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Beyond Verifiable Rewards: Scaling Reinforcement Learning for Language Models to Unverifiable Data

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arxiv 2503.19618 v2 pith:LYA2NSAF submitted 2025-03-25 cs.LG

Beyond Verifiable Rewards: Scaling Reinforcement Learning for Language Models to Unverifiable Data

classification cs.LG
keywords datajepoverifiableunverifiableboundevidencelowerrewards
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We propose to scale RL to unverifiable data with a novel algorithm JEPO (Jensen's Evidence lower bound Policy Optimization). While most prior efforts on scaling RL for LLMs focus on verifiable data where ground truth answers are typically short-form and can be matched easily; we investigate the case where such assumptions are less valid (e.g., when answers are long-form such as mathematical proofs). To scale RL training to unverifiable data with contemporary training constraints, we propose JEPO. JEPO applies Jensen's evidence lower bound, a pragmatic simplification of the evidence lower bound which views chain-of-thought as a latent variable in the generative process. We show that on verifiable data (math), JEPO is as effective as RL with verifiable rewards; on semi-verifiable data (numina), JEPO improves on soft-match based evaluations compared to RL with verifiable rewards which can only leverage a subset of the data source; finally, on unverifiable data (numina-proof), JEPO outperforms SFT and a few ablation baselines on likelihood evaluations.

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Cited by 8 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities

    cs.LG 2026-05 unverdicted novelty 7.0

    Presents a likelihood-based benchmark for equation-suffix prediction in technical papers with controls to detect shortcut vulnerabilities in model forecasts.

  2. From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning

    cs.LG 2026-06 conditional novelty 6.5

    SFT supplies entangled compositional traces of atomic skills and routing modules; RL identifies those modules and enables recombination on novel compositions outside the SFT support.

  3. From Reasoning Traces to Reusable Modules: Understanding Compositional Generalization in Language Model Reasoning

    cs.LG 2026-06 unverdicted novelty 6.0

    Introduces a hierarchical latent selection model showing SFT supplies raw module materials in compound traces while RL decomposes them to identify atomic modules and enable recombination for new reasoning configurations.

  4. Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities

    cs.LG 2026-05 unverdicted novelty 6.0

    A new benchmark uses separate predictor and scorer LLMs to test whether forecast strings improve likelihood of hidden mathematical equation continuations, with controls that detect priming shortcuts.

  5. Trust Your Memory: Verifiable Control of Smart Homes through Reinforcement Learning with Multi-dimensional Rewards

    cs.AI 2026-04 unverdicted novelty 6.0

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  6. Compute as Teacher: Turning Inference Compute Into Reference-Free Supervision

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  7. Coupled Variational Reinforcement Learning for Language Model General Reasoning

    cs.CL 2025-12 conditional novelty 5.0

    CoVRL trains an LLM on a mixture of question-only and answer-guided reasoning traces, using the model's own answer probability as reward, and reports consistent gains on math and general-reasoning benchmarks.

  8. Direct Reasoning Optimization: Token-Level Reasoning Reflectivity Meets Rubric Gates for Unverifiable Tasks

    cs.CL 2025-06 unverdicted novelty 5.0

    Direct Reasoning Optimization applies token-level Reasoning Reflection Reward (R3) focused on high-variance tokens and rubric-gating constraints to improve sample-efficient RL training of LLMs on unverifiable tasks.