Changing context search for BiasAddGrad rewrite from BFS to stricter check

tensorflow/core/graph/mkl_layout_pass.cc

@@ -247,16 +247,10 @@ namespace tensorflow {
 //
 //           P = Conv2DWithBiasBackpropBias(O, O_m)
 //
-// 'Distance' between input of BiasAddGrad and _MklConv2D in terms of hops is
+// Rewrite of BiasAddGrad into Conv2DWithBiasBackpropBias takes place depending
-// the context matching depth. If _MklConv2DWithBias is not within the context
+// on the matching 'context'. The term context is loosely related to which
-// matching depth, then we do not rewrite BiasAddGrad.
+// forward op is _associated_ to BiasAddGrad. If it is _MklConv2DWithBias then
-
+// we consider it Conv2D context; if it is MatMul, then it is MatMul context.
-// How many hops do we search for matching node in the backward dataflow graph?
-// We use maxhop of 10 based on empirical observations. Also, these are
-// maxhops in backward data-flow graph. Since input of forward nodes (Conv2D)
-// directly goes to backward nodes, we do not expect the hop-distance
-// would be more than few nodes.
-static size_t kNodeMergeContextMaxDepth = 10;
 
 class MklLayoutRewritePass : public GraphOptimizationPass {
  public:
@@ -280,6 +274,8 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
     csinfo_.max_pool = "MaxPool";
     csinfo_.max_pool_grad = "MaxPoolGrad";
     csinfo_.mkl_conv2d = "_MklConv2D";
+    csinfo_.mkl_conv2d_grad_input = "_MklConv2DBackpropInput";
+    csinfo_.mkl_conv2d_grad_filter = "_MklConv2DBackpropFilter";
     csinfo_.mkl_conv2d_with_bias = "_MklConv2DWithBias";
     csinfo_.mkl_conv2d_with_bias_backprop_bias =
                                    "_MklConv2DWithBiasBackpropBias";
@@ -360,16 +356,12 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
     minfo_.push_back({csinfo_.mkl_conv2d, csinfo_.bias_add, 0,
                       csinfo_.mkl_conv2d_with_bias});
 
-    // We use maxhop of 10 based on empirical observations. Also, these are
-    // maxhops in backward data-flow graph. Since input of forward nodes
-    // (Conv2D) directly goes to backward nodes, we do not expect the
-    // hop-distance would be more than few nodes.
     biasaddgrad_matmul_context_ = {csinfo_.bias_add_grad, csinfo_.matmul,
-                                   kNodeMergeContextMaxDepth};
+                                   IsBiasAddGradInMatMulContext};
 
     biasaddgrad_conv2dwithbias_context_ = {csinfo_.bias_add_grad,
                                    csinfo_.mkl_conv2d_with_bias,
-                                   kNodeMergeContextMaxDepth};
+                                   IsBiasAddGradInConv2DWithBiasContext};
 
     cinfo_.push_back(&biasaddgrad_matmul_context_);
     cinfo_.push_back(&biasaddgrad_conv2dwithbias_context_);
@@ -392,9 +384,7 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
     string node;     // Name of the node to be rewritten
     string fwd;      // Name of the node in the forward pass that this node
                      // corresponds to
-    size_t max_hop;  // Maximum number of hops the fwd is located
+    std::function<bool(const Node*, const Node**, void* c)> context_match_fn;
-                     // from this node. If the fwd is farther than max_hop
-                     // then we do not rewrite the node.
   } ContextInfo;
 
   /// Structure to specify the name of an original node, its new name after
@@ -438,7 +428,7 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
 
   /// Structure to store all constant strings
   /// NOTE: names are alphabetically sorted.
-  struct {
+  typedef struct {
     string avg_pool;
     string avg_pool_grad;
     string bias_add;
@@ -457,13 +447,15 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
     string max_pool;
     string max_pool_grad;
     string mkl_conv2d;
+    string mkl_conv2d_grad_input;
+    string mkl_conv2d_grad_filter;
     string mkl_conv2d_with_bias;
     string mkl_conv2d_with_bias_backprop_bias;
     string relu;
     string relu_grad;
     string reshape;
     string split;
-  } csinfo_;
+  } ConstStringsInfo;
 
  private:
   /// Maintain info about nodes to rewrite
@@ -478,6 +470,9 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
   /// Maintain info about nodes to rewrite
   static std::vector<ContextInfo*> cinfo_;
 
