[GitHub] [incubator-mxnet] kshitij12345 commented on a change in pull request #15413: [MXNET-978] Higher Order Gradient Support `reciprocal`, `abs`.

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kshitij12345 commented on a change in pull request #15413: [MXNET-978] Higher Order Gradient Support `reciprocal`, `abs`.
URL: https://github.com/apache/incubator-mxnet/pull/15413#discussion_r300449796
 
 

 ##########
 File path: src/operator/tensor/elemwise_unary_op_basic.cc
 ##########
 @@ -717,7 +717,38 @@ Example::
 
 MXNET_OPERATOR_REGISTER_BINARY(_backward_reciprocal)
 .set_attr<FCompute>("FCompute<cpu>",
-  ElemwiseBinaryOp::Compute<cpu, unary_bwd<mshadow_op::reciprocal_grad> >);
+  ElemwiseBinaryOp::Compute<cpu, unary_bwd<mshadow_op::reciprocal_grad> >)
+.set_attr<nnvm::FGradient>("FGradient",
+  [](const nnvm::NodePtr& n, const std::vector<nnvm::NodeEntry>& ograds) {
+    // ograds[0]: dL/dxgrad
+    // inputs[0]: dL/dy
+    // inputs[1]: x
+    // f(x) = y = 1/x
+    // f'(x) = -1/x^2
+    // f''(x) = 2/x^3 = -2 * (f'(x) * f(x))
+
+    const std::unordered_map<std::string, std::string> args = {{"scalar", "-2.0"}};
+
+    auto dydx_mul_dldy = nnvm::NodeEntry{n};  // f'(x) * head_grads
+    auto dydx = MakeNode("elemwise_div", n->attrs.name + "_dydx",
+                         {dydx_mul_dldy, n->inputs[0]}, nullptr, &n);
+    auto fx = MakeNode("reciprocal", n->attrs.name + "_fx",
+                       {n->inputs[1]}, nullptr, &n);
+
+    auto d2ydx2_mid = MakeNode("elemwise_mul", n->attrs.name + "_d2ydx2_mid",
+                               {dydx_mul_dldy, nnvm::NodeEntry{fx}}, nullptr, &n);
+
+    auto d2ydx2 = MakeNode("_mul_scalar", n->attrs.name + "_d2ydx2",
+                           {nnvm::NodeEntry{d2ydx2_mid}}, &args, &n);
+
+    std::vector<nnvm::NodeEntry> ret;
+
+    ret.emplace_back(MakeNode("elemwise_mul", n->attrs.name + "_backward_grad_grad",
 
 Review comment:
   Even I am not sure of its significance in literature. But if you look at `dL/dx = dL/dy * dy/dx` as just `c = a * b`, then `dc/da = b` while `dc/db=a`. 
   So that is all I am thinking, does `dL/dy` affect our `dL/dx`.

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