[GitHub] [incubator-mxnet] larroy commented on a change in pull request #14613: [MXNET-978] Higher order gradient support for some unary operators

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larroy commented on a change in pull request #14613: [MXNET-978] Higher order gradient support for some unary operators
URL: https://github.com/apache/incubator-mxnet/pull/14613#discussion_r290913262
 
 

 ##########
 File path: src/operator/tensor/elemwise_unary_op_trig.cc
 ##########
 @@ -46,7 +46,33 @@ The storage type of ``sin`` output depends upon the input storage type:
 )code" ADD_FILELINE)
 .set_attr<nnvm::FGradient>("FGradient", ElemwiseGradUseIn{ "_backward_sin" });
 
-MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU_DR(_backward_sin, unary_bwd<mshadow_op::sin_grad>);
+MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU_DR(_backward_sin, unary_bwd<mshadow_op::sin_grad>)
+.set_attr<nnvm::FGradient>("FGradient",
+    [](const nnvm::NodePtr& n, const std::vector<nnvm::NodeEntry>& ograds) {
+      // ograds[0]: d^2L/dx^2
+      // inputs[0]: dL/dy
+      // inputs[1]: x (ElemwiseUseIn)
+      // f(x) = sin(x)
+      // f'(x) = cos(x)
+      // f''(x) = -sin(x)
+      auto x_grad = MakeNode("cos", n->attrs.name + "_x_grad",
+                             {n->inputs[1]}, nullptr, &n);
+      auto x_grad_grad = MakeNode("negative", n->attrs.name + "_x_grad_grad",
 
 Review comment:
   as long as the nodes are themselves differentiable, then it would support additional differentiation. For some complex functions having just 2nd gradient should be good. In this case I would say it's N times differentiable. the _x_grad_grad is just the name of the node as far as I understand it. Why does it concern you?

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