+  /// Maintain structure of constant strings
+  static ConstStringsInfo csinfo_;
+
   /// Context variables used in referencing rules
   static ContextInfo biasaddgrad_matmul_context_;
   static ContextInfo biasaddgrad_conv2dwithbias_context_;
@@ -629,6 +624,173 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
     return false;
   }
 
+  // Is BiasAddGrad node in 'n' is associated with Conv2DWithBias node
+  // specified in contextinfo 'ci'. Function updates fwd_node to point
+  // to Conv2DWithBias node if 'n' is associated with Conv2DWithBias.
+  //
+  // Association checks for one of the following graphs:
+  //
+  // Graph A:
+  //
+  // _ = Conv2DWithBias(F, I, _)
+  // ..
+  // _ = Conv2DBackpropFilter(F, _, G)
+  // _ = Conv2DBackpropInput(_, I, G)
+  // _ = BiasAddGrad(G)
+  //
+  // OR
+  //
+  // Graph B:
+  //
+  // _ = Conv2DWithBias(F, _, _)
+  // ..
+  // _ = Conv2DBackpropFilter(F, _, G)
+  // _ = BiasAddGrad(G)
+  //
+  // Here F, G, and I are graph nodes; _ represents graph nodes that we
+  // don't care here.
+  //
+  // @return - true (if BiasAddGrad is associated with Conv2DWithBias);
+  //           false otherwise.
+  static bool IsBiasAddGradInConv2DWithBiasContext(const Node* n,
+                                                   const Node** fwd_node,
+                                                   void* ci) {
+    CHECK_NOTNULL(n);
+    CHECK_NOTNULL(fwd_node);
+    CHECK_NOTNULL(ci);
+    *fwd_node = nullptr;
+
+    CHECK_EQ(n->type_string(), csinfo_.bias_add_grad);
+
+    // Get the only 1 input of BiasAddGrad.
+    CHECK_EQ(n->num_inputs(), 1);
+    const Node* bias_add_grad_inp = nullptr;
+    TF_CHECK_OK(n->input_node(0, &bias_add_grad_inp));
+    CHECK_NOTNULL(bias_add_grad_inp);
+
+    // Check if this input also goes to BackpropFilter and BackpropInput
+    // as 3rd input.
+    bool found_backprop_input = false;
+    bool found_backprop_filter = false;
+    Node* backprop_filter_node = nullptr;
+    Node* backprop_input_node = nullptr;
+
+    for (const Edge* e : bias_add_grad_inp->out_edges()) {
+      Node* third_input = nullptr;
+      if (e->dst()->type_string() == csinfo_.conv2d_grad_input ||
+          e->dst()->type_string() == csinfo_.mkl_conv2d_grad_input) {
+        // Third input (index 2) of BackpropInput
+        TF_CHECK_OK(e->dst()->input_node(2, &third_input));
+        // Third input (index 2) of BackpropInput must be same as the input
+        // of BiasAddGrad.
+        if (third_input == bias_add_grad_inp) {
+          found_backprop_input = true;
+          backprop_input_node = e->dst();
+        }
+      }
+
+      if (e->dst()->type_string() == csinfo_.conv2d_grad_filter ||
+          e->dst()->type_string() == csinfo_.mkl_conv2d_grad_filter) {
+        // Third input (index 2) of BackpropFilter
+        TF_CHECK_OK(e->dst()->input_node(2, &third_input));
+        // Third input (index 2) of BackpropFilter must be same as the input
+        // of BiasAddGrad.
+        if (third_input == bias_add_grad_inp) {
+          found_backprop_filter = true;
+          backprop_filter_node = e->dst();
+        }
+      }
+
+      // If we found both the nodes, then we can stop the search.
+      if (found_backprop_input && found_backprop_filter) {
+        break;
+      }
+    }
+
+    // If BackpropFilter node is not found, then this is not
+    // Conv2DWithBias context. For 2nd graph in the example above, only
+    // BackpropFilter would be present.
+    if (!found_backprop_filter) {
+      return false;
+    }
+
+    // Otherwise, we found the nodes.
+    CHECK_NOTNULL(backprop_filter_node);
