diff --git a/src/flag_gems/ops/layernorm.py b/src/flag_gems/ops/layernorm.py
index 2d4a7a77..83fe1aa3 100644
--- a/src/flag_gems/ops/layernorm.py
+++ b/src/flag_gems/ops/layernorm.py
@@ -6,6 +6,7 @@
 import triton.language as tl
 
 from ..utils import libentry
+from ..utils.type_utils import get_accumulator_dtype
 
 
 @triton.jit
@@ -321,8 +322,12 @@ def forward(ctx, x, normalized_shape, weight, bias, eps=1e-5, cudnn_enable=True)
         weight = weight.contiguous()
         bias = bias.contiguous()
         y = torch.empty_like(x)
-        mean = torch.empty(M, dtype=x.dtype, device=x.device)
-        rstd = torch.empty(M, dtype=x.dtype, device=x.device)
+
+        # NOTE: when the input is half-precision(either float16 or bfloat16)
+        # these statistical data saved for backward is in single precision
+        acc_type = get_accumulator_dtype(x.dtype)
+        mean = torch.empty(M, dtype=acc_type, device=x.device)
+        rstd = torch.empty(M, dtype=acc_type, device=x.device)
 
         with torch.cuda.device(x.device):
             if N <= 128:
@@ -382,14 +387,17 @@ def backward(ctx, out_grad, mean_grad, rstd_grad):
         (x, weight, mean, rstd) = ctx.saved_tensors
         M = ctx.M
         N = ctx.N
-        in_grad = torch.empty_like(x)
-        grid = lambda meta: (triton.cdiv(M, meta["BLOCK_ROW_SIZE"]), 1, 1)
-        layer_norm_backward_kernel[grid](out_grad, x, weight, mean, rstd, in_grad, M, N)
-        grid = lambda meta: (triton.cdiv(N, meta["BLOCK_COL_SIZE"]), 1, 1)
-        weight_grad = torch.empty_like(weight)
-        bias_grad = torch.empty_like(weight)
 
         with torch.cuda.device(x.device):
+            in_grad = torch.empty_like(x)
+            grid = lambda meta: (triton.cdiv(M, meta["BLOCK_ROW_SIZE"]), 1, 1)
+            layer_norm_backward_kernel[grid](
+                out_grad, x, weight, mean, rstd, in_grad, M, N
+            )
+
+            grid = lambda meta: (triton.cdiv(N, meta["BLOCK_COL_SIZE"]), 1, 1)
+            weight_grad = torch.empty_like(weight)
+            bias_grad = torch.empty_like(weight)
             weight_bias_backward_kernel[grid](
                 out_grad, x, mean, rstd, weight_grad, bias_grad, M, N
             )
diff --git a/src/flag_gems/utils/type_utils.py b/src/flag_gems/utils/type_utils.py
index 91a86ddd..baff2bd0 100644
--- a/src/flag_gems/utils/type_utils.py
+++ b/src/flag_gems/utils/type_utils.py
@@ -1,3 +1,4 @@
+import torch
 from torch._prims_common import ELEMENTWISE_TYPE_PROMOTION_KIND, elementwise_dtypes
 
 
@@ -7,3 +8,14 @@ def type_promotion(*args, type_promotion: ELEMENTWISE_TYPE_PROMOTION_KIND):
         type_promotion_kind=type_promotion,
     )
     return computation_dtype, result_dtype
+
+
+_accumulator_dtype_map = {
+    torch.bfloat16: torch.float32,
+    torch.float16: torch.float32,
+    torch.complex32: torch.complex64,
+}
+
+
+def get_accumulator_dtype(dtype: torch.dtype) -> torch.dtype:
+    return _accumulator_dtype_map.get(dtype, dtype)
diff --git a/tests/test_norm_ops.py b/tests/test_norm_ops.py
index 2a3fba8e..89004858 100644
--- a/tests/test_norm_ops.py
+++ b/tests/test_norm_ops.py
@@ -74,11 +74,19 @@ def test_accuracy_groupnorm(N, C, H, W, num_groups, dtype):
     gems_assert_close(res_bias_grad, ref_bias_grad, dtype, reduce_dim=N * HW)
 
 
-# TODO: failed at (1, 2) (2~32, 40499) (200, 2~64) (200~4096, 40999)
 @pytest.mark.layer_norm
 @pytest.mark.native_layer_norm
 @pytest.mark.parametrize(
-    "shape", [(1, 40999)] if QUICK_MODE else [(1, 40999), (4096, 256), (4096, 100)]
+    "shape",
+    [(1, 40999)]
+    if QUICK_MODE
+    else [
+        (200, 36),
+        (4096, 100),
+        (1, 40999),
+        (100, 40499),
+        (4096, 256),
+    ],
 )
 @pytest.mark.parametrize("dtype", FLOAT_DTYPES)
 def test_accuracy_layernorm(shape, dtype):
@@ -110,8 +118,8 @@ def test_accuracy_layernorm(shape, dtype):
     ref_mean = torch.mean(ref_inp, dim=1)
     ref_var = torch.var(ref_inp, dim=1, correction=0)
     ref_rstd = torch.rsqrt(ref_var + eps)
-    gems_assert_close(res_mean, ref_mean, dtype)
-    gems_assert_close(res_rstd, ref_rstd, dtype)
+    gems_assert_close(res_mean, ref_mean, res_mean.dtype)
+    gems_assert_close(res_rstd, ref_rstd, res_rstd.dtype)
     gems_assert_close(res_out, ref_out, dtype)
 
     out_grad = torch.randn_like(inp)