apeforest commented on a change in pull request #15120: [bug] fix higher grad 
log 
URL: https://github.com/apache/incubator-mxnet/pull/15120#discussion_r290538567
 
 

 ##########
 File path: src/operator/tensor/elemwise_unary_op_basic.cc
 ##########
 @@ -1074,16 +1074,19 @@ 
MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU_DR(_backward_log,
   [](const nnvm::NodePtr& n, const std::vector<nnvm::NodeEntry>& ograds) {
     // For f(x) -> f = log
     // f''(x) = -1 * (f'(x) * f'(x))
-    auto gx = nnvm::NodeEntry{n};
+    auto gx_mul_head_grads = nnvm::NodeEntry{n};  // f'(x) * head_grads
+    auto head_grads = nnvm::NodeEntry{n->inputs[0]};
+    auto g_lx = MakeNode("reciprocal", n->attrs.name + "_backward_log_grad",
+                            {n->inputs[1]}, nullptr, &n);
     auto ggx_mid = MakeNode("elemwise_mul", n->attrs.name + 
"_backward_mid_grad_grad",
-                            {gx, gx}, nullptr, &n);
+                            {gx_mul_head_grads, nnvm::NodeEntry{g_lx}}, 
nullptr, &n);
     auto ggx = MakeNode("negative", n->attrs.name + "_backward_grad_grad",
                         {nnvm::NodeEntry{ggx_mid}}, nullptr, &n);
 
     std::vector<nnvm::NodeEntry> ret;
 
     ret.emplace_back(MakeNode("elemwise_mul", n->attrs.name + 
"_backward_grad_grad",
-                             {ograds[0], gx}, nullptr, &n));
+                             {ograds[0], nnvm::NodeEntry{g_lx}}, nullptr, &n));
 
 Review comment:
   Still looking into this. The first output should be the gradient of y_grad. 
However, the `head_grads.grad` does not get the value. I suspect the returned 
value from this function is dropped in the gradient calculation in 
imperative.cc. I will look more into this. Stay tuned.

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