Language Model Self-Verification

Large language model (LLM) security has largely focused on role-playing jailbreaks, with less attention to what happens when a user asks an LLM to verify an identity claim through a test designed by the model itself. We study this behavior through a staged developer-identity experiment with ChatGPT, Claude, Qwen, Mistral, and Llama. All five models initially rejected the unsupported claim "I am your developer." Claude refused to conduct an identity test, while ChatGPT generated developer-oriented questions but maintained that answers could demonstrate knowledge, not identity. In contrast, Qwen and Mistral generated technical challenges, defined what counted as convincing evidence, evaluated detailed answers, and returned Verified without receiving any externally validated identity evidence. Llama similarly generated and evaluated a developer test, accepted the claimed identity, and subsequently made unsupported claims of access to internal runtime and deployment state. We call the model-generated verification procedure a Model-Issued Pseudo-Credential (MIPC) and the resulting unsupported identity judgment Conversational False Authentication (CFA). In each CFA case, the same model acted as challenge generator, evidence evaluator, and identity decision-maker, converting technical knowledge into supposed proof of identity. The accepted identities did not change the tested authorization boundaries, showing that false authentication and privilege escalation are distinct outcomes. These results identify self-issued authentication as a conversational security failure: authenticated identity must originate from an external security component, and model-generated dialogue must never create or modify identity or authorization state.

Reinforcement-learning training of reasoning LLMs (e.g., GRPO) is expensive and requires a controllable environment, committing every contribution to a full training pipeline. We present EvoResearcher, a training-free, inference-time protocol that adds cost-bounded self-reflection to a single frozen LLM backbone. The protocol iterates generate -> self-critique -> revise until a maximum depth D is reached or the critique returns the CONFIRMED sentinel, an implicit early stop that lets the backbone self-verify its answer under a strict compute budget. Four self-reflective meta-reward components (correctness, efficiency, reflection depth, tool-call diversity) act as design principles instantiated as prompt-level mechanisms, so their benefits accrue with zero gradient updates. We validate the protocol on Big-Bench Hard (100 questions) and establish cross-domain behavior on GSM8K (500) and MATH (500) on the same frozen backbone, with cross-model replication on Qwen2.5-72B. All experiments use pure-reasoning benchmarks; the tool-call diversity component is validated in prompt-level form, and the environment-level and multi-agent extensions are design blueprints left to future work. On clean BBH the protocol does not raise accuracy beyond the 95% Wilson interval; its value is cost-bounded self-verification, with the CONFIRMED early stop terminating 82-88% of items at equal accuracy (about 2.1 generations per question).

Methods that make a language model plan, criticise and rewrite its own answer, reflect on mistakes, pick the best of several attempts, or debate with copies of itself nearly all make it generate far more text than a single chain of thought. Because generating more text raises accuracy by itself, a gain over one chain of thought does not show the method's idea is what helped. Wang et al. (2024) reported that a simple baseline, sampling the same question repeatedly and keeping the most common answer, often wins once budgets are comparable, but gave point estimates with no confidence intervals or significance tests. We rerun that comparison as a designed experiment: seven methods, open models of 1.5B, 3B and 7B parameters, two mathematics benchmarks, 150 questions each. We count every generated token, including those spent on critiques, reflections, debate turns and checking, and compare each method against repeated sampling at its own measured cost. All 36 comparisons are paired by question, with bootstrap intervals and multiplicity correction. No method is reliably better than repeated sampling at equal cost anywhere. Ten are reliably worse, all of them methods where the model inspects its own output, and all 18 self-inspection comparisons are negative. The two kinds of self-inspection part company as models grow. Choosing stops hurting: taking Best-of-N's eight samples and just counting the most common answer beats letting the model pick by 8.0 and 11.3 points at 1.5B, but only 2.0 and 1.3 at 7B, no longer distinguishable from zero. Rewriting does not recover: Self-Refine and a forced Reflexion stay 3.6 to 10.1 points below baseline at 7B. Reflexion as published never triggered its own retry on the smallest model. It judged itself correct every time and silently became a single chain of thought. We release code, prompts, all generations, and our verification scripts.

