diff --git a/src/lerobot/policies/g05/modeling_g05.py b/src/lerobot/policies/g05/modeling_g05.py
index 47697f5db..b53d6020b 100644
--- a/src/lerobot/policies/g05/modeling_g05.py
+++ b/src/lerobot/policies/g05/modeling_g05.py
@@ -178,6 +178,17 @@ class G05Policy(PreTrainedPolicy):
         apply_fp32_params = getattr(self.backend, "apply_fp32_params", None)
         if callable(apply_fp32_params):
             apply_fp32_params()
+        if self.config.predict_cot:
+            # The author Qwen3.5 final norm is an FP32 island and its fused CE
+            # kernel disables autocast, so the tied output projection must be
+            # FP32 as well. Otherwise CoT training reaches FLCE with FP32 hidden
+            # states and a BF16 weight and fails before computing text loss.
+            model = getattr(self.backend, "model", None)
+            vlm = getattr(model, "vlm", None)
+            output_proj = getattr(vlm, "output_proj", None)
+            weight = getattr(output_proj, "weight", None)
+            if isinstance(weight, nn.Parameter):
+                weight.data = weight.data.float()
 
     def to(self, *args, **kwargs) -> G05Policy:
         """Apply author inference precision and move the ActionCodec sidecar."""
diff --git a/tests/policies/g05/test_g05.py b/tests/policies/g05/test_g05.py
index 693a5dbf6..0c9173f63 100644
--- a/tests/policies/g05/test_g05.py
+++ b/tests/policies/g05/test_g05.py
@@ -648,6 +648,28 @@ def test_author_inference_precision_preserves_declared_fp32_parameters():
     assert backend.precision_weight.dtype is torch.float32
 
 
+def test_system2_precision_keeps_tied_lm_head_compatible_with_fp32_final_norm():
+    class CoTPrecisionBackend(TinyG05Backend):
+        def __init__(self):
+            super().__init__()
+            self.model = nn.Module()
+            self.model.vlm = nn.Module()
+            self.model.vlm.input_proj = nn.Embedding(8, 4)
+            self.model.vlm.output_proj = nn.Linear(4, 8, bias=False)
+            self.model.vlm.output_proj.weight = self.model.vlm.input_proj.weight
+
+        def apply_fp32_params(self):
+            pass
+
+    backend = CoTPrecisionBackend()
+    policy = G05Policy(_config(predict_cot=True, runtime_system="system2"), backend=backend)
+
+    policy._apply_author_inference_precision()
+
+    assert backend.model.vlm.output_proj.weight.dtype is torch.float32
+    assert backend.model.vlm.input_proj.weight is backend.model.vlm.output_proj.weight
+
+
 def test_batch_two_preserves_each_raw_task_and_every_camera_slot():
     backend = TinyG05Backend()
     policy = G05Policy(_config(), backend=backend)