Minor fix for ComputeBroadcastBackwardAxesDynamic; Fix for GradientGraphBuilder logging (microsoft#5313)

Co-authored-by: Sherlock Huang <bahuang@OrtTrainingDev3.af05slrtruoetgaxwwjv5nsq5e.px.internal.cloudapp.net>

Author: SherlockNoMad

orttraining/orttraining/core/framework/gradient_graph_builder.cc

@@ -63,7 +63,7 @@ GradientGraphBuilder::GradientGraphBuilder(Graph* graph,
   reachable_nodes_ = ReverseBFS(y_nodes_);
 
   std::string unreachable_nodes;
-  
+
   // building x_nodes_
   for (const auto& name : x_node_arg_names) {
     const NodeArg* node_arg = graph->GetNodeArg(name);
@@ -89,7 +89,9 @@ GradientGraphBuilder::GradientGraphBuilder(Graph* graph,
       }
     }
   }
-  LOGS(logger_, WARNING) << "Following nodes are unreachable for gradient back propagation: " << unreachable_nodes;
+  if (!unreachable_nodes.empty()) {
+    LOGS(logger_, WARNING) << "Following nodes are unreachable for gradient back propagation: " << unreachable_nodes;
+  }
 }
 
 NodeSet GradientGraphBuilder::ReverseBFS(const NodeSet& nodes) const {

orttraining/orttraining/core/graph/gradient_builder_base.cc

@@ -105,15 +105,12 @@ void ComputeBroadcastBackwardAxesDynamic(const ArgDef& a,
                                          const ArgDef* a_axes,
                                          const ArgDef* b_axes,
                                          std::vector<NodeDef>& output) {
+  // Populate the node names explicitly in case a and b are the same tensor and
+  // resulting in duplicated node name for Shape node. For example, y = x^2 is sometimes represented as Mul(x,x)
   output.push_back(
-      NodeDef("Shape",
-              {a},
-              {a_shape}));
-
+      NodeDef("Shape", {a}, {a_shape}, NodeAttributes(), a_shape.name + "_lhs"));
   output.push_back(
-      NodeDef("Shape",
-              {b},
-              {b_shape}));
+      NodeDef("Shape", {b}, {b_shape}, NodeAttributes(), b_shape.name + "_rhs"));
 
   ArgDef a_op = ArgDef(""), b_op = ArgDef("");
   if (a_axes)