Fix some x86 build warnings in training code (#20451)

### Description
<!-- Describe your changes. -->
Fix some misc build warnings from x86 Windows build


### 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. -->

orttraining/orttraining/test/training_api/core/checkpoint_test.cc

@@ -117,8 +117,8 @@ TEST(CheckpointApiTest, SaveOnnxModelAsCheckpoint_ThenLoad_CPU) {
 
   // Check loaded parameter's values are same with original ones.
   ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), restored_trainable_param_names.size());
-  ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), 7);
-  ASSERT_EQ(restored_param_name_to_ort_values.size(), 9);
+  ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), size_t{7});
+  ASSERT_EQ(restored_param_name_to_ort_values.size(), size_t{9});
 
   std::sort(expected_trainable_param_names.begin(), expected_trainable_param_names.end());
   std::sort(restored_trainable_param_names.begin(), restored_trainable_param_names.end());
@@ -225,8 +225,8 @@ TEST(CheckpointApiTest, SaveOnnxModelAsCheckpointThenLoadFromBufferCPU) {
 
   // Check loaded parameter's values are same with original ones.
   ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), restored_trainable_param_names.size());
-  ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), 7);
-  ASSERT_EQ(restored_param_name_to_ort_values.size(), 9);
+  ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), size_t{7});
+  ASSERT_EQ(restored_param_name_to_ort_values.size(), size_t{9});
 
   std::sort(expected_trainable_param_names.begin(), expected_trainable_param_names.end());
   std::sort(restored_trainable_param_names.begin(), restored_trainable_param_names.end());
@@ -308,7 +308,7 @@ TEST(CheckpointApiTest, SaveOptimizerStateAsCheckpoint_ThenLoad) {
 
   std::vector<Ort::Value> all_weights_values;
   data_loader.GetNextSampleBatch(all_weights_values);
-  ASSERT_EQ(all_weights_values.size(), 4);
+  ASSERT_EQ(all_weights_values.size(), size_t{4});
   NameMLValMap name_to_ort_value{
       {"fc1.weight", *all_weights_values[0]},
       {"fc1.bias", *all_weights_values[1]},
@@ -360,7 +360,7 @@ TEST(CheckpointApiTest, SaveOptimizerStateAsCheckpoint_ThenLoad) {
   InlinedHashMap<std::string, std::shared_ptr<GroupOptimizerState>>&
       group_optimizer_states = optimizer_state.group_named_optimizer_states;
 
-  ASSERT_EQ(group_optimizer_states.size(), 1);
+  ASSERT_EQ(group_optimizer_states.size(), size_t{1});
   ASSERT_EQ(group_optimizer_states.begin()->first, "group0");
 
   InlinedHashMap<std::string, ParameterOptimizerState>&
@@ -429,7 +429,7 @@ TEST(CheckpointApiTest, SaveCustomPropertyAsCheckpoint_ThenLoad_CPU) {
   CheckpointState checkpoint_state_to_load;
   ASSERT_STATUS_OK(LoadCheckpoint(checkpoint_path, checkpoint_state_to_load));
   PropertyBag& restored_property_bag = checkpoint_state_to_load.property_bag;
-  ASSERT_EQ(restored_property_bag.size(), 3);
+  ASSERT_EQ(restored_property_bag.size(), size_t{3});
   float restored_f_data = restored_property_bag.GetProperty<float>(f_property_name);
   ASSERT_FLOAT_EQ(f_data, restored_f_data);
   int64_t restored_i_data = restored_property_bag.GetProperty<int64_t>(i_property_name);
@@ -559,8 +559,8 @@ TEST(CheckpointApiTest, SaveOnnxModelAsCheckpoint_ThenLoad_WithExternalData) {
 
   // Check loaded parameter's values are same with original ones.
   ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), restored_trainable_param_names.size());
-  ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), 7);
-  ASSERT_EQ(restored_param_name_to_ort_values.size(), 9);
+  ASSERT_EQ(expected_trainable_param_name_to_ort_value.size(), size_t{7});
+  ASSERT_EQ(restored_param_name_to_ort_values.size(), size_t{9});
 
   std::sort(expected_trainable_param_names.begin(), expected_trainable_param_names.end());
   std::sort(restored_trainable_param_names.begin(), restored_trainable_param_names.end());

orttraining/orttraining/test/training_api/core/training_api_tests.cc

@@ -208,8 +208,8 @@ TEST(TrainingApiTest, ModuleParametersSize) {
   }
 
   // ((500*784) + 500 + (10*500) + 10) = 397510
-  ASSERT_EQ(params_size, 397510);
-  ASSERT_EQ(model->GetParametersSize(), 397510);
+  ASSERT_EQ(params_size, size_t{397510});
+  ASSERT_EQ(model->GetParametersSize(), size_t{397510});
 }
 