+    if (found_backprop_input) {
+      CHECK_NOTNULL(backprop_input_node);
+    }
+
+    // Now that we confirmed that this is Conv2DWithBias context, we need to
+    // get access to the forward node (Conv2DWithBias). 2nd input of
+    // Conv2DWithBias is same as the 2nd input of Conv2DBackpropInput; 1st
+    // input of Conv2DWithBias is same as the 1st input of Conv2DBackpropFilter
+    // (This comes from definition of gradient computation for Conv2D).
+    if (found_backprop_input) {
+      // Graph A in the example.
+      Node* second_inp_of_input = nullptr;
+      Node* first_inp_of_filter = nullptr;
+      TF_CHECK_OK(backprop_input_node->input_node(1, &second_inp_of_input));
+      TF_CHECK_OK(backprop_filter_node->input_node(0, &first_inp_of_filter));
+      CHECK_NOTNULL(second_inp_of_input);
+      CHECK_NOTNULL(first_inp_of_filter);
+
+      // Now we need to find out Conv2DWithBias node from these input nodes.
+      // Conv2DWithBias node is the node that accepts both the nodes
+      // second_inp_of_input and first_inp_of_filter in 2nd and 1st input slots.
+      for (const Edge* fe : first_inp_of_filter->out_edges()) {
+        if (fe->dst()->type_string() == csinfo_.mkl_conv2d_with_bias &&
+            fe->dst_input() == 0) {
+          for (const Edge* ie : second_inp_of_input->out_edges()) {
+            if (ie->dst()->type_string() == csinfo_.mkl_conv2d_with_bias &&
+                ie->dst_input() == 1 && fe->dst() == ie->dst()) {
+              VLOG(1) << "MklLayoutRewritePass: found "
+                      << fe->dst()->DebugString()
+                      << " as the forward node for matching context, backward"
+                      << " node is: " << n->DebugString();
+              *fwd_node = fe->dst();
+              return true;
+            }
+          }
+        }
+      }
+    } else {
+      // We did not find BackpropInput, so we work with BackpropFilter only.
+      // Graph B in the example.
+      Node* first_inp_of_filter = nullptr;
+      TF_CHECK_OK(backprop_filter_node->input_node(0, &first_inp_of_filter));
+      CHECK_NOTNULL(first_inp_of_filter);
+
+      // Now we need to find out Conv2DWithBias node from first input of
+      // BackpropFIlter. Conv2DWithBias node is the node that accepts
+      // first_inp_of_filter in 1st input slot.
+      for (const Edge* fe : first_inp_of_filter->out_edges()) {
+        if (fe->dst()->type_string() == csinfo_.mkl_conv2d_with_bias &&
+            fe->dst_input() == 0) {
+          VLOG(1) << "MklLayoutRewritePass: found "
+                  << fe->dst()->DebugString()
+                  << " as the forward node for matching context, backward"
+                  << " node is: " << n->DebugString();
+          *fwd_node = fe->dst();
+          return true;
+        }
+      }
+    }
+
+    return false;
+  }
+
+  // Is BiasAddGrad node in 'n' is associated with MatMul node
+  // specified in contextinfo 'ci'. Function does not update fwd_node.
+  //
+  // @return - true (if BiasAddGrad is associated with MatMul);
+  //           false otherwise.
+  static bool IsBiasAddGradInMatMulContext(const Node* n,
+                                           const Node** fwd_node,
+                                           void* ci) {
+    return (!IsBiasAddGradInConv2DWithBiasContext(n, fwd_node, ci));
+  }
+
+
   // Rewrite rule that uses context-information for matching,
   // used in scenario 2.
   //
@@ -639,8 +801,6 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
   static bool ContextMatchRewrite(const Node* n, const ContextInfo* c);
 
