diff --git a/Source/CNTKv2LibraryDll/Function.cpp b/Source/CNTKv2LibraryDll/Function.cpp
index fdff1da5e..6f490bf77 100644
--- a/Source/CNTKv2LibraryDll/Function.cpp
+++ b/Source/CNTKv2LibraryDll/Function.cpp
@@ -2386,10 +2386,14 @@ namespace CNTK
             InvalidArgument("Input argument epsilon must be non-negative.");
         auto operandPlaceholder = PlaceholderVariable(L"operand");
         size_t operandRank = operand.Shape().Rank();
-        if (operandRank < 2 && !useStatsAcrossChannels)
-            InvalidArgument("When rank of the operand is < 2, useStatsAcrossChannels must be set to false, because there is no channel dimension.");
+        size_t numAxesToReduce;
+        if (operandRank < 1)
+            InvalidArgument("The rank of the operand must be >= 1.");
+        else if (operandRank < 2)
+            numAxesToReduce = operandRank; // Operand's a vector, useStatsAcrossChannels is ignored and mean is computed over the vector.
+        else
+            numAxesToReduce = useStatsAcrossChannels ? operandRank : operandRank - 1; // Assuming last dim to be the channel dim.
 
-        auto numAxesToReduce = useStatsAcrossChannels ? operandRank : operandRank - 1; // Assuming last dim to be the channel dim.
         std::vector<Axis> axesToReduce(numAxesToReduce);
         for (size_t i = 0; i < numAxesToReduce; ++i)
             axesToReduce[i] = Axis(i);
diff --git a/Source/CNTKv2LibraryDll/proto/onnx/CNTKToONNX.cpp b/Source/CNTKv2LibraryDll/proto/onnx/CNTKToONNX.cpp
index 3124874c1..54f233a7d 100644
--- a/Source/CNTKv2LibraryDll/proto/onnx/CNTKToONNX.cpp
+++ b/Source/CNTKv2LibraryDll/proto/onnx/CNTKToONNX.cpp
@@ -1274,20 +1274,8 @@ std::tuple<std::vector<int>, bool, int, bool> CNTKToONNXHelper::CalculateBroadca
 }
 
 // prepare an input node arg with correct name and meta data so that LotusIR can make the connection. 
-void CNTKToONNXHelper::PrepareRNNInput(const Variable &X, std::vector<ONNXIR::NodeArg> &nodeInputs)
+void CNTKToONNXHelper::PrepareRNNInput(const Variable &input, std::vector<ONNXIR::NodeArg> &nodeInputs)
 {
-    Variable input;
-    wstring opName = X.Owner() ? X.Owner()->OpName() : L"";
-    if (X.BlockFunctionVariableMapping().IsInitialized() && !Operators::IsRNNOp(ToString(opName)))
-    {
-        input = X.BlockFunctionVariableMapping();
-    }
-    else
-    {
-        input = X;
-    }
-
-
     std::string inputName = ToString(input.Uid());
     onnx::TypeProto inputArgType = ToTypeProto(input.Shape(), (int)(input.DynamicAxes().size()));
     
@@ -3122,7 +3110,7 @@ ONNXIR::Node* CNTKToONNXHelper::AddNode(const FunctionPtr& src, ONNXIR::Graph* g
             mulNode->AddAttribute("broadcast", static_cast<int64_t>(1));
 
             auto input2 = inputs[biasIndexInOnnxInputs];
-            ONNXIR::NodeArg addTensorOutputArg(nodeName + string("_add_output0"), &input0ArgType);
+            ONNXIR::NodeArg addTensorOutputArg(nodeName + string("_Output_0"), &input0ArgType);
             node = graph->AddNode(nodeName + string("_add"), "Add",
                 "", { mulTensorOutputArg, input2 }, { addTensorOutputArg });
             node->AddAttribute("broadcast", static_cast<int64_t>(1));