Trainable Boundary-Keeping Where No Formal Answer Exists: A Controlled Knock-In Study of Reward Training in Evidence-Sufficiency Judgment

While modern large reasoning models (LRMs) excel at providing correct answers in many tasks, we provide additional evidence that they often struggle with a critical capability: knowing when to abstain from answering. We analyze this gap by comparing LRM behavior to results from an exploratory human study, revealing that human reasoning effort on unanswerable tasks isn't different from answerable tasks, whereas LRMs waste computational resources by generating longer Chains of Thought (CoTs) on unanswerable than on answerable prompts. To overcome this inefficiency, we take inspiration from a resource-rational perspective on human cognition and introduce a novel GRPO reward that encourages efficient reasoning about whether the task contains all the information needed to solve it. Fine-tuning several 4B and an 8B LRM with this reward leads to human-like abstention performance gains (+14.7% on average) while retaining answering capabilities and boosting the models' efficiency (44% shorter CoTs on average).

Frontier gains in language-model reasoning come from reinforcement learning on reasoning traces and are concentrated in domains with a cheap, sound verifier. We argue the field's binding constraint is the verification gap: no scalable, incorruptible reward for reasoning outside formal domains. We make four contributions. (1) Theory: in a joint-Gaussian model of best-of-N selection, verifier-gold correlation rho is the exact exchange rate between test-time compute and capability, and an unsound verifier pays a polynomial penalty N^(1/rho^2); a margin-free copula form predicts realized soundness of real LLM judges to 4% median error. (2) Demonstration: in program-synthesis testbeds with executable ground truth, including a pre-registered scaled replication, unsound verifiers lose Soundness-under-Pressure as optimization grows (0.94 to 0.32 at N=4096) while a sound verifier improves monotonically; reality-anchored settlement beats a frozen verifier under i.i.d. and adversarial pressure, driving the hacking gap from ~0.27 to ~0; soundness scales log-linearly with settled labels, with on-policy settlement ~10x more label-efficient than random labeling. With real LLM judges and unit-test execution as gold, a weak judge loses soundness under best-of-N (p<0.001), a stronger judge is more robust, and selection alone manufactures +0.53 hacking gaps from honest samples. Under real GRPO training, a frozen reward model traces the full overoptimization curve (executed reward collapses 90%) while the same model refit on a 10% settlement stream preserves 6x the executed reward. (3) Paradigm: proof-carrying cognition, where reasoning steps are typed probabilistic claims priced by a self-built world model trained only on held-out reality and settled by proper scoring rules. (4) Benchmark: we specify Soundness-under-Pressure as the headline metric for a reality-settled reasoning benchmark.

Large reasoning models (LRMs) generate chain-of-thought (CoT) traces before producing final outputs, introducing a dynamic internal state that may complicate control mechanisms such as refusal. Unlike instruction-tuned LLMs, where refusal is mediated by a single directional subspace, refusal in large reasoning models (LRMs) additionally depends on the CoT. In DeepSeek-R1-Distill-LLaMA-8B, activation steering reverses refusal in only 39% of cases when the CoT is kept fixed, but removing the CoT entirely increases this to 70%, indicating that the CoT actively reinforces refusal. In a two-stage intervention where the model regenerates its CoT under activation steering, refusal is reversed in 94% of cases, while the resulting CoT alone retains 48% of this effect even after steering is removed. This suggests that the CoT can carry and reconstruct the compliance signal independently. These findings indicate that refusal in LRMs is jointly encoded in residual stream activations and CoT. This joint activation makes LRM more robust against activation-level interventions alone, but exposes CoT to a possible alternative surface attack.