diff --git a/CHANGELOGS.rst b/CHANGELOGS.rst
index c0c4b39d..d3671fb5 100644
--- a/CHANGELOGS.rst
+++ b/CHANGELOGS.rst
@@ -4,6 +4,7 @@ Change Logs
 0.8.9
 +++++
 
+* :pr:`378`: implements the computation of discrepancies in ``method_to_onnx``
 * :pr:`379`: update the handling of cache after the removal of HybridCache, SlidingWindowCache in ``transformers>=5``,
 
 0.8.8
diff --git a/_doc/examples/plot_export_tiny_llm_method_generate.py b/_doc/examples/plot_export_tiny_llm_method_generate.py
index 8109a251..6568ffe4 100644
--- a/_doc/examples/plot_export_tiny_llm_method_generate.py
+++ b/_doc/examples/plot_export_tiny_llm_method_generate.py
@@ -17,6 +17,7 @@
 `arnir0/Tiny-LLM <https://huggingface.co/arnir0/Tiny-LLM>`_.
 """
 
+import pandas
 from transformers import AutoModelForCausalLM, AutoTokenizer
 from onnx_diagnostic import doc
 from onnx_diagnostic.export.api import method_to_onnx
@@ -108,10 +109,24 @@ def generate_text(
 
 
 # %%
-# Let's call generate again.
+# Let's call generate again. The conversion is triggered after
+# ``convert_after_n_calls=3`` calls to the method forward,
+# which exactly what the method generate is doing.
 generated_text = generate_text(prompt, model, tokenizer)
 print(generated_text)
 
+# %%
+# We finally need to check the discrepancies.
+# The exports produced an onnx file and dumped the input and output
+# of the torch model. We now run the onnx model to check
+# it produces the same results.
+# It is done after because the model may not hold twice in memory
+# (torch and onnxruntime).
+# verbose=2 shows more information about expected outputs.
+data = forward_replacement.check_discrepancies(verbose=1)
+df = pandas.DataFrame(data)
+print(df)
+
 
 # %%
 
diff --git a/_unittests/ut_export/test_api.py b/_unittests/ut_export/test_api.py
index 186a7472..4a47f362 100644
--- a/_unittests/ut_export/test_api.py
+++ b/_unittests/ut_export/test_api.py
@@ -19,6 +19,7 @@
 
 
 class TestValidate(ExtTestCase):
+    @ignore_warnings(FutureWarning)
     @hide_stdout()
     def test_to_onnx(self):
         class Model(torch.nn.Module):
@@ -142,6 +143,9 @@ def forward(self, x, y):
             feeds = make_feeds(input_names, args, use_numpy=True)
             got = sess.run(None, feeds)
             self.assertEqualArray(expected, got[0])
+        df = method_to_call.check_discrepancies()
+        self.assertIsInstance(df, list)
+        self.assertEqual(len(df), 2)
         self.clean_dump()
 
     @requires_experimental_experiment("0.1")
@@ -243,6 +247,7 @@ def forward(self, x, y=None):
             feeds = make_feeds(input_names, (args, kwargs), use_numpy=True)
             got = sess.run(None, feeds)
             self.assertEqualArray(expected, got[0])
+        method_to_call.check_discrepancies(verbose=1)
         self.clean_dump()
 
 
diff --git a/onnx_diagnostic/export/api.py b/onnx_diagnostic/export/api.py
index 244d6dfb..5d506bb8 100644
--- a/onnx_diagnostic/export/api.py
+++ b/onnx_diagnostic/export/api.py
@@ -1,11 +1,16 @@
 import inspect
 import os
 import textwrap
+import time
+from collections.abc import Mapping, Iterable
 from typing import Any, Callable, Dict, List, Optional, Sequence, Set, Tuple, Union
 import torch
 from .dynamic_shapes import ModelInputs
 from .onnx_plug import EagerDirectReplacementWithOnnx
-from ..helpers import string_type
+from ..helpers import flatten_object, max_diff, string_diff, string_type
+from ..helpers.torch_helper import torch_deepcopy
+from ..helpers.rt_helper import make_feeds
+from ..reference import OnnxruntimeEvaluator
 
 
 def get_main_dispatcher(
@@ -314,10 +319,11 @@ def to_onnx(
     raise ValueError(f"Unknown exporter={exporter!r}")
 
