Fix MatmulTransposeFusion when input A and B are the same (microsoft#24373)

### Description

MatmulTransposeFusion does not work correctly when input A and B are the
same for a `MatMul` node.


![image](https://github.com/user-attachments/assets/48a6afd8-13d0-48d4-b86f-53a866c47803)

Fixes microsoft#24341

### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->

Author: fs-eire

onnxruntime/core/optimizer/matmul_transpose_fusion.cc

@@ -310,6 +310,19 @@ Status MatmulTransposeFusion::ApplyImpl(Graph& graph, bool& modified, int graph_
       continue;
     }
 
+    NodeArg* right_input = node.MutableInputDefs()[1];
+    auto right_type = right_input->TypeAsProto()->tensor_type().elem_type();
+    if (!IsAllowedFusedMatMulDataType(static_cast<ONNX_NAMESPACE::TensorProto_DataType>(right_type))) {
+      continue;
+    }
+
+    if (left_input == right_input) {
+      // If both inputs are the same, we skip the fusion.
+      // Currently, this situation is not handled correctly in the code below.
+      // Otherwise, the model initialization may fail. See https://github.com/microsoft/onnxruntime/issues/24341.
+      continue;
+    }
+
     bool is_trans_left = false;
     bool is_trans_batch_left = false;
     Node* left = nullptr;
@@ -325,12 +338,6 @@ Status MatmulTransposeFusion::ApplyImpl(Graph& graph, bool& modified, int graph_
       }
     }
 
-    NodeArg* right_input = node.MutableInputDefs()[1];
-    auto right_type = right_input->TypeAsProto()->tensor_type().elem_type();
-    if (!IsAllowedFusedMatMulDataType(static_cast<ONNX_NAMESPACE::TensorProto_DataType>(right_type))) {
-      continue;
-    }
-
     bool is_trans_right = false;
     bool is_trans_batch_right = false;
     Node* right = nullptr;

onnxruntime/test/optimizer/graph_transform_test.cc

@@ -2946,6 +2946,24 @@ TEST_F(GraphTransformationTests, TransposeMatmulTransBatchNoFusion) {
   }
 }
 
+TEST_F(GraphTransformationTests, TransposeMatmulFusion_SameInput_gh_issue_24341) {
+  constexpr const ORTCHAR_T* model_uri = MODEL_FOLDER "fusion/gh_issue_24341.onnx";
+
+  std::shared_ptr<Model> p_model;
+  ASSERT_STATUS_OK(Model::Load(model_uri, p_model, nullptr, *logger_));
+  Graph& graph = p_model->MainGraph();
+  std::map<std::string, int> orig_op_to_count = CountOpsInGraph(graph);
+  onnxruntime::GraphTransformerManager graph_transformation_mgr{5};
+  ASSERT_STATUS_OK(graph_transformation_mgr.Register(
+      std::make_unique<MatmulTransposeFusion>(), TransformerLevel::Level1));
+  ASSERT_STATUS_OK(graph_transformation_mgr.ApplyTransformers(graph, TransformerLevel::Level1, *logger_));
+
+  std::map<std::string, int> op_to_count = CountOpsInGraph(graph);
+  ASSERT_EQ(op_to_count["Transpose"], orig_op_to_count["Transpose"]);
+  ASSERT_EQ(op_to_count["MatMul"], orig_op_to_count["MatMul"]);
+  ASSERT_EQ(op_to_count["Cast"], orig_op_to_count["Cast"]);
+}
+
 TEST_F(GraphTransformationTests, Gemm_LeakyRelu_Fusion) {
   constexpr const ORTCHAR_T* model_uri = MODEL_FOLDER "gemm_activation_fusion/gemm_activation_fusion.onnx";