Ring artifacts are prevalent in 3D cone-beam computed tomography (CBCT) due to non-ideal responses of X-ray detectors, substantially affecting image quality and diagnostic reliability. Existing state-of-the-art (SOTA) ring artifact reduction (RAR) methods rely on supervised learning with large-scale paired CT datasets. While effective in-domain, supervised methods tend to struggle to fully capture the physical characteristics of ring artifacts, leading to pronounced performance drops in complex real-world acquisitions. Moreover, their scalability to 3D CBCT is limited by high memory demands. In this work, we propose Riner, a new unsupervised RAR method. Based on a theoretical analysis of ring artifact formation, we reformulate RAR as a multi-parameter inverse problem, where the non-ideal responses of X-ray detectors are parameterized as solvable physical variables. Using a new differentiable forward model, Riner can jointly learn the implicit neural representation of artifact-free images and estimate the physical parameters directly from CT measurements, without external training data. Additionally, Riner is memory-friendly due to its ray-based optimization, enhancing its usability in large-scale 3D CBCT. Experiments on both simulated and real-world datasets show Riner outperforms existing SOTA supervised methods. The code will be publicly released for improving reproducibility.