 
-class _WrapperToExportMethodToOnnx(torch.nn.Module):
+class WrapperToExportMethodToOnnx(torch.nn.Module):
     """
     Wraps an existing models in order to spy on inputs.
-    This is used by :func:`onnx_diagnostic.export.api.method_to_onnx`.
+    This is used by :func:`onnx_diagnostic.export.api.method_to_onnx`
+    or :ref:`l-plot-tiny-llm-export-method-generate` for an example.
     """
 
     def __init__(
@@ -352,6 +358,7 @@ def __init__(
             else getattr(mod, method_name)
         )
         self._inputs: List[Tuple[Tuple[Any, ...], Dict[str, Any]]] = []
+        self._outputs: List[Any] = []
         self._convert_after_n_calls = convert_after_n_calls
         self._patch_kwargs = patch_kwargs
         self._method_src = None
@@ -375,6 +382,7 @@ def __init__(
             inline=inline,
         )
         self._export_done = False
+        self._serialization_classes: Set[type] = set()
 
     def __str__(self) -> str:
         return self.__repr__()
@@ -385,18 +393,41 @@ def __repr__(self) -> str:
             f"{self._method_name})"
         )
 
+    def _collect_classes(self, obj):
+        if obj is None or isinstance(obj, torch.Tensor):
+            return
+        cls = type(obj)
+        if cls.__module__ not in ("builtins",):
+            self._serialization_classes.add(cls)
+        if hasattr(obj, "__dict__"):
+            for v in vars(obj).values():
+                self._collect_classes(v)
+            return
+        if isinstance(obj, Mapping):
+            for v in obj.values():
+                self._collect_classes(v)
+            return
+        if isinstance(obj, Iterable) and not isinstance(obj, (str, bytes)):
+            for v in obj:
+                self._collect_classes(v)
+            return
+
     def forward(self, *args, **kwargs):
         if not self._export_done:
             self._inputs.append(
-                (
-                    args,
+                torch_deepcopy(
                     (
-                        kwargs
-                        if not kwargs or not self.skip_kwargs_names
-                        else {
-                            k: v for k, v in kwargs.items() if k not in self.skip_kwargs_names
-                        }
-                    ),
+                        args,
+                        (
+                            kwargs
+                            if not kwargs or not self.skip_kwargs_names
+                            else {
+                                k: v
+                                for k, v in kwargs.items()
+                                if k not in self.skip_kwargs_names
+                            }
+                        ),
+                    )
                 )
             )
             if self.verbose:
@@ -405,12 +436,45 @@ def forward(self, *args, **kwargs):
                     f"{string_type(self._inputs[-1], with_shape=True)}"
                 )
             if len(self._inputs) >= self._convert_after_n_calls:
+                name = os.path.splitext(self._to_onnx_kwargs["filename"])[0]
+                input_file = f"{name}.inputs.pt"
+                self._input_file = input_file
+                if self.verbose:
+                    print(
+                        f"[method_to_onnx] save {len(self._inputs)} inputs in {input_file!r}"
+                    )
+                torch.save(self._inputs, input_file)
                 self._convert_method_to_onnx()
-                del self._inputs[:]
                 self._export_done = True
-        return self._method_call(*args, **kwargs)
+
+        begin = time.perf_counter()
+        res = self._method_call(*args, **kwargs)
+        duration = time.perf_counter() - begin
+        self._collect_classes([args, kwargs, res])
+        if self._inputs:
+            self._outputs.append((torch_deepcopy(res), duration))
+            assert len(self._inputs) == len(self._outputs), (
+                f"Number of inputs {len(self._inputs)} and "
+                f"outputs {len(self._outputs)} are different."
+            )
+            if self._export_done:
+                name = os.path.splitext(self._to_onnx_kwargs["filename"])[0]
+                output_file = f"{name}.outputs.pt"
+                if self.verbose:
+                    print(
+                        f"[method_to_onnx] save {len(self._outputs)} "
+                        f"outputs in {output_file!r}"
+                    )
+                torch.save(self._outputs, output_file)
+                self._output_file = output_file
+                del self._inputs[:]
+                del self._outputs[:]
+        return res
 
     def _convert_method_to_onnx(self):
+        for args, kwargs in self._inputs:
+            self._serialization_classes |= {type(a) for a in args}
+            self._serialization_classes |= {type(a) for a in kwargs.values()}
 
         def make_method(self):
             inner_sig = inspect.signature(self._method_call)
@@ -477,6 +541,112 @@ def __init__(self, parent):
                 **self._to_onnx_kwargs,
             )
 