   // Helper function that searches the matching contextinfo for the node.
-  // Implements depth-first search in the data dependence graph for the
-  // gradient op in the backward direction.
   //
   // @input n - Node (gradient op) whose contextinfo is to be searched,
   //        fwd_node - pointer to node from the forward pass that this node
@@ -788,6 +948,7 @@ class MklLayoutRewritePass : public GraphOptimizationPass {
                                    Node* orig_node);
 };
 
+MklLayoutRewritePass::ConstStringsInfo MklLayoutRewritePass::csinfo_;
 MklLayoutRewritePass::ContextInfo
   MklLayoutRewritePass::biasaddgrad_conv2dwithbias_context_;
 MklLayoutRewritePass::ContextInfo
@@ -1667,12 +1828,12 @@ Status MklLayoutRewritePass::RewriteNode(std::unique_ptr<Graph>* g,
   const ContextInfo* ci = nullptr;
   bool is_context_based_rewrite = false;
   if ((ci = SearchMatchingContext(orig_node, &fwd_node)) != nullptr) {
-    CHECK_NOTNULL(fwd_node);
     is_context_based_rewrite = true;
 
     // Sanity checks for context-based rewrite (if any)
     if (orig_node->type_string() == csinfo_.bias_add_grad &&
         ri->new_name == csinfo_.mkl_conv2d_with_bias_backprop_bias) {
+      CHECK_NOTNULL(fwd_node);
       DataType orig_T, ctx_T;
       string orig_data_format, ctx_data_format;
       TF_CHECK_OK(GetNodeAttr(orig_node->def(), "T", &orig_T));
@@ -1784,69 +1945,17 @@ MklLayoutRewritePass::SearchMatchingContext(const Node* n,
   CHECK_NOTNULL(fwd_node);
   *fwd_node = nullptr;
 
-  // Search for matching contextinfo based on node name.
+  // Search for matching contextinfo based on node name and call
-  // There could be more than one matching contextinfos.
+  // callback function using matching contextinfo.
-  bool is_matching_cinfo_found = false;
+  // There could be more than one matching contextinfos but whichever
-  std::vector<const ContextInfo*> mci;
+  // matches first is returned.
   for (auto ci = cinfo_.cbegin(); ci != cinfo_.cend(); ++ci) {
-    if (n->type_string() == (*ci)->node) {
+    if (n->type_string() == (*ci)->node &&
-      mci.push_back(*ci);
+        (*ci)->context_match_fn(n, fwd_node, *ci)) {
-      is_matching_cinfo_found = true;
+      VLOG(1) << "Found context as matching: " << (*ci)->fwd;
+      return *ci;
     }
   }
-  // If no matching contextinfo is found, return immediately.
-  if (!is_matching_cinfo_found) {
-    return nullptr;
-  }
-
-  VLOG(1) << "MklLayoutRewritePass: Searching graph for: " << n->type_string()
-          << " in backwards.";
-
-  // Now we will check for forward op name for context info in data
-  // flow graph. Get the max hops we should search for the fwd node.
-  // We are now going to search (breadth-first) backwards in data
-  // dependence graph (for up to max hops) from n for the node
-  // specified in fwd.
-  // queue to maintain nodes to be visited and depth info for
-  // breadth-first search
-  std::queue<std::pair<const Node*, int>> nqueue;
-  const Node* curr_node = n;
-  size_t curr_depth = 0;
-  nqueue.push(std::make_pair(curr_node, curr_depth));
-
-  while (curr_depth < kNodeMergeContextMaxDepth && !nqueue.empty()) {
-    std::pair<const Node*, int> curr_pair = nqueue.front();
-    nqueue.pop();
-
-    std::set<const Node*> visited_nodes;
-    curr_node = curr_pair.first;
-    curr_depth = curr_pair.second;
-    CHECK_NOTNULL(curr_node);
-
-    VLOG(1) << "MklLayoutRewritePass: Visiting node: "
-            << curr_node->type_string() << " at depth: " << curr_depth
-            << " for node: " << n->type_string();
-
-    // If we find a match, we return immediately.
-    for (const ContextInfo* ci : mci) {
-      if (curr_node->type_string() == ci->fwd) {
-        *fwd_node = curr_node;
-        return ci;
-      }
-    }
-
-    // Else we explore backward edges from current node.
-    // Add the source nodes of all incoming edges of the node to the queue.
-    for (const Edge* e : curr_node->in_edges()) {
-      // We do not visit already visited node.
-      if (visited_nodes.find(e->src()) == visited_nodes.end()) {
-        // Depth of these nodes is 1 more than the depth of current node.
-        nqueue.push(std::make_pair(e->src(), curr_depth + 1));
-        visited_nodes.insert(e->src());
-      }
-    }
-  } /* while */
-
   return nullptr;
 }
 

tensorflow/core/graph/mkl_layout_pass_test.cc

@@ -345,7 +345,8 @@ TEST_F(MklLayoutPassTest, NodeMerge_Conv2DWithBias_Negative_AttrMismatch) {
 // Test set 2: _MklConv2D..BiasAddGrad -> _MklConv2DWithBiasBackpropBias
 // rewrite tests
 
