SAVeR$^2$: Reasoning-based Safety Alignment for Large Reasoning Models via Verifiable Rewards

Large Reasoning Models (LRMs) have achieved impressive performance via explicit Chain-of-Thought (CoT) reasoning, yet this process introduces critical safety risks. We formalize LRM safety objectives as requiring non-malicious reasoning and answers, safety consistency, and explicit intent identification. We argue that existing alignment methods suffer from poor adversarial generalization, a significant ``safety tax'' on reasoning, and unfaithful coarse-grained rewards, primarily due to their neglect of the LRM's intrinsic reasoning capabilities for safety. To address these, we propose \textbf{SAVeR$^2$}, a novel \textbf{S}afety \textbf{A}lignment method via \textbf{R}ewards with \textbf{R}easoning capability. SAVeR$^2$ decomposes the safety objective into four fine-grained verifiable reward signals and utilizes a difficulty-aware data selection strategy to stabilize training. Crucially, we introduce a reasoning-preserving gradient projection mechanism that analytically resolves conflicts between safety and reasoning gradients, effectively eliminating the safety tax. Extensive experiments on models ranging from 1.5B to 671B demonstrate that SAVeR$^2$ achieves superior safety performance and significantly lower over-refusal rates across multiple benchmarks without compromising general reasoning capabilities.