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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