-// D=_MklConv2D(A,M,B,N,C,O); E=Sub(D,A); F=BiasAddGrad(E)
+// BiasAddGrad rewrite to BackpropBias in the presence of BackpropFilter
+// and BackpropInput
 TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_Positive) {
   InitGraph(
       "node { name: 'A' op: 'Input'}"
@@ -364,16 +365,255 @@ TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_Positive) {
       "node { name: 'E' op: 'Sub'"
       " attr {key: 'T'                 value { type: DT_FLOAT } }"
       " input: ['D', 'A']}"
-      "node { name: 'F' op: 'BiasAddGrad'"
+      "node { name: 'F' op: 'Int32Input'}"
+      "node { name: 'G' op: '_MklConv2DBackpropFilter'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'F', 'E', 'M', 'N', 'O'] }"
+      "node { name: 'H' op: 'Int32Input'}"
+      "node { name: 'I' op: '_MklConv2DBackpropInput'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['H', 'B', 'E', 'M', 'N', 'O']}"
+      "node { name: 'J' op: 'BiasAddGrad'"
       " attr { key: 'T'                value { type: DT_FLOAT } }"
       " attr { key: 'data_format'      value { s: 'NCHW' } }"
       " input: ['E'] }");
   EXPECT_EQ(DoMklLayoutOptimizationPass(),
             "A(Input);B(Input);C(Input);D(_MklConv2DWithBias);DMT/_0(Const);"
-            "E(Sub);F(_MklConv2DWithBiasBackpropBias);M(_MklInput);"
+            "E(Sub);F(Int32Input);G(_MklConv2DBackpropFilter);H(Int32Input);"
-            "N(_MklInput);O(_MklInput)|A->D;A->E:1;B->D:1;C->D:2;D->E;"
+            "I(_MklConv2DBackpropInput);J(_MklConv2DWithBiasBackpropBias);"
-            "DMT/_0->F:1;E->F;E:control->DMT/_0:control;M->D:3;N->D:4;"
+            "M(_MklInput);N(_MklInput);O(_MklInput)|A->D;A->E:1;A->G;B->D:1;"
-            "O->D:5");
+            "B->I:1;C->D:2;D->E;DMT/_0->J:1;E->G:2;E->I:2;E->J;"
+            "E:control->DMT/_0:control;F->G:1;H->I;M->D:3;M->G:3;M->I:3;"
+            "N->D:4;N->G:4;N->I:4;O->D:5;O->G:5;O->I:5");
+}
+
+// BiasAddGrad rewrite to BackpropBias in the presence of BackpropFilter
+// and BackpropInput. But nodes do not match criteria for rewrite. So
+// rewrite should not happen.
+TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_Negative1) {
+  InitGraph(
+      "node { name: 'A' op: 'Input'}"
+      "node { name: 'B' op: 'Input'}"
+      "node { name: 'C' op: 'Input'}"
+      "node { name: 'M' op: '_MklInput'}"
+      "node { name: 'N' op: '_MklInput'}"
+      "node { name: 'O' op: '_MklInput'}"
+      "node { name: 'D' op: '_MklConv2DWithBias'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'B', 'C', 'M', 'N', 'O']}"
+      "node { name: 'E' op: 'Sub'"
+      " attr {key: 'T'                 value { type: DT_FLOAT } }"
+      " input: ['D', 'A']}"
+      "node { name: 'F' op: 'Int32Input'}"
+      "node { name: 'G' op: '_MklConv2DBackpropFilter'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['E', 'F', 'A', 'M', 'N', 'O'] }"
+      "node { name: 'H' op: 'Int32Input'}"
+      "node { name: 'I' op: '_MklConv2DBackpropInput'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['H', 'B', 'E', 'M', 'N', 'O']}"
+      "node { name: 'J' op: 'BiasAddGrad'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " input: ['E'] }");
+  EXPECT_EQ(DoMklLayoutOptimizationPass(),
+            "A(Input);B(Input);C(Input);D(_MklConv2DWithBias);"
+            "E(Sub);F(Int32Input);G(_MklConv2DBackpropFilter);H(Int32Input);"
