diff --git a/orttraining/orttraining/core/agent/training_agent.cc b/orttraining/orttraining/core/agent/training_agent.cc
index 055c78929f..db7d4eb942 100644
--- a/orttraining/orttraining/core/agent/training_agent.cc
+++ b/orttraining/orttraining/core/agent/training_agent.cc
@@ -64,7 +64,7 @@ common::Status TrainingAgent::RunForward(const std::vector<OrtValue>& feeds, std
   state.SetProgramCounterStart(0);
   state.SetProgramCounterEnd(fw_program_counter_end_);
 
-  const int32_t partial_graph_index = 0;
+  constexpr int32_t partial_graph_index = 0;
   return RunCore(feeds, fetches, state, *fw_feeds_fetches_manager_, cache, partial_graph_index);
 }
 
@@ -72,7 +72,7 @@ common::Status TrainingAgent::RunBackward(const std::vector<OrtValue>& feeds, st
                                           PartialGraphExecutionState& state) {
   state.SetProgramCounterStart(fw_program_counter_end_);
   state.SetProgramCounterEnd(bw_program_counter_end_);
-  const int32_t partial_graph_index = 1;
+  constexpr int32_t partial_graph_index = 1;
   return RunCore(feeds, fetches, state, *bw_feeds_fetches_manager_, nullptr, partial_graph_index);
 }
 
diff --git a/orttraining/orttraining/training_ops/cuda/loss/softmax_cross_entropy_loss_impl.cc b/orttraining/orttraining/training_ops/cuda/loss/softmax_cross_entropy_loss_impl.cc
index dcc3e2fef0..c2526a44fc 100644
--- a/orttraining/orttraining/training_ops/cuda/loss/softmax_cross_entropy_loss_impl.cc
+++ b/orttraining/orttraining/training_ops/cuda/loss/softmax_cross_entropy_loss_impl.cc
@@ -147,7 +147,7 @@ Status SoftmaxCrossEntropyLoss<T, Tin>::ComputeInternal(OpKernelContext* ctx) co
         reduction_buffer.get(),
         buffer_size));
   } else {
-    const TBuf normalize_factor = static_cast<TBuf>(1.0f);
+    constexpr TBuf normalize_factor = static_cast<TBuf>(1.0f);
     CUDA_RETURN_IF_ERROR(cudaMemcpyAsync(normalize_factor_data.get(), &normalize_factor, sizeof(TBuf), cudaMemcpyHostToDevice, Stream()));
   }