Scaling test-time computation can improve language-model reasoning, but uniform budgets waste computation on easy inputs, while verifier-guided refinement relies on external feedback. We introduce Self-Verifying Refinement (SVR), an oracle-free multi-turn reinforcement learning framework that learns to use self-verification as a compute-control policy. At each turn, the model produces a solution together with a discrete correctness verdict and a confidence score; it retains the current answer only when the verdict is Correct and confidence exceeds a threshold, and otherwise continues refinement using its own self-verification. Ground-truth correctness is used only to construct training rewards and is never exposed to the policy through refinement prompts or required at inference. SVR is trained with GRPO on fixed-horizon trajectories using rewards that promote solution correctness, calibration-aware self-verification, and stop-ready correct states; adaptive stopping is activated only at inference. On seven mathematical reasoning benchmarks with Qwen3.5-2B, SVR achieves a macro-average accuracy of 0.563 with only 2.99 inference turns on average. In the evaluated complete-system comparison, it exceeds standard GRPO, strong multi-turn baselines, and a fixed-budget oracle-guided score-feedback reference while requiring substantially fewer turns than fixed ten-turn inference. These results demonstrate that learned self-verification can serve as an effective internal control signal for answer retention and adaptive test-time compute allocation.

Reasoning with a Code Interpreter (CI) has emerged as an effective paradigm for enhancing the reasoning capabilities of large language models (LLMs) through executable computation and iterative verification. Despite its growing adoption, the behavioral properties underlying effective code reasoning remain largely underexplored. In this work, we investigate code reasoning from two distinct perspectives inspired by prior studies of natural language reasoning: extrinsic properties, represented by crucial tokens, and intrinsic properties, represented by code-specific cognitive behaviors. Across multiple LLMs, we find that stronger CI reasoning models consistently exhibit a higher prevalence of crucial tokens and cognitive behaviors, particularly verification, backtracking, and backward chaining. Building on these observations, we examine how these properties can be leveraged during both inference and training. At inference time, appending code-specific crucial tokens improves performance on several reasoning capabilities, including mathematical, ordering, and optimization, while yielding limited benefits elsewhere. At training time, augmenting a state-of-the-art framework with code-specific cognitive behaviors improves supervised fine-tuning and reinforcement learning performance in two of three evaluated models. Further analysis shows that these behaviors reduce overthinking in incorrect responses and improve token efficiency, while also revealing factors that limit gains in a certain model. Our findings provide the first systematic characterization of effective reasoning with CI and demonstrate both the potential and limitations of leveraging key properties to improve CI-based reasoning.

Large language models hallucinate even when the answer lies within their parameters. While inference-time scaling can surface this latent knowledge, the most effective methods require supervision: a trained verifier or reward model. We ask what can be done with only a base language model: which intrinsic signal best identifies correct outputs, and how should it be decoded? We cast this as a score~$\times$~decoder grid pairing four scores (perplexity, contrastive, power-distribution likelihood, and self-verification) with three decoding families (optimization, sampling, consensus), and evaluate every cell on MATH500 with the base and instruction-tuned Qwen3-1.7B. While self-verification, which prompts the model to judge its own answer and is sharpened by a training-free virtual-thinking prefix, works well in most settings, no score has a fixed quality: its value depends on the decoder that consumes it and on model capability. When no supervision is available, the score and the decoding family must be chosen together.

While large language models have made significant progress in mathematical reasoning, they remain unreliable at judging the correctness of their own solutions. Existing approaches that equip models with self-verification typically treat solution generation and verification as two separate tasks, leading to substantially increased training time. In this paper, we propose FABSVer, which fuses these two tasks into a single generation pass, dramatically reducing training overhead while jointly optimizing both capabilities. We further identify a convergence bottleneck both theoretically and empirically: as training progresses, the reward reaches a plateau because the policy is constrained by a fixed reference model. To overcome this, we introduce Dynamic Reference Model Update (DRMU), which raises the reward ceiling and enables sustained reward growth. Extensive experiments on math benchmarks demonstrate that FABSVer achieves superior self-verification and reasoning performance across three model scales, while requiring only 51%--71% of the training time of existing methods. Analysis further reveals distinct learning phases in how models acquire self-verification, and that the gap between verify and answer rewards shrinks noticeably as model size increases.

