[GitHub] [incubator-mxnet] kshitij12345 commented on a change in pull request #15288: [MXNET-978] Higher order gradient for sigmoid

[GitBox <gi...@apache.org>]

kshitij12345 commented on a change in pull request #15288: [MXNET-978] Higher order gradient for sigmoid
URL: https://github.com/apache/incubator-mxnet/pull/15288#discussion_r299580908
 
 

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 File path: src/operator/tensor/elemwise_unary_op_basic.cc
 ##########
 @@ -121,7 +121,30 @@ The storage type of ``sigmoid`` output is always dense
 .set_attr<nnvm::FGradient>("FGradient", ElemwiseGradUseOut{"_backward_sigmoid"});
 
 MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU(_backward_sigmoid,
-                                               unary_bwd<mshadow_op::sigmoid_grad>);
+                                               unary_bwd<mshadow_op::sigmoid_grad>)
+.set_attr<nnvm::FGradient>("FGradient",
+    [](const nnvm::NodePtr& n, const std::vector<nnvm::NodeEntry>& ograds) {
+      // n->inputs[0] : y_grad
+      // n->inputs[1] : f(x) = sigmoid(x)
+      // ograds[0] : head_grads
+      // f''(x) = f'(x) * (1 - 2*f(x))
+      auto ones = MakeNode("ones_like", n->attrs.name + "_grad_ones", {n->inputs[1]}, nullptr, &n);
+      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 one_minus_two_y = MakeNode("elemwise_sub", n->attrs.name + "_grad_sub",
+                                    {nnvm::NodeEntry{ones}, nnvm::NodeEntry{two_y}}, nullptr, &n);
+      auto grad_grad_mid = MakeNode("elemwise_mul", n->attrs.name + "_grad_mul",
+                                    {n->inputs[0], nnvm::NodeEntry{one_minus_two_y}}, nullptr, &n);
+      // when building gradient graph, the backward node of n->inputs[1] will be
+      // added to the graph again, therefore f`(x) will be multiplied
 
 Review comment:
   LGTM.

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