diff --git a/mldaikon/collect_trace.py b/mldaikon/collect_trace.py
index e9a92fd9..715c414d 100644
--- a/mldaikon/collect_trace.py
+++ b/mldaikon/collect_trace.py
@@ -122,6 +122,13 @@ def get_default_output_folder(args: argparse.Namespace) -> str:
         action="store_true",
         help="Only instrument and dump the modified file",
     )
+    parser.add_argument(
+        "--instr-descriptors",
+        action="store_true",
+        help="""Instrument functions that can only be accessed through descriptors, 
+        Set this to true if you want to instrument built-in types like torch.Tensor, 
+        at the cost of larger (5x) instrumentation overhead and more interference with the program""",
+    )
     parser.add_argument(
         "--profiling",
         type=str,  # @ziming-zh: why is this a string?
@@ -321,6 +328,7 @@ def get_default_output_folder(args: argparse.Namespace) -> str:
         API_dump_stack_trace=args.API_dump_stack_trace,
         cond_dump=args.cond_dump,
         output_dir=output_dir,
+        instr_descriptors=args.instr_descriptors,
     )
 
     # call into the program runner
diff --git a/mldaikon/config/config.py b/mldaikon/config/config.py
index 874d4750..cd6e92cb 100644
--- a/mldaikon/config/config.py
+++ b/mldaikon/config/config.py
@@ -27,7 +27,6 @@
     # "torch._VariableFunctionsClass",
     # "torch.get_default_dtype",
 ]
-
 ANALYSIS_SKIP_FUNC_NAMES = [
     "cuda.is_available",
     "torch.get_default_dtype",
@@ -123,3 +122,4 @@
 ]
 
 ENABLE_COND_DUMP = False
+INSTR_DESCRIPTORS = False
diff --git a/mldaikon/instrumentor/dumper.py b/mldaikon/instrumentor/dumper.py
index 0a3149c3..ff019b76 100644
--- a/mldaikon/instrumentor/dumper.py
+++ b/mldaikon/instrumentor/dumper.py
@@ -223,15 +223,17 @@ def convert_var_to_dict(var, include_tensor_data=True) -> dict:
             if type(attr) in primitive_types:
                 result[attr_name] = attr
 
-            elif include_tensor_data and isinstance(attr, torch.Tensor):
-                result[attr_name] = dump_tensor(attr)
+            elif isinstance(attr, torch.Tensor):
+                result[f"_ML_DAIKON_{attr_name}_ID"] = id(attr)
+                if include_tensor_data:
+                    result[attr_name] = dump_tensor(attr)
 
-            elif include_tensor_data and isinstance(attr, torch.nn.parameter.Parameter):
-                result[attr_name] = attr.__class__.__name__ + "(Parameter)"
-                result[attr_name] = dump_tensor(attr.data)
+            elif isinstance(attr, torch.nn.parameter.Parameter):
+                result[f"_ML_DAIKON_{attr_name}_ID"] = id(attr)
+                if include_tensor_data:
+                    result[attr_name] = dump_tensor(attr.data)
 
             elif include_tensor_data and isinstance(attr, torch.nn.Module):
-                result[attr_name] = attr.__class__.__name__ + "(nn.Module)"
                 # dump out all tensors inside the nn.Module
                 for name, param in attr.named_parameters():
                     result[attr_name] += f"\n{name}: {dump_tensor(param)}"  # type: ignore
diff --git a/mldaikon/instrumentor/source_file.py b/mldaikon/instrumentor/source_file.py
index 2bc96601..0d05c7a0 100644
--- a/mldaikon/instrumentor/source_file.py
+++ b/mldaikon/instrumentor/source_file.py
@@ -329,6 +329,7 @@ def instrument_file(
     API_dump_stack_trace: bool,
     cond_dump: bool,
     output_dir: str,
+    instr_descriptors: bool,
 ) -> str:
     """
     Instruments the given file and returns the instrumented source code.
@@ -358,6 +359,7 @@ def instrument_file(
     general_config_update = f"""
 import mldaikon.config.config as general_config
 general_config.ENABLE_COND_DUMP = {cond_dump}
+general_config.INSTR_DESCRIPTORS = {instr_descriptors}
 """
 
     if models_to_track:
diff --git a/mldaikon/instrumentor/tracer.py b/mldaikon/instrumentor/tracer.py
index 9fcab3d7..caccacf7 100644
--- a/mldaikon/instrumentor/tracer.py
+++ b/mldaikon/instrumentor/tracer.py
@@ -14,6 +14,7 @@
 import torch
 import torch.utils
 
