code: def backward(ctx, dy):
      x, w, b, m, v = ctx.saved_tensors
      # heuristics for amount of parallel reduction stream for DW/DB
      N = w.shape[0]
      GROUP_SIZE_M = 64
      if N <= 8192:
          GROUP_SIZE_M = 96
      if N <= 4096:
          GROUP_SIZE_M = 128
      if N <= 1024:
          GROUP_SIZE_M = 256
      # allocate output
      locks = torch.zeros(
          2 * GROUP_SIZE_M, dtype=torch.int32, device="cuda"
      )
      _dw = torch.empty(
          (GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device
      )
      _db = torch.empty(
          (GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device
      )
      dw = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device)
      db = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device)
      dx = torch.empty_like(dy)
      # enqueue kernel using forward pass heuristics
      # also compute partial sums for DW and DB
      x_arg = x.reshape(-1, x.shape[-1])
      M, N = x_arg.shape
      _layer_norm_bwd_dx_fused[(M,)](  #
          dx,
          dy,
          _dw,
          _db,
          x,
          w,
          b,
          m,
          v,
          locks,  #
          x_arg.stride(0),
          N,
          ctx.eps,  #
          BLOCK_SIZE_N=ctx.BLOCK_SIZE,  #
          GROUP_SIZE_M=GROUP_SIZE_M,  #
          num_warps=ctx.num_warps,
      )
      grid = lambda meta: [triton.cdiv(N, meta["BLOCK_SIZE_N"])]
      # accumulate partial sums in separate kernel
      _layer_norm_bwd_dwdb[grid](
          _dw,
          _db,
          dw,
          db,
          min(GROUP_SIZE_M, M),
          N,  #
          BLOCK_SIZE_M=32,  #
          BLOCK_SIZE_N=128,
          num_ctas=1,
      )
      return dx, None, dw, db, None
  
file_path: triton/python/tutorials/05-layer-norm.py
imports: import torch
  import triton
  import triton.language
label_desc: Use image node_id 2 for calling the LayerNorm obj's underlying member method code with example usage: obj.backward(ctx, dy) and returns: dx,  None,  dw,  db,  None