Optimize Transpose around QLinearSoftmax (#22849)

### Description
<!-- Describe your changes. -->

- Improved Transpose around QLinearSoftmax in Level 3 NHWC Transformer.
- Removed redundant code HandleQLinearConcat, HandleQLinearBinaryOp.

### 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. -->

By merging and eliminating redundant transpose , the Image Segmentation
i8 model (MobileNetv2 + DeepLabv3) achieves a 2.34X speedup.

onnxruntime/core/optimizer/transpose_optimization/onnx_transpose_optimization.cc

@@ -1654,14 +1654,14 @@ static bool HandleSplit(HandlerArgs& args) {
 
 constexpr HandlerInfo split_handler = {&FirstInput, &HandleSplit};
 
-static bool HandleConcat(HandlerArgs& args) {
+bool HandleConcat(HandlerArgs& args) {
   return HandleSimpleNodeWithAxis(args);
 }
 
 constexpr HandlerInfo concat_handler = {&AllInputs, &HandleConcat};
 
 // Handles Softmax, Hardmax, and LogSoftmax
-static bool HandleSoftHardMax(HandlerArgs& args) {
+bool HandleSoftHardMax(HandlerArgs& args) {
   if (args.ctx.opset >= 13) {
     return HandleSimpleNodeWithAxis(args, /*default_axis*/ -1);
   }

onnxruntime/core/optimizer/transpose_optimization/onnx_transpose_optimization.h

@@ -71,6 +71,9 @@ bool HandleSimpleNodeBroadcast(HandlerArgs& args);
 // Transposes all inputs and all outputs. Updates axis attribute.
 bool HandleSimpleNodeWithAxis(HandlerArgs& args, std::optional<int64_t> default_axis = std::nullopt);
 
+bool HandleConcat(HandlerArgs& args);
+bool HandleSoftHardMax(HandlerArgs& args);
+
 // base handlers that are used by extended handlers. add from transpose_optimizer.cc as needed.
 bool HandleReduceOps(HandlerArgs& args);
 bool HandleResize([[maybe_unused]] HandlerArgs& args);

onnxruntime/core/optimizer/transpose_optimization/ort_transpose_optimization.cc

@@ -34,10 +34,6 @@ static bool EPAwareHandleResize(HandlerArgs& args) {
 
 constexpr HandlerInfo ep_aware_resize_handler = {&FirstInput, &EPAwareHandleResize};
 
-static bool HandleQLinearConcat(HandlerArgs& args) {
-  return HandleSimpleNodeWithAxis(args);
-}
-
 std::vector<size_t> QLinearConcatInputs(OptimizerCtx& ctx, api::NodeRef& node) {
   (void)ctx;
   std::vector<size_t> indices;
@@ -48,19 +44,15 @@ std::vector<size_t> QLinearConcatInputs(OptimizerCtx& ctx, api::NodeRef& node) {
   return indices;
 }
 
-constexpr HandlerInfo q_linear_concat_handler = {&QLinearConcatInputs, &HandleQLinearConcat};
-
-static bool HandleQLinearBinaryOp(HandlerArgs& args) {
-  return HandleSimpleNodeBroadcast(args);
-}
+constexpr HandlerInfo q_linear_concat_handler = {&QLinearConcatInputs, &HandleConcat};
 
 std::vector<size_t> QLinearBinaryOpInputs(OptimizerCtx&, api::NodeRef&) {
   // Inputs are: [A, A_scale, A_zero_point, B, B_scale, B_zero_point, C_scale, C_zero_point],
   // we want [A, B].
   return {0, 3};
 }
 
-constexpr HandlerInfo q_linear_binary_op_handler = {&QLinearBinaryOpInputs, &HandleQLinearBinaryOp};
+constexpr HandlerInfo q_linear_binary_op_handler = {&QLinearBinaryOpInputs, &HandleSimpleNodeBroadcast};
 
 static bool HandleQLinearPoolOp(HandlerArgs& args) {
   // Swap between channel first/last variants. Only works for applicable values of perm.
@@ -129,6 +121,7 @@ constexpr HandlerInfo max_pool_op_handler = {&FirstInput, &HandleMaxPool};
 
 constexpr HandlerInfo node_1_inp_handler = {&FirstInput, &HandleSimpleNode};
 constexpr HandlerInfo reduce_op_handler = {&FirstInput, &HandleReduceOps};
+constexpr HandlerInfo soft_hard_max_handler = {&FirstInput, &HandleSoftHardMax};
 constexpr HandlerInfo contrib_quantize_dequantize_linear_handler = {&FirstInput,
                                                                     &HandleContribQuantizeDequantizeLinear};
 
