[GitHub] [incubator-mxnet] larroy commented on a change in pull request #15253: [MXNET-978] Add higher order gradient support `tan`, `tanh`

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larroy commented on a change in pull request #15253: [MXNET-978] Add higher order gradient support `tan`, `tanh`
URL: https://github.com/apache/incubator-mxnet/pull/15253#discussion_r302241795
 
 

 ##########
 File path: src/operator/tensor/elemwise_unary_op_trig.cc
 ##########
 @@ -139,7 +139,31 @@ The storage type of ``tan`` output depends upon the input storage type:
 )code" ADD_FILELINE)
 .set_attr<nnvm::FGradient>("FGradient", ElemwiseGradUseOut{ "_backward_tan" });
 
-MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU_DR(_backward_tan, unary_bwd<mshadow_op::tan_grad>);
+MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU_DR(_backward_tan, unary_bwd<mshadow_op::tan_grad>)
+.set_attr<nnvm::FGradient>("FGradient",
+  [](const nnvm::NodePtr& n, const std::vector<nnvm::NodeEntry>& ograds) {
+      // NodeEntry{n} : y_grad * f'(x)
+      // n->inputs[0] : y_grad
+      // n->inputs[1] : f(x) = tan(x)
+      // ograds[0] : head_grads
+      // f'(x) = sec^2(x)
+      // f''(x) = 2 * f'(x) * f(x)
+      const std::unordered_map<std::string, std::string> args = {{"scalar", "2.0"}};
+      auto two_y = MakeNode("_mul_scalar", n->attrs.name + "_mul_two", {n->inputs[1]}, &args, &n);
+      auto grad_grad_mid = MakeNode("elemwise_mul", n->attrs.name + "_grad_mul",
 
 Review comment:
   Can we clarify / add a comment on why is correct to multiply by y_grad (the first head gradient?) again? This would help readers as is not obvious, as well as the very non-obvious implicit multiplication by f'(x) it compounds.

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