+import mldaikon.config.config as config  # needed to allow for change of values after import
 from mldaikon.config.config import (
     INSTR_MODULES_TO_SKIP,
     TRAIN_STEP_NAMES,
@@ -756,6 +757,18 @@ def _should_skip_module_or_cls(self, pymodule: object) -> str | None:
     def _should_skip_instr_attr(self, attr_name: str, pymodule: object) -> str | None:
         # 1. skip attrs with no objects (e.g. __abstractmethods__ and C extension functions)
         attr = pymodule.__dict__.get(attr_name, None)
+        if attr is None:
+            # try getting it in case it is a descriptor (almost certainly will be)
+            try:
+                attr = getattr(pymodule, attr_name)
+                if not (
+                    config.INSTR_DESCRIPTORS and "method_descriptor" in str(type(attr))
+                ):
+                    # print("TRIGGERED", attr_name)
+                    attr = None
+            except Exception:
+                pass
+
         if attr is None:
             return "Skipping attribute as it is None"
 
@@ -778,17 +791,22 @@ def _should_skip_instr_attr(self, attr_name: str, pymodule: object) -> str | Non
         ):
             return "Skipping magic functions"
 
+        attr_full_name = typename(attr)
         # 4. Skip if the attribute is in INSTR_MODULES_TO_SKIP | MANUAL CONFIG
-        if typename(attr) in INSTR_MODULES_TO_SKIP:
+        if attr_full_name in INSTR_MODULES_TO_SKIP:
             return "Skipping attribute as it is one of INSTR_MODULES_TO_SKIP"
 
         # 5. Skip if the attribute is in modules_to_skip_prefix | MANUAL CONFIG
         for modules_to_skip_prefix in INSTR_MODULES_TO_SKIP:
-            if typename(attr).startswith(modules_to_skip_prefix):
+            if attr_full_name.startswith(modules_to_skip_prefix):
                 return "Skipping attribute as it is in INSTR_MODULES_TO_SKIP"
 
         # 6. Skip if the attribute does not belong to the target root module
-        if not typename(attr).startswith(self.root_module):
+        if not attr_full_name.startswith(self.root_module) and not (
+            config.INSTR_DESCRIPTORS
+            and ("method_descriptor" in attr_full_name or "Tensor" in attr_full_name)
+        ):
+            # builtin methods in torch.Tensor's qualname does not start with torch for some reason
             return "Skipping attribute as it does not belong to the root module"
 
         return None
@@ -858,10 +876,7 @@ def _instrument_module(
             if attr is None:
                 # try access this attribute to handle lazy loading
                 try:
-                    _ = getattr(pymodule, attr_name)
-                    attr = pymodule.__dict__.get(
-                        attr_name
-                    )  # this attr should be loaded now
+                    attr = getattr(pymodule, attr_name)
                 except Exception as e:
                     get_instrumentation_logger_for_process().debug(
                         f"Depth: {depth}, lazy loading failed for attribute: {attr_name}, Module: {target_name}: {e}"
@@ -882,7 +897,10 @@ def _instrument_module(
 
             if isinstance(
                 attr, (types.FunctionType, types.BuiltinFunctionType, _instancemethod_t)
-            ):
+            ) or (
+                config.INSTR_DESCRIPTORS and "method_descriptor" in str(type(attr))
+            ):  # instrumented with potential accuracy issues as descriptor-controlled method access might change what to return based on given information, but is needed to get tensor method invocations
+                assert callable(attr), f"{attr} is not callable"
                 assert not (
                     recurse_into_sub_module and is_API_instrumented(attr)
                 ), f"{attr} is already instrumented"
diff --git a/mldaikon/invariant/DistinctArgumentRelation.py b/mldaikon/invariant/DistinctArgumentRelation.py
index a9a12f92..26ee667e 100644
--- a/mldaikon/invariant/DistinctArgumentRelation.py
+++ b/mldaikon/invariant/DistinctArgumentRelation.py
@@ -89,6 +89,26 @@ def get_event_data_per_function_per_step(trace: Trace, function_pool: Set[Any]):
     return function_pool, listed_arguments
 