@@ -148,6 +141,7 @@ const HandlerMap& OrtExtendedHandlers() {
         {"com.microsoft.QLinearMul", q_linear_binary_op_handler},
         {"com.microsoft.QLinearReduceMean", reduce_op_handler},
         {"com.microsoft.QLinearSigmoid", node_1_inp_handler},
+        {"com.microsoft.QLinearSoftmax", soft_hard_max_handler},
     };
 
     return map;

onnxruntime/test/optimizer/transpose_optimizer_test.cc

@@ -22,6 +22,7 @@
 #include "test/optimizer/graph_transform_test_builder.h"
 #include "test/providers/internal_testing/internal_testing_execution_provider.h"
 #include "test/util/include/asserts.h"
+#include "test/util/include/default_providers.h"
 #include "test/util/include/inference_session_wrapper.h"
 #include "test/util/include/test_utils.h"
 
@@ -3800,6 +3801,46 @@ TEST(TransposeOptimizerTests, TestCast) {
                     /*opset_version*/ {15, 18});
 }
 
+TEST(TransposeOptimizerTests, TestQLinearSoftmax) {
+  auto build_test_case_1 = [&](ModelTestBuilder& builder) {
+    auto* input0_arg = MakeInput<uint8_t>(builder, std::nullopt, {1, 384, 384, 21}, 0, 255);
+    auto* transpose_1_out_0 = builder.MakeIntermediate();
+    auto* input_x_scale = builder.MakeScalarInitializer<float>(0.5086354613304138);
+    auto* input_x_zero_point = builder.MakeScalarInitializer<uint8_t>(74);
+    auto* input_y_scale = builder.MakeScalarInitializer<float>(0.003921568859368563);
+    auto* input_y_zero_point = builder.MakeScalarInitializer<uint8_t>(0);
+    auto* qlinearsoftmax_1_out_0 = builder.MakeIntermediate();
+    auto* transpose_2_out_0 = builder.MakeOutput();
+
+    auto& transpose_1 = builder.AddNode("Transpose", {input0_arg}, {transpose_1_out_0});
+    transpose_1.AddAttribute("perm", std::vector<int64_t>{0, 3, 1, 2});
+    auto& qlinearsoftmax_1 = builder.AddNode("QLinearSoftmax",
+                                             {transpose_1_out_0, input_x_scale, input_x_zero_point, input_y_scale, input_y_zero_point},
+                                             {qlinearsoftmax_1_out_0}, kMSDomain);
+    qlinearsoftmax_1.AddAttribute("axis", static_cast<int64_t>(1));
+    qlinearsoftmax_1.AddAttribute("opset", static_cast<int64_t>(13));
+    auto& transpose_2 = builder.AddNode("Transpose", {qlinearsoftmax_1_out_0}, {transpose_2_out_0});
+    transpose_2.AddAttribute("perm", std::vector<int64_t>{0, 2, 3, 1});
+  };
+
+  auto check_optimized_graph_1 = [&](InferenceSessionWrapper& session) {
+    int transpose_cost = EstimateTransposeCost(session.GetGraph());
+    EXPECT_EQ(transpose_cost, 0);
+  };
+
+  TransformerTester(build_test_case_1,
+                    check_optimized_graph_1,
+                    TransformerLevel::Level2,
+                    TransformerLevel::Level3,
+                    /*opset_version*/ 13,
+                    /*per_sample_tolerance*/ 0.0,
+                    /*relative_per_sample_tolerance*/ 0.0,
+                    /*transformer*/ nullptr,
+                    /*add_session_options*/ {},
+                    /*disabled_optimizers*/ {},
+                    /*ep*/ DefaultCpuExecutionProvider());
+}
+
 TEST(TransposeOptimizerTests, TestBroadcastReusedInputs) {
   auto build_test_case_1 = [&](ModelTestBuilder& builder) {
     auto* input0_arg = MakeInput<float>(builder, {{-1, -1, 3, 4}}, {1, 2, 3, 4}, 0.0, 1.0);