Verifier-Free Learning

• Verifier-free learning is an approach that omits external verifiers, instead relying on intrinsic signals and expert demonstrations to guide training and inference.
• Methods like RARO and NOVER leverage adversarial optimization and proxy rewards to enhance model reasoning and performance across diverse benchmarks.
• Inference-time strategies such as majority voting, best-of-N sampling, and dynamic allocation boost output quality and compute efficiency without external validation.

Verifier-free learning encompasses algorithmic regimes for training and inference with LLMs or other complex models without relying on any externally trained verifier or reward model. This paradigm leverages only expert demonstrations, base model outputs, or intrinsic signals—eschewing automated correctness reward assignment from hand-crafted rules, learned reward models, or external evaluators. Verifier-free approaches are pivotal for domains where verifiable ground truth is absent, reward models are infeasible to construct, or “correctness” is inherently subjective or multi-faceted.

1. Fundamental Concepts and Definitions

Verifier-free learning is characterized by the exclusion of external verifiers from both training and inference phases. In the training context, it includes frameworks such as Relativistic Adversarial Reasoning Optimization (RARO) and NOVER (NO-VERifier Reinforcement Learning), which induce reward signals from expert demonstrations or proxy measures instead of automated validation (Cai et al., 26 Nov 2025, Liu et al., 21 May 2025). In the inference context, verifier-free scaling methods such as majority voting, best-of-N sampling, and dynamic sampling operate using the base LLM for all sampling, evaluation, or revision steps—again without any verifier (Wang et al., 18 Apr 2025, Wang et al., 19 Jun 2025).

Formally, in verifier-free inference-time scaling, let $C$ be the compute budget (e.g., number of forward passes) and $Q$ a quality metric (e.g., exact-match accuracy). A verifier-free ITC (inference-time compute) method $m$ computes $Q(m)$ using only model-internal processes, in contrast to verifier-based approaches where an auxiliary model $V$ scores and selects outputs (Wang et al., 18 Apr 2025).

2. Verifier-Free Reinforcement Learning Approaches

2.1 RARO – Relativistic Adversarial Reasoning Optimization

RARO utilizes an adversarial loop with a generator policy $\pi_\theta$ and a relativistic critic $C_\phi$, both trained purely from expert demonstrations (Cai et al., 26 Nov 2025). The critic estimates which of two solutions—an expert demonstration $z^E$ or policy-generated $z^\pi$—is superior for a given prompt $x$, using the relativistic GAN-style loss: $$L_D(\phi) = - \mathbb{E}_{x; z^E, z^\pi}\left[ \log \sigma(C_\phi(z^E|x) - C_\phi(z^\pi|x)) + \log \sigma(C_\phi(z^\pi|x) - C_\phi(z^E|x)) \right],$$ with $\sigma(u) = 1/(1 + e^{-u})$. The policy then receives dense RL rewards proportional to the critic's relative preference. RARO implements Proximal Policy Optimization (PPO) for practical stability, using two-time-scale updates, entropy regularization, gradient penalty, and spectral normalization for robust adversarial training.

Empirical results demonstrate RARO surpasses strong verifier-free baselines in factual reasoning (Countdown), formal theorem proving (DeepMath), and creative tasks (poetry writing), with scaling trends similar to RLHF on verifiable domains (Cai et al., 26 Nov 2025).

2.2 NOVER – Verifier-Free Incentive Training

NOVER dispenses with both rule-based and learned verifiers by constructing a proxy reward solely from model-internal perplexity and reasoning structure (Liu et al., 21 May 2025). The policy $\pi_\theta(t, a|p)$ generates a reasoning prefix $t$ and answer $a$ for each prompt $p$. Rewards are composed of:

• Format reward $R_f$ (ensures outputs follow prescribed tags)
• Reasoning reward $R_r$ (best perplexity gets maximal reward)
• Efficiency reward $R_e$ (favors shorter supporting reasoning)

The reasoning perplexity proxy measures how well $t$ predicts the ground truth $g$, and group-normalized advantages are computed for policy optimization. The training employs the Group-Relative Policy Optimization (GRPO) procedure with periodic synchronization of the proxy model and failsafes to prevent degenerate strategies (e.g., gibberish or trivial outputs).

NOVER achieves significant improvements on a diverse array of reasoning, creative, social, and multilingual benchmarks, outperforming SFT and even distilled models from large instructor LLMs (Liu et al., 21 May 2025). Additionally, NOVER supports "inverse incentive learning," using alternative targets (e.g., rubrics instead of final outputs) as the reward.

3. Verifier-Free Inference-Time Scaling Methods

Verifier-free inference-time scaling seeks to boost model performance during deployment via extra sampling or self-consistency without post-hoc verification (Wang et al., 18 Apr 2025, Wang et al., 19 Jun 2025). Representative methods include:

• Majority Voting (Self-Consistency): Draw $N$ chain-of-thought samples, extract final answers $a_i$, and select $$\hat{a}_{\text{MV}} = \arg\max_a \sum_i \mathbf{1}\{a_i = a\}$$.
• Best-of-N Sampling (BoN): Generate $N$ candidates, score each with the same LLM acting as a judge, and select the highest.
• Sequential Revisions: Iteratively revise initial responses using model-generated feedback and select the best after $T$ iterations.
• Parallel-then-Sequential (Hybrid): Combine $M$ initial responses with $T$ sequential refinements.