 
+def get_event_list(trace: Trace, function_pool: Iterable[str]):
+    listed_events: List[dict[str, Any]]= []
+    # for all func_ids, get their corresponding events
+    for func_name in function_pool:
+        func_call_ids = trace.get_func_call_ids(func_name)
+        for func_call_id in func_call_ids:
+            event = trace.query_func_call_event(func_call_id)
+            listed_events.extend(
+                # [event.pre_record, event.post_record]
+                [event.pre_record]
+            )
+
+    # sort the listed_events
+    # for (process_id, thread_id), events_list in listed_events.items():
+    #     listed_events[(process_id, thread_id)] = sorted(
+    #         events_list, key=lambda x: x["time"]
+    #     )
+
+    return listed_events
+
 def compare_argument(value1, value2, IOU_criteria = True):
     if type(value1) != type(value2):
         return False
@@ -114,7 +134,7 @@ def compare_argument(value1, value2, IOU_criteria = True):
         return abs(value1 - value2) < 1e-8
     return value1 == value2
 
-def is_arguments_list_distinct(args1: list, args2: list):
+def is_arguments_list_same(args1: list, args2: list):
     if len(args1) != len(args2):
         return False
     for index in range(len(args1)):
@@ -206,7 +226,7 @@ def infer(trace: Trace) -> Tuple[List[Invariant], List[FailedHypothesis]]:
                 for PT_pair1, PT_pair2 in combinations(records.keys(), 2):
                     for event1 in records[PT_pair1]:
                         for event2 in records[PT_pair2]:
-                            if(not is_arguments_list_distinct(event1["args"], event2["args"])):
+                            if(not is_arguments_list_same(event1["args"], event2["args"])):
                                 flag = True
                                 pos = Example()
                                 pos.add_group(EXP_GROUP_NAME, [event1, event2])
@@ -218,7 +238,7 @@ def infer(trace: Trace) -> Tuple[List[Invariant], List[FailedHypothesis]]:
                     
                 for PT_pair in records.keys():
                     for event1, event2 in combinations(records[PT_pair], 2):
-                        if(not is_arguments_list_distinct(event1["args"], event2["args"])):
+                        if(not is_arguments_list_same(event1["args"], event2["args"])):
                             flag = True
                             pos = Example()
                             pos.add_group(EXP_GROUP_NAME, [event1, event2])
@@ -295,6 +315,34 @@ def static_check_all(
         """
         assert inv.precondition is not None, "Invariant should have a precondition."
 
+        # 1. Pre-process all the events
+        print("Start preprocessing....")
+        listed_arguments: Dict[str, Dict[int, Dict[Tuple[str, str], List[dict[str, Any]]]]] = {}
+        function_pool: Set[Any] = set()
+        func= inv.params[0]
+
+        assert isinstance(
+            func, APIParam
+        ), "Invariant parameters should be APIParam."
+
+        func_name = func.api_full_name
+        function_pool.add(func_name)
+
+        function_pool, listed_arguments = get_event_data_per_function_per_step(
+            trace, function_pool
+        )
+
+        if not function_pool:
+            return CheckerResult(
+                trace=None,
+                invariant=inv,
+                check_passed=True,
+                triggered=False,
+            )
+
+        events_list = get_event_list(trace, function_pool)
+        print("End preprocessing")
+
         if not inv.precondition.verify([events_list], EXP_GROUP_NAME):
             return CheckerResult(
                 trace=None,
@@ -303,7 +351,27 @@ def static_check_all(
                 triggered=False,
             )
 
-        # TODO: checking process
+        for step, records in listed_arguments[func_name].items():
+                for PT_pair1, PT_pair2 in combinations(records.keys(), 2):
+                    for event1 in records[PT_pair1]:
+                        for event2 in records[PT_pair2]:
+                            if(is_arguments_list_same(event1["args"], event2["args"])):
+                                return CheckerResult(
+                                    trace=[event1, event2],
+                                    invariant=inv,
+                                    check_passed=True,
+                                    triggered=True,
+                                )
+         
+                for PT_pair in records.keys():
+                    for event1, event2 in combinations(records[PT_pair], 2):
+                        if(is_arguments_list_same(event1["args"], event2["args"])):
+                            return CheckerResult(
+                                trace=[event1, event2],
+                                invariant=inv,
+                                check_passed=True,
+                                triggered=True,
+                            )
 
         return CheckerResult(
             trace=None,