VeriFree: Verifier-Free RL for LLM Reasoning

• VeriFree is a verifier-free reinforcement learning methodology designed to improve large language model reasoning capabilities in domains where external answer verification is unfeasible or impractical.
• Unlike verifier-based methods, VeriFree utilizes the LLM’s own conditional probability of the reference answer as a smooth, dense reward signal, eliminating the need for separate verifier models.
• This approach enables scalable and efficient RL training applicable to diverse reasoning tasks and real-world domains, demonstrating performance competitive with or superior to verifier-dependent systems.

VeriFree is a verifier-free reinforcement learning (RL) methodology for improving the general reasoning capabilities of LLMs in domains where external answer verification—either rule-based or model-based—is unfeasible or impractical. Introduced as an alternative to RL systems dependent on explicit verifiable signals, VeriFree utilizes the LLM’s own conditional likelihood of the reference answer as its reward function. This approach enables scalable, efficient RL-based training for reasoning tasks across diverse domains, including those traditionally inaccessible to rule-based or model-verifier approaches.

1. Methodological Foundations

VeriFree departs from previous DeepSeek-R1-Zero-style RL pipelines, which require the generation of candidate answers followed by answer validation via explicit verifiers or an external LLM-based judge. Instead, VeriFree defines the training objective as the maximization of the expected conditional probability that the policy assigns to the reference answer, conditioned on both the input and the generated reasoning trace.

Let $q$ denote the input question, $r$ the generated reasoning trace, $a^*$ the reference answer, and $\pi_\theta(\cdot)$ the LLM's policy parameterized by $\theta$. The core objective is:

$$J_\text{VeriFree}(\theta; q, a^*) = \mathbb{E}_{r \sim \pi_\theta(\cdot|q)}\big[ \pi_\theta(a^*|q, r) \big]$$

The gradient estimator used for learning is:

$$\nabla_\theta J_\text{VeriFree} = \mathbb{E}_{r \sim \pi_\theta(\cdot|q)} \left[ \pi_\theta(a^*|q, r) \left( \nabla_\theta \log \pi_\theta(r|q) + \nabla_\theta \log \pi_\theta(a^*|q, r) \right) \right]$$

This estimator leverages the model’s probability on the reference answer as a smooth, dense reward signal. The reward is thus continuous and informative, addressing the sparsity of typical RL signals in natural language reasoning contexts.

Practically, for each input prompt, multiple reasoning traces are sampled. For each, the model's answer is replaced with the dataset’s reference answer, and the conditional probability $\pi_\theta(a^*|q, r)$ is evaluated in a single forward pass. This process is computationally efficient compared to approaches requiring an external verifier, enabling scalable RL training runs.

2. Comparison to Verifier-Based and RLVR Approaches

Verifier-based RL approaches—also termed RLVR (Reinforcement Learning with Verifiable Rewards)—require explicit answer verification mechanisms, such as symbolic testers for mathematics/code or model-based verifiers for more general domains. These approaches are limited by:

• The need for rule-based or model-based verifiers, which may not exist for open-ended or real-world tasks.
• Increased computational/storage overhead from maintaining and querying separate verifier modules during training.
• Susceptibility to "reward hacking," where the policy exploits weaknesses in the verifier.

VeriFree obviates these dependencies, relying solely on the LLM’s intrinsic probability as the reward, thus reducing both the resource burden and risk of artificially optimizing for quirks in the verification signal.

Empirical results demonstrate that VeriFree matches or surpasses performance of RL systems trained with explicit verifiers on a range of benchmarks, including MMLU-Pro, SuperGPQA, GPQA, and mathematical tasks (AIME24, AMC, etc.). For example, on Qwen3-8B-Base, VeriFree attains 67.2% accuracy on MMLU-Pro and 38.0% on SuperGPQA, outperforming verifier-based RL.

