  Reflectional symmetry is ubiquitous in nature. While extrinsic reflectional
symmetry can be easily parametrized and detected, intrinsic symmetry is much
harder due to the high solution space. Previous works usually solve this
problem by voting or sampling, which suffer from high computational cost and
randomness. In this paper, we propose \YL{a} learning-based approach to
intrinsic reflectional symmetry detection. Instead of directly finding
symmetric point pairs, we parametrize this self-isometry using a functional map
matrix, which can be easily computed given the signs of Laplacian
eigenfunctions under the symmetric mapping. Therefore, we train a novel deep
neural network to predict the sign of each eigenfunction under symmetry, which
in addition takes the first few eigenfunctions as intrinsic features to
characterize the mesh while avoiding coping with the connectivity explicitly.
Our network aims at learning the global property of functions, and consequently
converts the problem defined on the manifold to the functional domain. By
disentangling the prediction of the matrix into separated basis, our method
generalizes well to new shapes and is invariant under perturbation of
eigenfunctions. Through extensive experiments, we demonstrate the robustness of
our method in challenging cases, including different topology and incomplete
shapes with holes. By avoiding random sampling, our learning-based algorithm is
over 100 times faster than state-of-the-art methods, and meanwhile, is more
robust, achieving higher correspondence accuracy in commonly used metrics.
