diff --git a/python/llm/test/inference_gpu/test_transformers_api_layernorm.py b/python/llm/test/inference_gpu/test_transformers_api_layernorm.py
new file mode 100644
index 00000000..0dbb4fe8
--- /dev/null
+++ b/python/llm/test/inference_gpu/test_transformers_api_layernorm.py
@@ -0,0 +1,117 @@
+#
+# Copyright 2016 The BigDL Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+#
+ 
+import os
+import pytest
+import gc
+ 
+import torch
+from bigdl.llm.transformers import AutoModelForCausalLM, AutoModel
+from transformers import LlamaTokenizer, AutoTokenizer
+ 
+device = os.environ['DEVICE']
+print(f'Running on {device}')
+ 
+PROMPT = "Once upon a time, there existed a little girl who liked to have adventures. She wanted to go to places and meet new people, and have fun"
+TEST_MODEL_LIST = [
+    ("Falcon-7B", AutoModelForCausalLM, AutoTokenizer, os.environ.get('FALCON_7B_ORIGIN_PATH'))
+]
+ 
+class Test_Optimize_Gpu_Model:
+    def setup_method(self):
+        self.layer_outputs = []
+        self.pre_layer_outputs = []
+ 
+    def run_optimize_gpu_model(self, Name, Model, Tokenizer, model_path, LayerNorm_layer, layer_before_LayerNorm, lower_bound):
+        with torch.inference_mode():
+            def pre_forward_hook(module, input, output, layer_name):
+                self.pre_layer_outputs.append(output)
+                
+            def forward_hook(module, input, output, layer_name):
+                self.layer_outputs.append(output)
+ 
+            tokenizer = Tokenizer.from_pretrained(model_path, trust_remote_code=True)
+            input_ids = tokenizer.encode(PROMPT, return_tensors="pt").to(device)
+ 
+            model = Model.from_pretrained(model_path,
+                                        load_in_4bit=True,
+                                        optimize_model=False,
+                                        trust_remote_code=True)
+            model = model.to(device)
+            for layer_name, layer_module in model.named_modules():
+                if layer_name == layer_before_LayerNorm:
+                    layer_module.register_forward_hook(
+                        lambda module, input, output, layer_name=layer_name: pre_forward_hook(module, input,
+                                                                                            output, layer_name))
+                if layer_name == LayerNorm_layer:
+                    layer_module.register_forward_hook(
+                        lambda module, input, output, layer_name=layer_name: forward_hook(module, input,
+                                                                                        output, layer_name))
+            logits_base_model = (model(input_ids)).logits
+            # the list `layer_output` has only one element.
+            layer_tensor = self.layer_outputs.pop()
+            model.to('cpu')
+ 
+            opt_model = Model.from_pretrained(model_path,
+                                            load_in_4bit=True,
+                                            optimize_model=True,
+                                            trust_remote_code=True)
+            opt_model = opt_model.to(device)
+ 
+ 
+            def replace_forward_hook(module, input, output, layer_name):
+                output = self.pre_layer_outputs[0]
+                return output
+ 
+            for layer_name, layer_module in opt_model.named_modules():
+                if layer_name == layer_before_LayerNorm:
+                    layer_module.register_forward_hook(
+                        lambda module, input, output, layer_name=layer_name: replace_forward_hook(module, input,
+                                                                                                output, layer_name))
+                if layer_name == LayerNorm_layer:
+                    layer_module.register_forward_hook(
+                        lambda module, input, output, layer_name=layer_name: forward_hook(module, input,
+                                                                                        output, layer_name))
+            logits_optimized_model = (opt_model(input_ids)).logits
+            # the list `layer_output` has only one element.
+            opt_layer_tensor = self.layer_outputs[0]
+            opt_model.to('cpu')
+ 
+ 
+            LayerNorm_output_diff = []
+            for i, (t1, t2) in enumerate(zip(layer_tensor, opt_layer_tensor)):
+                LayerNorm_output_diff.append(t1 - t2)
+ 
+            max_diff_tensor = [torch.max(item).item() for item in LayerNorm_output_diff]
+            print(max_diff_tensor)
+            torch.xpu.empty_cache()
+            del model
+            del opt_model
+            gc.collect()
+            assert all(max_diff <= lower_bound for max_diff in max_diff_tensor)
+   
+    @pytest.mark.parametrize('Name, Model, Tokenizer, model_path',TEST_MODEL_LIST)
+    def test_dynamic_functions(self, Name, Model, Tokenizer, model_path):
+        if Name == "Falcon-7B":
+            self.Falcon_7B_gpu_model(Name, Model, Tokenizer, model_path)
+
+    
+    def Falcon_7B_gpu_model(self, Name, Model, Tokenizer, model_path):
+        # currently only compare the output of the last LayerNorm layer.
+        layer_before_LayerNorm = "transformer.h.30"
+        LayerNorm_layer = "transformer.h.31.input_layernorm"
+        lower_bound = 0
+        self.run_optimize_gpu_model(Name, Model, Tokenizer, model_path, LayerNorm_layer, layer_before_LayerNorm, lower_bound)
\ No newline at end of file
diff --git a/python/llm/test/inference_gpu/test_transformers_api_mlp.py b/python/llm/test/inference_gpu/test_transformers_api_mlp.py
index 16431cba..1c01b259 100644
--- a/python/llm/test/inference_gpu/test_transformers_api_mlp.py
+++ b/python/llm/test/inference_gpu/test_transformers_api_mlp.py
@@ -28,7 +28,8 @@ print(f'Running on {device}')
 PROMPT = "Once upon a time, there existed a little girl who liked to have adventures. She wanted to go to places and meet new people, and have fun"
 TEST_MODEL_LIST = [
     ("Qwen-7B-Chat", AutoModelForCausalLM, AutoTokenizer, os.environ.get('QWEN_7B_ORIGIN_PATH')),
-    ("Mistral-7B-Instruct-v0.1", AutoModelForCausalLM, AutoTokenizer, os.environ.get('MISTRAL_7B_INSTRUCT_V0_1_ORIGIN_PATH'))
+    ("Mistral-7B-Instruct-v0.1", AutoModelForCausalLM, AutoTokenizer, os.environ.get('MISTRAL_7B_INSTRUCT_V0_1_ORIGIN_PATH')),
+    ("Llama2-7B", AutoModelForCausalLM, LlamaTokenizer, os.environ.get('LLAMA2_7B_ORIGIN_PATH'))
 ]
  