+    def check_discrepancies(
+        self, atol: float = 1e-4, rtol: float = 0.1, hist=(0.1, 0.01), verbose: int = 0
+    ) -> List[Dict[str, Union[str, int, float]]]:
+        """
+        Computes the discrepancies between the saved inputs and outputs
+        with the saved onnx model.
+
+        :param atol: absolute tolerance, recommended values, 1e-4 for float, 1e-2 flot float16
+        :param rtol: relative tolerance
+        :param hist: thresholds, the function determines the number of discrepancies
+            above that threshold.
+        :param verbose: verbosity
+        :return: results, a list of dictionaries, ready to be consumed by a dataframe
+        """
+        assert self._export_done, "The onnx export was not done."
+        assert os.path.exists(self._input_file), f"input file {self._input_file!r} not found"
+        assert os.path.exists(
+            self._output_file
+        ), f"output file {self._output_file!r} not found"
+        filename = self._to_onnx_kwargs["filename"]
+        assert isinstance(filename, str) and os.path.exists(
+            filename
+        ), f"onnx file {filename!r} not found"
+        classes = [
+            cls
+            for cls in self._serialization_classes
+            if cls not in {int, float, bool, str, torch.Tensor, list, set, dict, torch.device}
+        ]
+        if verbose:
+            print(f"[method_to_onnx.check_discrepancies] register classes {classes}")
+            print(f"[method_to_onnx.check_discrepancies] load {self._input_file!r}")
+        with torch.serialization.safe_globals(classes):
+            inputs = torch.load(self._input_file)
+        if verbose:
+            print(f"[method_to_onnx.check_discrepancies] load {self._output_file!r}")
+        with torch.serialization.safe_globals(classes):
+            outputs = torch.load(self._output_file)
+        assert len(inputs) == len(outputs), (
+            f"Unexpected number of inputs {len(inputs)} and outputs {len(outputs)}, "
+            f"inputs={string_type(inputs, with_shape=True)}, "
+            f"outputs={string_type(outputs, with_shape=True)}"
+        )
+        if verbose:
+            print(f"[method_to_onnx.check_discrepancies] create onnx session {filename!r}")
+        sess = OnnxruntimeEvaluator(filename, whole=True)
+        input_names = sess.input_names
+        if verbose:
+            print(f"[method_to_onnx.check_discrepancies] input_names={input_names}")
+        data = []
+        for i, (input, (output, latency)) in enumerate(zip(inputs, outputs)):
+            if verbose:
+                if verbose > 1:
+                    print(
+                        f"[method_to_onnx.check_discrepancies] process input {i}: "
+                        f"{string_type(input, with_shape=True)}"
+                    )
+                    print(
+                        f"[method_to_onnx.check_discrepancies] expects: "
+                        f"{string_type(output, with_shape=True)}"
+                    )
+                else:
+                    print(f"[method_to_onnx.check_discrepancies] process input {i}")
+
+            flat_inputs = flatten_object(input, drop_keys=True)
+            if len(flat_inputs) < len(input_names):
+                # not implemented yet, it is caused by a missing cache,
+                # which requires an empty cache instead
+                data.append(dict(index=i, duration_torch=latency, n_inputs=len(flat_inputs)))
+                continue
+            assert len(flat_inputs) == len(input_names), (
+                f"Length mismatch, expecting {len(input_names)} onnx inputs and got "
+                f"{len(flat_inputs)} flat torch inputs"
+            )
+            feeds = make_feeds(input_names, flat_inputs)
+            begin = time.perf_counter()
+            ort_outputs = sess.run(None, feeds)
+            duration = time.perf_counter() - begin
+            diff = max_diff(output, ort_outputs, hist=hist)
+            if "rep" in diff and isinstance(diff["rep"], dict):
+                diff.update(diff["rep"])
+                del diff["rep"]
+            diff["SUCCESS"] = (
+                isinstance(diff["abs"], float)
+                and isinstance(diff["rel"], float)
+                and diff["abs"] < atol
+                and diff["rel"] < rtol
+            )
+            diff.update(
+                dict(
+                    index=i,
+                    duration_torch=latency,
+                    ort_duration=duration,
+                    n_inputs=len(flat_inputs),
+                )
+            )
+            if verbose > 1:
+                print(
+                    f"[method_to_onnx.check_discrepancies] ort output "
+                    f"{string_type(ort_outputs, with_shape=True)}"
+                )
+                print(f"[method_to_onnx.check_discrepancies] diff {string_diff(diff)}")
+            data.append(diff)
+        if verbose:
+            print("[method_to_onnx.check_discrepancies] done")
+        return data
+
 
 def method_to_onnx(
     mod: "torch.nn.Module",
@@ -533,7 +703,7 @@ def method_to_onnx(
 
     See :ref:`l-plot-tiny-llm-export-method-generate` for an example.
     """
-    wrapped_model = _WrapperToExportMethodToOnnx(
+    wrapped_model = WrapperToExportMethodToOnnx(
         mod=mod,
         method_name=method_name,
         input_names=input_names,