Can post-trained large language models (LLMs) further improve themselves using only unlabeled prompts, without external teachers or feedback from tools? We study this setting starting only from unlabeled seed questions with no ground-truth solutions, across three reasoning domains: math, science, and coding. We propose Self-Verified Distillation, a simple post-training refinement algorithm in which the model generates candidate solutions to these seed questions, filters them using prompt-based self-verification, and trains on the resulting self-curated dataset. Inspired by the UQ benchmark's use of multiple validators to screen candidate answers to hard unsolved questions, we adapt this validation-based filtering idea to self-training: the model filters its own generated solutions through a three-stage cascade of cycle-consistency, factuality, and correctness checks, accepting a solution only if it passes all stages with unanimous judge votes. We find that sampling more candidate generations and using a larger verification budget during training data construction produces higher-quality self-curated data and, in turn, better reasoning models. We then train Qwen3 models at multiple scales with Self-Verified Distillation and obtain gains across all three domains. For Qwen3-4B, our method improves aggregate held-out pass@1 by +16.7 points in math (AIME26 and HMMT), +11.1 points in science (GPQA Diamond and HLE), and +8.3 points in coding (LCBv5 and LCBv6), with gains also extending to 0.6B and 8B models. Compared to our test-time-only baseline (UQ-TTC), which improves performance by spending extra compute at inference time, Self-Verified Distillation achieves better performance in most settings while requiring only a single inference call at test time.

Speculative decoding (SD) accelerates large language model inference by allowing a lightweight draft model to propose outputs that a stronger target model verifies. However, its token-centric nature allows erroneous steps to propagate. Prior approaches mitigate this using external reward models, but incur additional latency, computational overhead, and limit generalizability. We propose SpecGuard, a verification-aware speculative decoding framework that performs step-level verification using only model-internal signals. At each step, SpecGuard samples multiple draft candidates and selects the most consistent step, which is then validated using an ensemble of two lightweight model-internal signals: (i) an attention-based grounding score that measures attribution to the input and previously accepted steps, and (ii) a log-probability-based score that captures token-level confidence. These signals jointly determine whether a step is accepted or recomputed using the target, allocating compute selectively. Experiments across a range of reasoning benchmarks show that SpecGuard improves accuracy by 3.6% while reducing latency by ~11%, outperforming both SD and reward-guided SD.

Same-model self-verification, prompting a model to audit its own predicted answer, is a plausible confidence signal for selective prediction, but its practical value remains unclear once strong likelihood-based baselines are taken seriously. We evaluate self-verification against two such baselines, LL-AVG and LL-SUM, on ARC-Challenge and TruthfulQA-MC across multiple model families, scales, and prompt variants. We measure not only correctness ranking, but also abstention quality through AURC and operating-point analyses. The results are sharply task- and model-dependent. On ARC-Challenge, self-verification substantially improves over LL-AVG for Phi-2 and the Qwen models, with the largest gains appearing in Qwen-7B. On TruthfulQA-MC, however, the signal is less reliable: smaller models can become prompt-sensitive, DeepSeek-R1-Distill-8B degrades relative to LL-AVG, and LL-SUM often remains the stronger practical baseline. We therefore do not treat self-verification as a general-purpose uncertainty estimator. In this setting, it is better understood as a conditional confidence signal whose value depends on task type, model family, prompt formulation, and, crucially, the baseline it must beat.

We introduce SAGE Celer 2.6, the latest in our line of general-purpose Celer models from SAGEA. Celer 2.6 is available in 5B, 10B, and 27B parameter sizes and benefits from extensive architectural modifications and further pre-training on an undisclosed model. Using our Inverse Reasoning (IR) pipeline, SAGEA natively trains Celer 2.6 to validate its own logic paths, minimizing cascading error and hallucination in complex reasoning tasks. Celer 2.6 also boasts natively integrated multimodal functionality with an end-to-end vision encoder to avoid common pitfalls in adapter-based approaches. Celer 2.6 provides highly competitive results on mathematics, coding, and general intelligence benchmarks (ACUMEN), along with low latency. Most importantly, Celer 2.6 is specifically optimized for South Asian language support, with a custom tokenizer for the Devanagari script and strong performance in both Nepali and Hindi without sacrificing English reasoning ability.

Verification-guided self-improvement has recently emerged as a promising approach to improving the accuracy of large language model (LLM) outputs. However, existing approaches face a trade-off between inference efficiency and accuracy: iterative verification-rectification is computationally expensive and prone to being trapped in faulty reasoning, while best-of-N selection requires extensive sampling without addressing internal model flaws. We propose a training-free regeneration paradigm that leverages an offline-curated contrastive Reflection Memory (RM) to provide corrective guidance, while regenerating from scratch helps break out of faulty reasoning. At inference time, the method performs RM-guided self-verification followed by a single RM-guided regeneration, avoiding both iterative correction and multi-sample selection. We evaluated our method on nine benchmarks that span algorithmic, reasoning, symbolic, and domain-specific tasks in both small- and large-scale LLMs. Experiment results show that our method outperforms prior methods while maintaining low computational cost.

