Title: Towards Robust Model Watermark via Reducing Parametric Vulnerability. Abstract: Deep neural networks are valuable assets considering their commercial benefits and huge demands for costly annotation and computation resources. To protect the copyright of these deep models, backdoor-based ownership verification becomes popular recently, in which the model owner can watermark the model by embedding a specific behavior before releasing it. The defender (usually the model owner) can identify whether a suspicious third-party model is ``stolen'' from it based on the presence of the behavior. Unfortunately, these watermarks are proven to be vulnerable to removal attacks even like fine-tuning. To further explore this vulnerability, we investigate the parametric space and find there exist many watermark-removed models in the vicinity of the watermarked one, which may be easily used by removal attacks. Inspired by this finding, we propose a minimax formulation to find these watermark-removed models and recover their watermark behavior. Extensive experiments demonstrate that our method improves the robustness of the model watermarking against parametric changes and numerous watermark-removal attacks.