 class Test_Optimize_Gpu_Model:
@@ -91,16 +92,13 @@ class Test_Optimize_Gpu_Model:
             opt_layer_tensor = self.layer_outputs[0]
             opt_model.to('cpu')
  
- 
             MLP_output_diff = []
             for i, (t1, t2) in enumerate(zip(layer_tensor, opt_layer_tensor)):
-                if t1 is not None and t2 is not None:
-                    if isinstance(t1, torch.Tensor) and isinstance(t2, torch.Tensor):
-                        MLP_output_diff.append(t1 - t2)
-                    else:
-                        # 'past_key_value'is of type tuple as default.
-                        for i, (t3, t4) in enumerate(zip(t1, t2)):
-                            MLP_output_diff.append(t3 - t4)
+                if isinstance(t1, torch.Tensor) and isinstance(t2, torch.Tensor):
+                    MLP_output_diff.append(t1 - t2)
+                else:
+                    for i, (t3, t4) in enumerate(zip(t1, t2)):
+                        MLP_output_diff.append(t3 - t4)
  
             max_diff_tensor = [torch.max(item).item() for item in MLP_output_diff]
             print(max_diff_tensor)
@@ -116,8 +114,10 @@ class Test_Optimize_Gpu_Model:
             self.Qwen_7B_gpu_model(Name, Model, Tokenizer, model_path)
         elif Name == "Mistral-7B-Instruct-v0.1":
             self.Mistral_7B_Instruct_gpu_model(Name, Model, Tokenizer, model_path)
+        elif Name == "Llama2-7B":
+            self.Llama2_7B_gpu_model(Name, Model, Tokenizer, model_path)
+
  
-   
     def Qwen_7B_gpu_model(self, Name, Model, Tokenizer, model_path):
         # currently only compare the output of the last mlp layer.
         layer_before_MLP = "transformer.h.31.ln_2"
@@ -130,4 +130,12 @@ class Test_Optimize_Gpu_Model:
         layer_before_MLP = "model.layers.31.post_attention_layernorm"
         MLP_layer = "model.layers.31.mlp"
         lower_bound = 0
-        self.run_optimize_gpu_model(Name, Model, Tokenizer, model_path, MLP_layer, layer_before_MLP, lower_bound)
\ No newline at end of file
+        self.run_optimize_gpu_model(Name, Model, Tokenizer, model_path, MLP_layer, layer_before_MLP, lower_bound)
+    
+    def Llama2_7B_gpu_model(self, Name, Model, Tokenizer, model_path):
+        # The tests are actually testing the mlp layer. We can't test the mlp layer directly 
+        # since the original Llama2 code adds residual after the mlp layer, which differs from the implementation of bigdl
+        layer_before_Decoder = "model.layers.30"
+        Decoder_layer = "model.layers.31"
+        lower_bound = 5e-2
+        self.run_optimize_gpu_model(Name, Model, Tokenizer, model_path, Decoder_layer, layer_before_Decoder, lower_bound)
diff --git a/python/llm/test/run-llm-inference-tests-gpu.sh b/python/llm/test/run-llm-inference-tests-gpu.sh
index 130d58d3..ea1abb51 100644
--- a/python/llm/test/run-llm-inference-tests-gpu.sh
+++ b/python/llm/test/run-llm-inference-tests-gpu.sh
@@ -18,6 +18,7 @@ start=$(date "+%s")
 # fi
 # export OMP_NUM_THREADS=$THREAD_NUM
 pytest ${LLM_INFERENCE_TEST_DIR}/test_transformers_api.py -v -s
+pytest ${LLM_INFERENCE_TEST_DIR}/test_transformers_api_layernorm.py -v -s
 export BIGDL_LLM_XMX_DISABLED=1
 pytest ${LLM_INFERENCE_TEST_DIR}/test_transformers_api_final_logits.py -v -s
 pytest ${LLM_INFERENCE_TEST_DIR}/test_transformers_api_attention.py -v -s -k "not Mistral"