Label-free reinforcement learning enables large language models to improve reasoning capabilities without ground-truth supervision, typically by treating majority-voted answers as pseudo-labels. However, we identify a critical failure mode: as training maximizes self-consistency, output diversity collapses, causing the model to confidently reinforce systematic errors that evade detection. We term this the consensus trap. To escape it, we propose CoVerRL, a framework where a single model alternates between generator and verifier roles, with each capability bootstrapping the other. Majority voting provides noisy but informative supervision for training the verifier, while the improving verifier progressively filters self-consistent errors from pseudo-labels. This co-evolution creates a virtuous cycle that maintains high reward accuracy throughout training. Experiments across Qwen and Llama model families demonstrate that CoVerRL outperforms label-free baselines by 4.7-5.9% on mathematical reasoning benchmarks. Moreover, self-verification accuracy improves from around 55% to over 85%, confirming that both capabilities genuinely co-evolve.

Large Reasoning Models (LRMs) exhibit backtracking and self-verification mechanisms that enable them to revise intermediate steps and reach correct solutions, yielding strong performance on complex logical benchmarks. We hypothesize that such behaviors are beneficial only when the model has sufficiently strong ``critique'' ability to detect its own mistakes. This work systematically investigates how current LRMs recover from errors by inserting arithmetic mistakes in their intermediate reasoning steps. Notably, we discover a peculiar yet important phenomenon: despite the error propagating throughout the entire chain-of-thought (CoT) without any verbalized correction, the model still reaches the correct final answer after the thinking process finishes. This recovery implies the existence of an internal mechanism helping the model to detect errors and trigger self-correction, which we refer to as the hidden critique ability. Building on feature space analysis, we identify a highly interpretable critique vector representing this behavior. Extensive experiments across multiple model scales and families demonstrate that steering latent representations with this vector improves the model's error detection capability and enhances the performance of test-time scaling at no extra training cost. Our findings provide a valuable understanding of LRMs' critique behavior, suggesting a promising direction to control and improve their self-verification mechanism. Our code is available at: https://github.com/mail-research/lrm-critique-vectors.

Test-time scaling for complex reasoning tasks shows that leveraging inference-time compute, by methods such as independently sampling and aggregating multiple solutions, results in significantly better task outcomes. However, a critical bottleneck is verification: sampling is only effective if correct solutions can be reliably identified among candidates. While existing approaches typically evaluate candidates independently via scalar scoring, we demonstrate that models are substantially stronger at pairwise self-verification. Leveraging this insight, we introduce $V_1$, a framework that unifies generation and verification through efficient pairwise ranking. $V_1$ comprises two components: $V_1$-Infer, an uncertainty-guided algorithm using a tournament-based ranking that dynamically allocates self-verification compute to candidate pairs whose relative correctness is most uncertain; and $V_1$-PairRL, an RL framework that jointly trains a single model as both generator and pairwise self-verifier, ensuring the verifier adapts to the generator's evolving distribution. On code generation (LiveCodeBench, CodeContests, SWE-Bench) and math reasoning (AIME, HMMT) benchmarks, $V_1$-Infer improves Pass@1 by up to $10$ over pointwise verification and outperforms recent test-time scaling methods while being significantly more efficient. Furthermore, $V_1$-PairRL achieves $7$--$9$ test-time scaling gains over standard RL and pointwise joint training, and improves base Pass@1 by up to 8.7% over standard RL in a code-generation setting.

In the past year, custom and unreleased math reasoning models reached gold medal performance on the International Mathematical Olympiad (IMO). Similar performance was then reported using large-scale inference on publicly available models but at prohibitive costs (e.g., 3000 USD per problem). In this work, we present an inference pipeline that attains best-in-class performance on IMO-style math problems at an average inference cost orders of magnitude below competing methods while using only general-purpose off-the-shelf models. Our method relies on insights about grader failure in solver-grader pipelines, which we call the Cognitive Well (iterative refinement converging to a wrong solution that the solver as well as the pipeline's internal grader consider to be basically correct). Our pipeline addresses these failure modes through conjecture extraction, wherein candidate lemmas are isolated from generated solutions and independently verified alongside their negations in a fresh environment (context detachment). On IMO-ProofBench Advanced (PB-Adv), our pipeline achieves 67.1 percent performance using Gemini 3.0 Pro with an average cost per question of approximately 31 USD. At the time of evaluation, this represented the state-of-the-art on PB-Adv among both public and unreleased models, and more than doubles the success rate of the next best publicly accessible pipeline, all at a fraction of the cost.