larroy commented on a change in pull request #15515: [MXNET-978] Higher Order
Gradient Support `arcsin`, `arccos`.
URL: https://github.com/apache/incubator-mxnet/pull/15515#discussion_r330752970
##########
File path: src/operator/tensor/elemwise_unary_op_trig.cc
##########
@@ -188,7 +188,31 @@ The storage type of ``arcsin`` output depends upon the
input storage type:
.set_attr<nnvm::FGradient>("FGradient", ElemwiseGradUseIn{ "_backward_arcsin"
});
MXNET_OPERATOR_REGISTER_BINARY_WITH_SPARSE_CPU_DR(_backward_arcsin,
-
unary_bwd<mshadow_op::arcsin_grad>);
+
unary_bwd<mshadow_op::arcsin_grad>)
+.set_attr<nnvm::FGradient>("FGradient",
+ [](const nnvm::NodePtr& n, const std::vector<nnvm::NodeEntry>& ograds) {
+ // ograds[0]: head_grad_grads (dL/dxgrad)
+ // inputs[0]: dL/dy
+ // inputs[1]: x (ElemwiseGradUseIn)
+ // f(x) = arcsin(x)
+ // n: f'(x) = 1/(1-x^2)^1/2
+ // f''(x) = f'(x) * x/(1-x^2)
+ // Note: x/(1-x^2) = x * f'(x)^2
+ auto dydx = n->inputs[0];
+ auto x = n->inputs[1];
+ auto dydx_mul_grad_x = nnvm::NodeEntry{n};
+ auto op = mxnet::util::NodeOpGen{n};
+
+ auto grad_x = op.div(dydx_mul_grad_x, dydx);
+ auto grad_x_square = op.square(grad_x);
+ auto grad_x_square_mul_x = op.mul(grad_x_square, x);
+ auto grad_grad_x = op.mul(dydx_mul_grad_x, grad_x_square_mul_x);
+
+ std::vector<nnvm::NodeEntry> ret;
+ ret.emplace_back(op.mul(ograds[0], grad_x));
Review comment:
if the first input is y_grad or dL/dy, this gradient should be dL/(dy*dx) ?
didn't we have the convention of x_grad instead of grad_x?
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