diff --git a/tests/test_torch_preprocessing/test_torch_squashing_scaler.py b/tests/test_torch_preprocessing/test_torch_squashing_scaler.py
index e63c499b3..c290ba8f0 100644
--- a/tests/test_torch_preprocessing/test_torch_squashing_scaler.py
+++ b/tests/test_torch_preprocessing/test_torch_squashing_scaler.py
@@ -439,3 +439,23 @@ def test__blocked_transform_does_not_write_to_its_input(
             _run_with_budgets(patch, _FORCE_BLOCKED, x, 64, 3.0)
 
         _assert_bit_identical("input tensor", x, before)
+
+
+@pytest.mark.parametrize("outlier", [1000.0, -1000.0])
+@pytest.mark.parametrize("dtype", [torch.float16, torch.bfloat16])
+def test__call__low_precision_outlier_does_not_overflow(
+    outlier: float, dtype: torch.dtype
+) -> None:
+    # Both low-precision dtypes take the upcast path, so both need the cover.
+    scaler = TorchSquashingScaler()
+    x = torch.tensor(
+        [0, 1, 1, 1, 2, outlier],
+        dtype=dtype,
+    ).unsqueeze(-1)
+
+    out = scaler(x, num_train_rows=5)
+
+    assert out.dtype == dtype
+    assert torch.isfinite(out).all()
+    assert 2.5 < abs(out[-1, 0].item()) <= 3.0
+    assert out[-1, 0].item() * outlier > 0