code: def mha_reference_bwd(
      q,
      k,
      v,
      ab,
      segment_ids: SegmentIds | None,
      o,
      l,
      m,
      do,
      causal: bool = False,
      mask_value: float = DEFAULT_MASK_VALUE,
      sm_scale: float = 1.0,
  ):
      if sm_scale != 1.0:
          raise NotImplementedError
  
      logits = jnp.einsum(
          "bhqc,bhkc->bhqk",
          q.astype(jnp.float32),
          k.astype(jnp.float32),
      )
      if ab is not None:
          logits += ab
  
      mask = None
      if segment_ids is not None:
          mask = segment_ids.q[:, :, None] == segment_ids.kv[:, None, :]
          mask = mask[:, None, :, :]
  
      if causal:
          _, _, q_seq_len, _ = q.shape
          _, _, kv_seq_len, _ = k.shape
          mask_shape = (q_seq_len, kv_seq_len)
          row_ids = jax.lax.broadcasted_iota(jnp.int32, mask_shape, 0)
          col_ids = jax.lax.broadcasted_iota(jnp.int32, mask_shape, 1)
          causal_mask = (col_ids <= row_ids)[None, None, :, :]
          mask = (
              causal_mask
              if mask is None
              else jnp.logical_and(mask, causal_mask)
          )
  
      logits = (
          logits
          if mask is None
          else logits + jnp.where(mask, 0.0, mask_value)
      )
  
      unnormalized = jnp.exp(logits - m[..., None])
      p = unnormalized / l[..., None]
      dv = jnp.einsum(
          "bhpt,bhpd->bhtd", p, do.astype(jnp.float32)
      ).astype(v.dtype)
  
      dp = jnp.einsum(
          "bhpd,bhtd->bhpt",
          do.astype(jnp.float32),
          v.astype(jnp.float32),
      )
  
      di = jnp.sum(
          o.astype(jnp.float32) * do.astype(jnp.float32), axis=-1
      )[
          ..., None
      ]  # [batch_size, num_heads, q_seq_len]
  
      ds = (dp - di) * p
      dk = jnp.einsum(
          "bhsd,bhst->bhtd", q.astype(jnp.float32), ds
      ).astype(k.dtype)
      dq = jnp.einsum(
          "bhst,bhtd->bhsd", ds, k.astype(jnp.float32)
      ).astype(q.dtype)
  
      # dab is just ds
      dab = ds if ab is not None else None
      return dq, dk, dv, dab
  
imports: from __future__ import annotations
  import dataclasses
  import functools
  from typing import Any, NamedTuple
  import jax
  from jax import lax
  from jax.experimental import pallas
  from jax.experimental.pallas import tpu
  import jax.numpy
label_desc: Use image node_id 18 for calling a global function with example usage: mha_reference_bwd(q, k, v, ab, segment_ids, o, l, m, do, causal, mask_value, sm_scale) and returns: dq,  dk,  dv,  dab