Surface reconstruction from point clouds has been a well-studied research topic with applications in computer vision and computer graphics. Recently, several learning-based methods were proposed for 3D shape representation through implicit functions which among others can be used for point cloud-based reconstruction. Although delivering compelling results for synthetic object datasets of overseeable size, they fail to represent larger scenes accurately, presumably due to the use of only one global latent code for encoding an entire scene or object. We propose to encode only parts of objects with features attached to unstructured point clouds. To this end we use a hierarchical feature map in 3D space, extracted from the input point clouds, with which local latent shape encodings can be queried at arbitrary positions. We use a permutohedral lattice to process the hierarchical feature maps sparsely and efficiently. This enables accurate and detailed point cloud-based reconstructions for large amounts of points in a time-efficient manner, showing good generalization capabilities across different datasets. Experiments on synthetic and real world datasets demonstrate the reconstruction capability of our method and compare favorably to state-of-the-art methods.