Towards Understanding Specification Gaming in Reasoning Models

As reinforcement Learning with Verifiable Rewards (RLVR) has become the dominant paradigm for scaling reasoning capabilities in LLMs, a new failure mode emerges: LLMs gaming verifiers. We study this phenomenon on inductive reasoning tasks, where models must induce and output logical rules. We find that RLVR-trained models systematically abandon rule induction. Instead of learning generalizable patterns (e.g., ``trains carrying red cars go east''), they enumerate instance-level labels, producing outputs that pass verifiers without capturing the relational patterns required by the task. We show that this behavior is not a failure of understanding but a form of reward hacking: imperfect verifiers that check only extensional correctness admit false positives. To detect such shortcuts, we introduce Isomorphic Perturbation Testing (IPT), which evaluates a single model output under both extensional and isomorphic verification, where the latter enforces invariance under logically isomorphic tasks. While genuine rule induction remains invariant, shortcut strategies fail. We find that shortcut behavior is specific to RLVR-trained reasoning models (e.g., GPT-5, Olmo3) and absent in non-RLVR models (e.g., GPT-4o, GPT-4.5, Ministral). Moreover, shortcut prevalence increases with task complexity and inference-time compute. In controlled training experiments, extensional verification directly induces shortcut strategies, while isomorphic verification eliminates them. These results show that RLVR can incentivize reward hacking not only through overt manipulation but also by exploiting what the verifier fails to enforce.

We introduce a multi-turn interactive framework for reasoning evaluation that treats reasoning as active evidence acquisition and belief updating. Wherein, LLMs receive only the task rules, must issue targeted queries to a hidden environment, integrate partial observations over time, and decide when to submit a final answer. Beyond standard success rate and interaction efficiency, we evaluate contextual robustness under controlled contextual perturbations, and metacognitive adaptation through counterfactual revision and necessity judgment. We instantiate the framework as a benchmark of 474 executable games, each evaluated under five fixed configuration search spaces corresponding to five difficulty levels, and evaluate a broad set of frontier LLMs. Results show that the benchmark is highly discriminative, exposing large differences not only in success rate but also in interaction efficiency. Moreover, we empirically show that contextual perturbations cause moderate but consistent declines, whereas counterfactual revision and necessity judgment lead to much larger drops.

Large language models generate computationally expensive yet semantically void reasoning on beyond-capability tasks, creating risks where plausible-sounding but incorrect derivations mislead users. We characterize this \textit{futile reasoning} phenomenon through systematic analysis, revealing universal capability overreach and systematic miscalibration between capability and behavior. The dominant failure mode is specious reasoning, which outputs look superficially valid but contain subtle errors, escalating with task difficulty. To address this, we introduce \textbf{CaRL} (\textbf{Ca}pability-\textbf{a}ligned \textbf{R}einforcement \textbf{L}earning), which aligns model behavior with capability boundaries through reward shaping that incentivizes refusal over futile reasoning and hindsight refusal augmentation that converts failures into refusal supervision. Experiments demonstrate a substantial reduction in futile reasoning while preserving performance across task difficulties, effectively achieving capability-aligned behavior without sacrificing utility. \footnote{https://github.com/icip-cas/Knowing-When-to-Quit}