+            "I(_MklConv2DBackpropInput);J(BiasAddGrad);"
+            "M(_MklInput);N(_MklInput);O(_MklInput)|A->D;A->E:1;A->G:2;B->D:1;"
+            "B->I:1;C->D:2;D->E;E->G;E->I:2;E->J;F->G:1;H->I;M->D:3;M->G:3;"
+            "M->I:3;N->D:4;N->G:4;N->I:4;O->D:5;O->G:5;O->I:5");
+}
+
+// BiasAddGrad rewrite to BackpropBias in the presence of BackpropFilter
+// and BackpropInput. But nodes do not match criteria for rewrite. So
+// rewrite should not happen.
+TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_Negative2) {
+  InitGraph(
+      "node { name: 'A' op: 'Input'}"
+      "node { name: 'B' op: 'Input'}"
+      "node { name: 'C' op: 'Input'}"
+      "node { name: 'M' op: '_MklInput'}"
+      "node { name: 'N' op: '_MklInput'}"
+      "node { name: 'O' op: '_MklInput'}"
+      "node { name: 'D' op: '_MklConv2DWithBias'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['B', 'A', 'C', 'M', 'N', 'O']}"
+      "node { name: 'E' op: 'Sub'"
+      " attr {key: 'T'                 value { type: DT_FLOAT } }"
+      " input: ['D', 'A']}"
+      "node { name: 'F' op: 'Int32Input'}"
+      "node { name: 'G' op: '_MklConv2DBackpropFilter'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'F', 'E', 'M', 'N', 'O'] }"
+      "node { name: 'H' op: 'Int32Input'}"
+      "node { name: 'I' op: '_MklConv2DBackpropInput'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['H', 'B', 'E', 'M', 'N', 'O']}"
+      "node { name: 'J' op: 'BiasAddGrad'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " input: ['E'] }");
+  EXPECT_EQ(DoMklLayoutOptimizationPass(),
+            "A(Input);B(Input);C(Input);D(_MklConv2DWithBias);"
+            "E(Sub);F(Int32Input);G(_MklConv2DBackpropFilter);H(Int32Input);"
+            "I(_MklConv2DBackpropInput);J(BiasAddGrad);"
+            "M(_MklInput);N(_MklInput);O(_MklInput)|A->D:1;A->E:1;A->G;B->D;"
+            "B->I:1;C->D:2;D->E;E->G:2;E->I:2;E->J;F->G:1;H->I;M->D:3;M->G:3;"
+            "M->I:3;N->D:4;N->G:4;N->I:4;O->D:5;O->G:5;O->I:5");
+}
+
+
+// BiasAddGrad rewrite to BackpropBias in the presence of BackpropFilter only
+TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_BpropFilter_Positive) {
+  InitGraph(
+      "node { name: 'A' op: 'Input'}"
+      "node { name: 'B' op: 'Input'}"
+      "node { name: 'C' op: 'Input'}"
+      "node { name: 'M' op: '_MklInput'}"
+      "node { name: 'N' op: '_MklInput'}"
+      "node { name: 'O' op: '_MklInput'}"
+      "node { name: 'D' op: '_MklConv2DWithBias'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'B', 'C', 'M', 'N', 'O']}"
+      "node { name: 'E' op: 'Sub'"
+      " attr {key: 'T'                 value { type: DT_FLOAT } }"
+      " input: ['D', 'A']}"
+      "node { name: 'F' op: 'Int32Input'}"
+      "node { name: 'G' op: '_MklConv2DBackpropFilter'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'F', 'E', 'M', 'N', 'O'] }"
+      "node { name: 'H' op: 'BiasAddGrad'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " input: ['E'] }");
+  EXPECT_EQ(DoMklLayoutOptimizationPass(),
+            "A(Input);B(Input);C(Input);D(_MklConv2DWithBias);DMT/_0(Const);"
+            "E(Sub);F(Int32Input);G(_MklConv2DBackpropFilter);"
+            "H(_MklConv2DWithBiasBackpropBias);M(_MklInput);N(_MklInput);"
+            "O(_MklInput)|A->D;A->E:1;A->G;B->D:1;C->D:2;D->E;DMT/_0->H:1;"
