@triton.jit
def causal_product_kernel(q_ptr, k_ptr, v_ptr, output_ptr, batch, length,
    dim, vdim, **meta):
    BLOCK_SIZE = meta['BLOCK_SIZE']
    pid = tl.program_id(axis=0)
    state = tl.zeros((BLOCK_SIZE, BLOCK_SIZE), dtype=tl.float32)
    cur_qk_pos = pid * length * dim
    cur_v_pos = pid * length * vdim
    dim_ptrs = tl.arange(0, BLOCK_SIZE)
    qk_mask = dim_ptrs < dim
    v_mask = dim_ptrs < vdim
    for _ in range(0, length, 1):
        qk_row_offsets = cur_qk_pos + dim_ptrs
        v_row_offsets = cur_v_pos + dim_ptrs
        k = tl.load(k_ptr + qk_row_offsets, mask=qk_mask, other=0)
        v = tl.load(v_ptr + v_row_offsets, mask=v_mask, other=0)
        context = tl.dot(k[:, None], v[None, :])
        state += context
        q = tl.load(q_ptr + qk_row_offsets, mask=qk_mask, other=0)
        output = tl.dot(q[None, :], state)
        tl.store(output_ptr + v_row_offsets[None, :], output, mask=v_mask[
            None, :])
        cur_qk_pos += dim
        cur_v_pos += vdim
