Edge detection plays a fundamental role in computer vision tasks and gains wide applications. In particular, semantic edge detection recently draws more attention due to the high demand for a fine-grained understanding of visual scenes. However, detecting high-level semantic edges hidden in visual scenes is quite challenging. Existing semantic edge detection methods focus on category-aware semantic edges and require elaborate category annotations. Instead, we first propose the category-agnostic semantic edge detection task without additional semantic category annotations. To achieve this goal, we propose to utilize only edge position annotations and leverage the information randomness of semantic edges. Specifically, we align semantic edge positions to the ground truth by maximizing randomness on edge regions and minimizing randomness on non-edge regions in the training process. In the inference process, we first obtain neural representations by the trained network, and then generate semantic edges by measuring neural randomness. We evaluate our method by comparisons with alternative methods on two well-known datasets: Cityscapes (Cordts et al., 2016) and SBD (Hariharan et al., 2014). The results demonstrate our superiority over the alternatives, which is more significant under weak annotations. We also provide comprehensive mechanism studies to verify the generalizability, rationality, and validity of our working mechanism.