+            "E->G:2;E->H;E:control->DMT/_0:control;F->G:1;M->D:3;M->G:3;"
+            "N->D:4;N->G:4;O->D:5;O->G:5");
+}
+
+// BiasAddGrad rewrite to BackpropBias in the presence of BackpropFilter only
+// But BackpropFilter node inputs do not satisfy criteria for rewrite.
+TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_BpropFilter_Negative1) {
+  InitGraph(
+      "node { name: 'A' op: 'Input'}"
+      "node { name: 'B' op: 'Input'}"
+      "node { name: 'C' op: 'Input'}"
+      "node { name: 'M' op: '_MklInput'}"
+      "node { name: 'N' op: '_MklInput'}"
+      "node { name: 'O' op: '_MklInput'}"
+      "node { name: 'D' op: '_MklConv2DWithBias'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'B', 'C', 'M', 'N', 'O']}"
+      "node { name: 'E' op: 'Sub'"
+      " attr {key: 'T'                 value { type: DT_FLOAT } }"
+      " input: ['D', 'A']}"
+      "node { name: 'F' op: 'Int32Input'}"
+      "node { name: 'G' op: '_MklConv2DBackpropFilter'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['E', 'F', 'A', 'M', 'N', 'O'] }"
+      "node { name: 'H' op: 'BiasAddGrad'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " input: ['E'] }");
+  EXPECT_EQ(DoMklLayoutOptimizationPass(),
+            "A(Input);B(Input);C(Input);D(_MklConv2DWithBias);"
+            "E(Sub);F(Int32Input);G(_MklConv2DBackpropFilter);H(BiasAddGrad);"
+            "M(_MklInput);N(_MklInput);O(_MklInput)|A->D;A->E:1;A->G:2;B->D:1;"
+            "C->D:2;D->E;E->G;E->H;F->G:1;M->D:3;M->G:3;N->D:4;N->G:4;O->D:5;"
+            "O->G:5");
+}
+
+// BiasAddGrad rewrite to BackpropBias in the presence of BackpropFilter only
+// But BackpropFilter node inputs do not satisfy criteria for rewrite.
+TEST_F(MklLayoutPassTest, NodeMerge_Conv2DBackprop_BpropFilter_Negative2) {
+  InitGraph(
+      "node { name: 'A' op: 'Input'}"
+      "node { name: 'B' op: 'Input'}"
+      "node { name: 'C' op: 'Input'}"
+      "node { name: 'M' op: '_MklInput'}"
+      "node { name: 'N' op: '_MklInput'}"
+      "node { name: 'O' op: '_MklInput'}"
+      "node { name: 'D' op: '_MklConv2DWithBias'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['B', 'A', 'C', 'M', 'N', 'O']}"
+      "node { name: 'E' op: 'Sub'"
+      " attr {key: 'T'                 value { type: DT_FLOAT } }"
+      " input: ['D', 'A']}"
+      "node { name: 'F' op: 'Int32Input'}"
+      "node { name: 'G' op: '_MklConv2DBackpropFilter'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " attr { key: 'use_cudnn_on_gpu' value { b: false } }"
+      " attr { key: 'strides'          value { list: {i: 1, i:1, i:1, i:1} } }"
+      " attr { key: 'padding'          value { s: 'SAME' } }"
+      " input: ['A', 'F', 'E', 'M', 'N', 'O'] }"
+      "node { name: 'H' op: 'BiasAddGrad'"
+      " attr { key: 'T'                value { type: DT_FLOAT } }"
+      " attr { key: 'data_format'      value { s: 'NCHW' } }"
+      " input: ['E'] }");
+  EXPECT_EQ(DoMklLayoutOptimizationPass(),
+            "A(Input);B(Input);C(Input);D(_MklConv2DWithBias);"
+            "E(Sub);F(Int32Input);G(_MklConv2DBackpropFilter);H(BiasAddGrad);"
+            "M(_MklInput);N(_MklInput);O(_MklInput)|A->D:1;A->E:1;A->G;B->D;"
+            "C->D:2;D->E;E->G:2;E->H;F->G:1;M->D:3;M->G:3;N->D:4;N->G:4;O->D:5;"
+            "O->G:5");
 }
 
 // No _MklConv2DWithBias in context, but _MklConv2D in context.