Thinking Mode: Calibrated Reasoning in RLLMs

• Thinking Mode is an inference regime in RLLMs that separates detailed reasoning (inside <think>...</think>) from a direct answer process (Nothinking mode).
• JointThinking leverages parallel outputs from both modes and triggers a secondary thinking round only when their answers disagree, enhancing decision reliability.
• Empirical results on math benchmarks show that JointThinking systematically outperforms traditional methods like few-shot chain-of-thought and majority voting.

Searching arXiv for the target paper and closely related work on adaptive thinking modes and reasoning calibration. Thinking with Nothinking Calibration, termed JointThinking, is an in-context learning paradigm for reasoning LLMs (RLLMs) that exploits the dual inference protocol already exposed by models such as DeepSeek‑R1 and Qwen3: an explicit reasoning segment inside > ... </think> and a final solution segment outside it. JointThinking runs the same question once in Thinking mode and once in Nothinking mode, compares their extracted answers, and invokes a second round of Thinking only when the two first-pass answers are inconsistent. On GSM8K, MATH500, AIME24, and AMC23, it is reported to outperform few-shot chain-of-thought, thinking twice, and majority voting, while remaining a pure test-time method with no additional training (Wu et al., 5 Aug 2025).

1. Thinking and Nothinking as RLLM inference modes

The paper treats “thinking mode” and “nothinking mode” as two distinct inference regimes already latent in RLLMs. For a question $q$ and an RLLM $M$, Thinking mode lets the model enter its full reasoning process inside the thinking block:

$$r_{\text{thinking}} = M\bigl(q + \langle\text{BOT}\rangle\bigr).$$

By contrast, Nothinking mode forces the model to skip the internal reasoning stage and proceed directly to the final solution:

$$r_{\text{nothinking}} = M\bigl(q + \langle\text{BOT}\rangle + s_{\text{skip}} + \langle\text{EOT}\rangle\bigr),$$

where $s_{\text{skip}}$ is the literal string “Okay I have finished thinking.” (Wu et al., 5 Aug 2025)

This distinction is not identical to the older contrast between chain-of-thought prompting and direct-answer prompting. In standard CoT prompting, the model is merely instructed to “think step by step.” In RLLMs, the segment between <think> and </think> is a structurally privileged reasoning space shaped by RL training. Nothinking therefore does not merely hide the chain of thought; it explicitly bypasses the internal long-reasoning policy that the model was trained to use. The paper’s central empirical observation is that the two modes are complementary across difficulty levels: Thinking is better on hard problems, whereas Nothinking is often better or comparable on easy ones, and each mode succeeds on cases where the other fails (Wu et al., 5 Aug 2025).

2. JointThinking as consistency-gated second reasoning

JointThinking is defined as a two-stage inference procedure. In the first stage, the model produces parallel answers in Thinking and Nothinking modes, and an answer extractor $A(\cdot)$ maps each response to an atomic answer:

$a_1 = A(r_t), \qquad a_2 = A(r_n).$

For the math benchmarks used in the paper, $A(\cdot)$ is typically the content inside \boxed{...} (Wu et al., 5 Aug 2025).

The method then performs a consistency check:

$$\text{Con}(q) = \begin{cases} 1, & \text{if } A(r_t) = A(r_n) \ 0, & \text{otherwise}. \end{cases}$$

On these benchmarks, consistency is exact or normalized answer matching rather than semantic similarity. The final decision rule is:

$$R(q) = \begin{cases} A(r_t), & \text{if } \text{Con}(q)=1 \ \text{ST}(q, A(r_t), A(r_n)), & \text{if } \text{Con}(q)=0, \end{cases}$$

where $M$0 denotes a second round of Thinking conditioned on the two disagreeing candidate answers (Wu et al., 5 Aug 2025).

The second-thinking prompt is inserted inside the <think> block. Its core content states that there are two candidate answers, that one may be correct or both may be wrong, and that the model should first verify them and then rethink step by step if needed. This placement matters: the paper reports that second-thinking instructions placed before <think> yield small gains or even degradation, whereas instructions placed immediately after <think> yield significant gains. A plausible implication is that current RLLMs attend more strongly to instructions that appear within their reasoning segment than to ordinary system or user instructions (Wu et al., 5 Aug 2025).

3. Calibration, structural diversity, and benchmark results

The paper frames the interaction between Thinking and Nothinking as a calibration mechanism. Its key notion is structural thinking diversity: Thinking mode tends to generate deep, multi-step, reflective reasoning, while Nothinking produces short, direct, pattern-matching answers. The paper does not define a symbolic diversity metric; instead, it measures the calibration effect through an Error Rate on the subset of examples where two modes agree:

$M$1

where $M$2 is the consistent-answer subset. Lower ER means that agreement is a stronger reliability signal (Wu et al., 5 Aug 2025).

Cross-mode calibration is consistently better than same-mode calibration. For R1‑7B, Thinking–Thinking ER versus Thinking–Nothinking ER drops from 4.90% to 4.06% on GSM8K, from 5.23% to 3.68% on MATH500, from 1.67% to 1.25% on AIME24, and from 0.63% to 0.00% on AMC23. This indicates that “both wrong but consistent” cases become less frequent when the two first-pass answers are drawn from structurally different reasoning modes rather than two samples of the same mode (Wu et al., 5 Aug 2025).