3. Variance Reduction and Learning Stability

A notable advantage of VeriFree is its low-variance gradient estimator. Traditional RL approaches in this context exhibit high estimator variance due to binary or sparse rewards. By marginalizing out answer sampling (Rao-Blackwellization), VeriFree’s reward-weighted estimator stabilizes learning:

$$\mathrm{Var}\big[\hat{G}_\text{VeriFree}\big] \leq \mathrm{Var}\big[\hat{G}_\text{Verifier}\big]$$

VeriFree utilizes additional standard RL variance reduction techniques, such as RLOO (Reward Leave-One-Out baselines) and length normalization, to further ensure stable policy updates within the RL training regime.

4. Theoretical Perspectives

VeriFree integrates two conceptual perspectives:

• Implicit Verifier Fusion: The method unifies the traditionally separate “reasoner” (policy generating rationales) and “verifier” (module or rule ascertaining correctness) into the policy network. The LLM both produces and implicitly validates its own reasoning via the reference answer’s likelihood.
• Variational Optimization: VeriFree’s expectation over reasoning traces with respect to the conditional likelihood of the reference answer can be interpreted as a variational optimization over latent reasoning processes. Specifically, for single-answer settings, the approach maximizes:

$$\mathbb{E}_{r \sim \pi_\theta(\cdot|q)} [\pi_\theta(a^*|q, r)]$$

This contrasts with related approaches (e.g., JLB, LaTRO) that target a variational lower bound on the log-probability, with VeriFree optimizing the expected value directly. This reward-weighting mitigates the issue of the model learning to "bridge" between incorrect reasoning and correct answers via spurious latent traces.

5. Practical Implementation and Domain Coverage

VeriFree is directly applicable in settings where the gold reference answer is known for each training instance, which encompasses a broad spectrum of question-answer collections in natural language, scientific, and professional domains. It does not impose restrictions on the structure, length, or format of the reference answer within the limitations outlined in the paper. Resource-wise, VeriFree significantly reduces operational complexity by eliminating ancillary model requirements, maintaining only the main policy model in training memory.

The approach is effective in chemistry, healthcare, engineering, law, business, biology, economics, and other real-world domains, addressing cases where neither symbolic rules nor robust model verifiers are feasible. This suggests that the method generalizes the advantages of RLVR beyond mathematical and code-oriented tasks.

6. Known Limitations and Open Challenges

The core equivalence of the VeriFree objective with standard RL objectives holds most strongly in contexts where a single canonical reference answer exists. When answer equivalence classes are large or semantic (as in many open-ended natural language tasks), reliance on a single reference may underrepresent broader success criteria. There is potential for performance drop if the dataset contains multiple equally correct but diverse answers, which are not all reflected in the training targets.

Reward shaping and careful curation of reference answers are critical to avoid spurious optimization for artifact patterns or overfitting to narrow string matches. The paper additionally highlights the need for responsible deployment and further work in supporting answer equivalence and robust alignment in sensitive decision-support domains.

7. Comparative Table: VeriFree and Related Approaches

Feature	Verifier-Based RL	VeriFree
Requires explicit verifier	Yes	No
Reward signal	Binary or model-judged	Policy’s own answer likelihood
Computational overhead	High (additional models)	Low (single forward)
Applicability	Verifiable domains	All reference-answer domains
Empirical performance	Domain-dependent	Comparable or superior

8. Future Research Directions

VeriFree may be further extended by:

• Incorporating mechanisms to support multiple reference answers or answer equivalence classes, increasing robustness in tasks with broader answer diversity.
• Developing procedures for automated reward shaping and enhanced variance control in longer or more complex reasoning tasks.
• Exploring integration with other alignment frameworks (such as DPO or self-improvement paradigms) and establishing guarantees under data distributional shifts for real-world deployment.

9. Summary

VeriFree constitutes a verifier-free, reward likelihood–based RL approach for LLM reasoning post-training, allowing the development of scalable, efficient, and domain-general LLMs. By directly maximizing the probability of reference answers as a reward, it circumvents bottlenecks inherent in verifier-dependent RL, enabling effective learning even in domains with complex, subjective, or uncheckable answers. This method thus expands the applicability of RL-based LLM training to the full diversity of real-world reasoning tasks.