Surface reconstruction from point clouds is a fundamental problem in the computer vision and graphics community. Recent state-of-the-arts solve this problem by individually optimizing each local implicit field during inference. Without considering the geometric relationships between local fields, they typically require accurate normals to avoid the sign conflict problem in overlapping regions of local fields, which severely limits their applicability to raw scans where surface normals could be unavailable. Although SAL breaks this limitation via sign-agnostic learning, it is still unexplored that how to extend this pipeline to local shape modeling. To this end, we propose to learn implicit surface reconstruction by sign-agnostic optimization of convolutional occupancy networks, to simultaneously achieve advanced scalability, generality, and applicability in a unified framework. In the paper, we also show this goal can be effectively achieved by a simple yet effective design, which optimizes the occupancy fields that are conditioned on convolutional features from an hourglass network architecture with an unsigned binary cross-entropy loss. Extensive experimental comparison with previous state-of-the-arts on both object-level and scene-level datasets demonstrate the superior accuracy of our approach for surface reconstruction from un-orientated point clouds.