s4, _d4 = grad_out_shape
      assert (
          b == _b2 == _b3 == _b4
          and h == _h2 == _h3 == _h4
          and d_q == _d2
      )
      assert d_v == _d4 and s_k == _s3 and s_q == _s4
      total_flops = 0
      # Step 1: We recompute the scores matrix.
      # q: [b, h, s_q, d_q] @ k: [b, h, d_q, s_k] -> scores: [b, h, s_q, s_k]
      total_flops += bmm_flop((b * h, s_q, d_q), (b * h, d_q, s_k))
  
      # Step 2: We propagate the gradients through the score @ v operation.
      # gradOut: [b, h, s_q, d_v] @ v: [b, h, d_v, s_k] -> gradScores: [b, h, s_q, s_k]
      total_flops += bmm_flop((b * h, s_q, d_v), (b * h, d_v, s_k))
      # scores: [b, h, s_k, s_q] @ gradOut: [b, h, s_q, d_v] -> gradV: [b, h, s_k, d_v]
      total_flops += bmm_flop((b * h, s_k, s_q), (b * h, s_q, d_v))
  
      # Step 3: We propagate th gradients through the k @ v operation
      # gradScores: [b, h, s_q, s_k] @ k: [b, h, s_k, d_q] -> gradQ: [b, h, s_q, d_q]
      total_flops += bmm_flop((b * h, s_q, s_k), (b * h, s_k, d_q))
      # q: [b, h, d_q, s_q] @ gradScores: [b, h, s_q, s_k] -> gradK: [b, h, d_q, s_k]
      total_flops += bmm_flop((b * h, d_q, s_q), (b * h, s_q, s_k))
      return total_flops
  
imports: import torch
  import torch.nn
  from torch.utils._pytree import tree_map, tree_flatten, tree_unflatten
  from typing import List, Any, Dict, Optional, Union, NamedTuple
  from collections import defaultdict
  from torch.utils._python_dispatch import TorchDispatchMode
  from torch.utils.hooks import RemovableHandle
  from torch._decomp import register_decomposition
  from math import prod
  from functools import wraps
label_desc: Use image node_id 14 for calling a global function with example usage: sdpa_backward_flop_count(grad_out_shape, query_shape, key_shape, value_shape) and returns: total_flops