The class-agnostic counting (CAC) problem has caught increasing attention recently due to its wide societal applications and arduous challenges. To count objects of different categories, existing approaches rely on user-provided exemplars, which is hard-to-obtain and limits their generality. In this paper, we aim to empower the framework to recognize adaptive exemplars within the whole images. A zero-shot Generalized Counting Network (GCNet) is developed, which uses a pseudo-Siamese structure to automatically and effectively learn pseudo exemplar clues from inherent repetition patterns. In addition, a weakly-supervised scheme is presented to reduce the burden of laborious density maps required by all contemporary CAC models, allowing GCNet to be trained using count-level supervisory signals in an end-to-end manner. Without providing any spatial location hints, GCNet is capable of adaptively capturing them through a carefully-designed self-similarity learning strategy. Extensive experiments and ablation studies on the prevailing benchmark FSC147 for zero-shot CAC demonstrate the superiority of our GCNet. It performs on par with existing exemplar-dependent methods and shows stunning cross-dataset generality on crowd-specific datasets, e.g., ShanghaiTech Part A, Part B and UCF_QNRF.