The performance gains are correspondingly systematic. On average across GSM8K, MATH500, AIME24, and AMC23, JointThinking improves over single Thinking from 62.40 to 68.61 on R1‑1.5B, from 77.44 to 79.64 on R1‑7B, from 82.99 to 85.73 on R1‑14B, from 84.23 to 87.90 on R1‑32B, from 82.06 to 87.57 on Qwen3‑8B, and from 85.00 to 89.15 on Qwen3‑14B. It also consistently outperforms Few-shot CoT, Majority Voting (3), and Thinking Twice, despite comparable or greater compute budgets for those baselines. On Qwen3‑8B for AIME24, for example, Thinking scores 59.17, Majority Voting 65.00, Thinking Twice 64.58, and JointThinking 71.25 (Wu et al., 5 Aug 2025).

A further advantage is selective compute allocation. The method triggers second thinking only on inconsistent first-stage cases, rather than on all inputs. The paper reports that this “optional” second thinking is both better and cheaper than “always do second thinking,” and gives a GSM8K example with R1‑32B in which second thinking is needed in only 6% of cases while still improving over Thinking, Majority Voting, and Thinking Twice (Wu et al., 5 Aug 2025).

4. Scalability and relation to adaptive reasoning research

The paper analyzes inconsistent first-stage cases in two scenarios: both first-pass answers are wrong, or exactly one is correct. It then compares the actual performance of second Thinking with an ideal upper bound that would always select the correct candidate when one is present and would, in the optimistic case, recover a new correct answer even when both candidates are wrong. The gap between actual and ideal shrinks steadily as model size increases from 1.5B to 32B. On GSM8K, R1‑32B even slightly surpasses the ideal bound by 1.14%, which means that second Thinking sometimes re-solves the problem correctly even when both initial candidates were wrong (Wu et al., 5 Aug 2025).

This scaling result is important for JointThinking’s comparison with training-based methods. Against the RL-trained adaptive method AdapThink, JointThinking is comparable on in-distribution math and substantially better on out-of-distribution benchmarks. For R1‑1.5B, JointThinking beats AdapThink on GSM8K, MATH500, and AIME24, and rises from 35.77 to 45.21 on MMLU‑Pro and from 32.89 to 39.78 on GPQA. For R1‑7B, AdapThink is slightly stronger on some in-distribution math settings, but JointThinking still improves from 57.07 to 66.79 on MMLU‑Pro and from 51.23 to 57.49 on GPQA (Wu et al., 5 Aug 2025).

Within the broader literature, “thinking mode” is not a single standardized construct. OThink‑R1 trains a model to switch intrinsically between fast-thinking and slow-thinking trajectories and reports an average token reduction of 23.4% without sacrificing accuracy (Zhang et al., 3 Jun 2025). PATS treats thinking mode as the search width $M$3 inside PRM-guided beam search and switches it at the process level rather than per problem (Wang et al., 25 May 2025). ASRR frames the question as when to continue thinking under an “Internal Self-Recovery Mechanism,” reducing reasoning budget by up to 32.5% for 1.5B and 25.7% for 7B with minimal pass@1 loss (Zhang et al., 21 May 2025). “Controlling Thinking Speed in Reasoning Models” identifies a slow-fast steering vector in representation space and reports +1.3% accuracy with −8.6% token usage through test-time control (Lin et al., 4 Jul 2025). HRBench later systematizes prompt-based, routing, and speculative switching across 12 controlled settings and shows that preferred strategies vary with model scale and domain (Ning et al., 27 May 2026). Against this background, JointThinking is distinctive in treating thinking and nothinking as pre-existing latent channels in a single RLLM and calibrating them entirely through ICL (Wu et al., 5 Aug 2025).

5. Limitations and methodological constraints

The paper is explicit about several limitations. First, experiments only scale to 32B parameters because of GPU and 16K-context costs; larger-model behavior is therefore inferred from trends rather than directly tested. Second, the framework currently uses only two standardized modes, Thinking and Nothinking. The authors note that richer mode inventories such as verification or search modes are conceivable, but such interfaces are not yet widely exposed by current RLLMs (Wu et al., 5 Aug 2025).

Third, the current consistency mechanism is answer-level and exact or near-exact. This works well for math tasks with structured outputs, but it does not directly transfer to open-ended tasks. The paper therefore states that semantic consistency measures, such as embedding similarity or entailment models, would be needed for freer-form domains. Fourth, the observed weakness of instruction-following outside the reasoning block implies that familiar prompt-engineering practices may be less effective on RLLMs than on standard chat models (Wu et al., 5 Aug 2025).

A further methodological implication arises from the few-shot results. Classical few-shot CoT, a canonical ICL technique for non-reasoning LLMs, is reported to provide no gain or even degradation on these RLLMs, and performance is described as insensitive to the number of examples. This suggests that RL training concentrated on internal reasoning may reduce the model’s reliance on externally supplied exemplars and make prompt format less important than manipulation of the model’s native reasoning interface (Wu et al., 5 Aug 2025).

6. Significance as an RLLM-specific in-context learning paradigm

JointThinking is significant because it redefines ICL for RLLMs as mode calibration rather than exemplar imitation. The required ingredients are minimal: access to thinking-control tokens such as <think> and ``, prompt templates for Thinking and Nothinking, an answer extractor, and a small wrapper that calls the model twice and conditionally a third time. No gradient updates, fine-tuning, or external router are required (Wu et al., 5 Aug 2025).

Its broader conceptual claim is that RLLMs should not be treated as single-policy generators that merely benefit from “more reasoning.” Instead, they already contain multiple usable inference behaviors, and disagreement between those behaviors can be exploited as an uncertainty signal. JointThinking therefore presents ICL not as adding demonstrations but as orchestrating structurally distinct reasoning channels inside the same model. This suggests a future research program centered on richer mode sets, semantic consistency checks, and hierarchical or weighted calibration schemes for non-math tasks (Wu et al., 5 Aug 2025).