 TEST(TrainingApiTest, ModuleCopyBufferToParameters) {
@@ -269,7 +269,7 @@ TEST(TrainingApiTest, ModuleTrainStep) {
   auto model = std::make_unique<onnxruntime::training::api::Module>(model_identifier,
                                                                     &state, session_option,
                                                                     *env, std::vector<std::shared_ptr<IExecutionProvider>>());
-  ASSERT_EQ(model->GetTrainingModelOutputCount(), 1);
+  ASSERT_EQ(model->GetTrainingModelOutputCount(), size_t{1});
   OrtValue input, target;
   GenerateRandomInput(std::array<int64_t, 2>{2, 784}, input);
   target = onnxruntime::test::CreateInputOrtValueOnCPU<int32_t>(
@@ -659,7 +659,7 @@ TEST(TrainingApiTest, ModuleAndOptimizerWithNominalState) {
     ASSERT_STATUS_OK(model_with_complete_state->TrainStep(inputs, complete_fetches));
     ASSERT_STATUS_OK(model_with_nominal_state->TrainStep(inputs, nominal_fetches));
 
-    ASSERT_GT(complete_fetches.size(), 0);
+    ASSERT_GT(complete_fetches.size(), size_t{0});
     for (size_t i = 0; i < complete_fetches.size(); ++i) {
       ASSERT_TRUE(complete_fetches[i].IsTensor());
       ASSERT_TRUE(nominal_fetches[i].IsTensor());
@@ -730,7 +730,7 @@ TEST(TrainingApiTest, ModuleAndOptimizerWithNominalState) {
     ASSERT_STATUS_OK(model_with_complete_state->EvalStep(inputs, complete_eval_fetches));
     ASSERT_STATUS_OK(model_with_nominal_state->EvalStep(inputs, nominal_eval_fetches));
 
-    ASSERT_GT(complete_eval_fetches.size(), 0);
+    ASSERT_GT(complete_eval_fetches.size(), size_t{0});
     for (size_t i = 0; i < complete_eval_fetches.size(); ++i) {
       ASSERT_TRUE(complete_eval_fetches[i].IsTensor());
       ASSERT_TRUE(nominal_eval_fetches[i].IsTensor());

orttraining/orttraining/test/training_ops/cpu/nn/dropout_op_test.cc

@@ -78,7 +78,7 @@ void RunDropoutTest(const bool use_mask, const std::vector<int64_t>& input_shape
   }
 
   auto output_verifier = [&](const std::vector<OrtValue>& fetches, const std::string& provider_type) {
-    ASSERT_GE(fetches.size(), 1);
+    ASSERT_GE(fetches.size(), size_t{1});
     const auto& output_tensor = fetches[0].Get<Tensor>();
     auto output_span = output_tensor.DataAsSpan<float>();
 
@@ -99,7 +99,7 @@ void RunDropoutTest(const bool use_mask, const std::vector<int64_t>& input_shape
     }
 
     if (use_mask) {
-      ASSERT_GE(fetches.size(), 2);
+      ASSERT_GE(fetches.size(), size_t{2});
       const auto& mask_tensor = fetches[1].Get<Tensor>();
       auto mask_span = mask_tensor.DataAsSpan<bool>();
       ASSERT_EQ(mask_span.size(), output_span.size()) << "provider: " << provider_type;

orttraining/orttraining/training_api/module.cc

@@ -517,7 +517,7 @@ Status Module::CopyParametersToBuffer(OrtValue& parameters_buffer, const bool tr
                 "Only float is supported.");
     }
     ORT_RETURN_IF_ERROR(sess_data_transfer_manager.CopyTensor(*weight_tensor, *p_tensor.get()));
-    offset += shape.Size();
+    offset += narrow<size_t>(shape.Size());
   }
   return Status::OK();
 }
@@ -601,7 +601,7 @@ Status Module::CopyBufferToParameters(OrtValue& parameters_buffer, const bool tr
       ORT_THROW_IF_ERROR(sess_data_transfer_manager.CopyTensor(*src_tensor.get(), *weight_tensor));
     }
 
-    offset += shape.Size();
+    offset += narrow<size_t>(shape.Size());
   }
 
   if (state_->module_checkpoint_state.is_nominal_state) {