All methods exclusively utilize the base LLM, without recourse to external models for output selection or rating.

4. Dynamic Inference and Budget Allocation Frameworks

Recent work introduces more sophisticated inference-time strategies to match practical budget constraints and optimize performance:

4.1 Integrated Parallel–Sequential Sampling and Bandit Allocation

DynScaling (Wang et al., 19 Jun 2025) develops an integrated approach, combining:

• Parallel initialization: Collect diverse completions via breadth sampling.
• Synthetic chain construction: Build pseudo-sequential chains by randomly concatenating parallel completion fragments.
• Sequential refinement: Use concatenated chains as extended prompts for new completions, enhancing depth and coherence.

Budget allocation per query is posed as a multi-armed bandit problem, allocating inference budget adaptively based on the variation ratio—a measure of output diversity/uncertainty from the model itself. Upper Confidence Bound (UCB) policies guide additional sampling, prioritizing queries with highest uncertainty and thus potential information gain.

The combined procedure sequentially allocates compute, applies integrated sampling, and finalizes answers via majority voting, always verifier-free.

4.2 Efficiency Guarantees and Empirical Performance

DynScaling achieves substantial improvements in both task performance and compute efficiency, consistently outperforming alternative verifier-free baselines in science QA and advanced math, particularly within low to moderate compute budgets (Wang et al., 19 Jun 2025). Sublinear regret guarantees ensure that the allocation converges towards optimal resource use as budget increases.

5. Comparative Evaluation and Empirical Insights

Comprehensive studies (Wang et al., 18 Apr 2025) establish the empirical Pareto frontier of compute vs. output quality:

• Reasoning-specialized models dominate non-reasoning models: even with large samples ($N=256$), non-reasoning models underperform reasoning models with fewer samples ($N=100$).
• Majority voting (self-consistency) is robustly competitive and often outperforms more complex procedures (BoN, sequential revisions, hybrid).
• Budget-quality saturation: Accuracy often plateaus beyond 50–100 samples for reasoning models, indicating diminishing returns for additional compute.
• Practical guidance: The optimal regime is reasoning-specialized models with majority voting and lightweight post-hoc response filtering (e.g., by length and discourse marker density).

The following table summarizes quality metrics across paradigms for reasoning tasks:

Method / Model	MATH-500 (Accuracy)	AIME (Accuracy)	Additional Notes
Non-reasoning, MV, $N=256$	~42%	~18%	Large compute budget
DeepSeek-R1-Distill, MV	~60%	~30%	$N=100$, reasoning-specialized
DeepSeek-R1-Distill, BoN	59%	–	$N=100$, marginal gain vs MV
DeepSeek-R1-Distill, Seq	59%	–	$T=3$, no significant gain over MV

Major gains are attributed to model specialization and majority/self-consistency voting; additional complexity yields minimal uplift (<1%) but with increased compute cost (Wang et al., 18 Apr 2025).

6. Analysis of Output Features and Quality Correlates

Empirical feature analyses reveal that response length and linguistic markers can serve as potent heuristic signals for post-hoc filtering:

• Shorter response lengths are positively correlated with correctness in reasoning models (e.g., $-10$ tokens on AIME, $-5$ on MATH).
• Marker analysis: Discourse markers (e.g., "therefore") are more prevalent in correct outputs, while hedging or thinking markers (e.g., "perhaps," "however") are more prevalent in incorrect outputs.
• Marker-based classifiers achieve $\mathrm{F1} \approx 0.75$ (70B model) to $0.86$ (14B model) for predicting correctness, offering an efficient, low-overhead quality filter (Wang et al., 18 Apr 2025).

This suggests that integrating lightweight output filtering based on such features can further close the quality gap to verifier-guided regimes.

7. Practical Guidelines and Applicability

Verifier-free learning provides broadly applicable techniques when verifiers are costly, unavailable, or ill-defined:

• Training: Use adversarial IRL (e.g., RARO) or internal proxy rewards (NOVER) to leverage available demonstrations or SFT data for robust reasoning training (Cai et al., 26 Nov 2025, Liu et al., 21 May 2025).
• Inference: Employ majority voting with moderate sampling, and post-hoc feature-based filters for maximal cost-quality efficiency. Use advanced allocation (e.g., DynScaling) when batch processing and compute are limited (Wang et al., 19 Jun 2025, Wang et al., 18 Apr 2025).
• Domains: Especially suitable for creative, open-ended, social, or subjective tasks without clear-cut external correctness criteria.

A plausible implication is that as model capabilities and dataset diversity increase, verifier-free setups—combined with strong reasoning-focused architectures and feature-aware post-processing—may become the dominant paradigm wherever verifier construction is impractical, thus broadening the reach of RL-based learning and inference in LLMs.