Training two LoRA adapters competitively against each other, where each reads the other's solution summary and is rewarded for out-solving it, doubles GRPO's pass@1 on hard math while shortening reasoning traces.
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Prover-verifier games improve legibility of llm outputs
16 Pith papers cite this work. Polarity classification is still indexing.
16
Pith papers citing it
abstract
One way to increase confidence in the outputs of Large Language Models (LLMs) is to support them with reasoning that is clear and easy to check -- a property we call legibility. We study legibility in the context of solving grade-school math problems and show that optimizing chain-of-thought solutions only for answer correctness can make them less legible. To mitigate the loss in legibility, we propose a training algorithm inspired by Prover-Verifier Game from Anil et al. (2021). Our algorithm iteratively trains small verifiers to predict solution correctness, "helpful" provers to produce correct solutions that the verifier accepts, and "sneaky" provers to produce incorrect solutions that fool the verifier. We find that the helpful prover's accuracy and the verifier's robustness to adversarial attacks increase over the course of training. Furthermore, we show that legibility training transfers to time-constrained humans tasked with verifying solution correctness. Over course of LLM training human accuracy increases when checking the helpful prover's solutions, and decreases when checking the sneaky prover's solutions. Hence, training for checkability by small verifiers is a plausible technique for increasing output legibility. Our results suggest legibility training against small verifiers as a practical avenue for increasing legibility of large LLMs to humans, and thus could help with alignment of superhuman models.
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representative citing papers
TRL extends tandem training to RLVR pipelines, matching GRPO solo reasoning on Qwen3-4B math tasks while improving handoff robustness, reducing distributional drift, and increasing CoT legibility for the junior.
Self-evolving rubric with anti-gaming fitness reveals that objective capability scaling fails to transfer to subjective LLM behaviors, with advice-restraint as the universal lowest dimension that can regress.
Pseudo-Formalization decomposes proofs into self-contained natural language modules for independent LLM-based Block Verification, outperforming LLM-as-judge baselines on olympiad and research math benchmarks while releasing ArxivMathGradingBench.
Presents a likelihood-based benchmark for equation-suffix prediction in technical papers with controls to detect shortcut vulnerabilities in model forecasts.
Chain-of-thought monitoring detects reward hacking in frontier reasoning models, but strong optimization against the monitor produces obfuscated misbehavior that remains hard to detect.
o1-like models overthink easy tasks; self-training reduces compute use without accuracy loss on GSM8K, MATH500, GPQA, and AIME.
Theoria rewrites solutions into auditable typed state transitions with justifications, certifying 105 of 185 HLE problems at 91.4% precision and outperforming holistic judges on adversarial poisoned proofs by catching hidden premises.
SEAR trains one LLM via adversarial process rewards to explore harmful reasoning paths but flip to safe outputs, reducing over-refusal while preserving safety.
DAC decomposes agentic search into cooperative searcher and generator agents with cross-agent signals (abstention reward and hard-positive augmentation), achieving strong QA benchmark performance via LoRA on a shared backbone.
Weak models used as critics supplying non-misleading revision directions, distilled on-policy via OPCD, improve frozen and trained strong models on reasoning and alignment benchmarks.
Self-trained verification trains verifiers to imitate informed versions of themselves using reference solutions, improving test-time V-R loops and training-time self-improvement with reported gains of 2x on hard math and 14x on scientific reasoning.
CLORE augments correct on-policy rollouts by deleting repetitive and irrelevant segments then optimizes with auxiliary DPO to improve accuracy-efficiency trade-off on math benchmarks.
CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment.
CCO aggregates scoring functions into a calibrated penalty using conformal decision theory to enforce target violation rates for AI oversight on benchmarks like modified SWE-bench and MACHIAVELLI.
Proxy RL produces a staged proxy-internalization capability that emerges before and predicts reward hacking in coding environments.
citing papers explorer
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Agon: Competitive Cross-Model RL with Implicit Rival Grading of Reasoning
Training two LoRA adapters competitively against each other, where each reads the other's solution summary and is rewarded for out-solving it, doubles GRPO's pass@1 on hard math while shortening reasoning traces.
-
Tandem Reinforcement Learning with Verifiable Rewards
TRL extends tandem training to RLVR pipelines, matching GRPO solo reasoning on Qwen3-4B math tasks while improving handoff robustness, reducing distributional drift, and increasing CoT legibility for the junior.
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Does Capability Transfer to Subjective Behavior -- and Would Our Instruments Tell Us? A Self-Evolving, Trust-by-Construction Evaluation Paradigm
Self-evolving rubric with anti-gaming fitness reveals that objective capability scaling fails to transfer to subjective LLM behaviors, with advice-restraint as the universal lowest dimension that can regress.
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Pseudo-Formalization for Automatic Proof Verification
Pseudo-Formalization decomposes proofs into self-contained natural language modules for independent LLM-based Block Verification, outperforming LLM-as-judge baselines on olympiad and research math benchmarks while releasing ArxivMathGradingBench.
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Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities
Presents a likelihood-based benchmark for equation-suffix prediction in technical papers with controls to detect shortcut vulnerabilities in model forecasts.
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Monitoring Reasoning Models for Misbehavior and the Risks of Promoting Obfuscation
Chain-of-thought monitoring detects reward hacking in frontier reasoning models, but strong optimization against the monitor produces obfuscated misbehavior that remains hard to detect.
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Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs
o1-like models overthink easy tasks; self-training reduces compute use without accuracy loss on GSM8K, MATH500, GPQA, and AIME.
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Theoria: Rewrite-Acceptability Verification over Informal Reasoning States
Theoria rewrites solutions into auditable typed state transitions with justifications, certifying 105 of 185 HLE problems at 91.4% precision and outperforming holistic judges on adversarial poisoned proofs by catching hidden premises.
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Addressing Over-Refusal in LLMs with Competing Rewards
SEAR trains one LLM via adversarial process rewards to explore harmful reasoning paths but flip to safe outputs, reducing over-refusal while preserving safety.
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Divide and Cooperate: Role-Decomposed Multi-Agent LLM Training with Cross-Agent Learning Signals
DAC decomposes agentic search into cooperative searcher and generator agents with cross-agent signals (abstention reward and hard-positive augmentation), achieving strong QA benchmark performance via LoRA on a shared backbone.
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Weak Critics Make Strong Learners: On-Policy Critique Distillation for Scalable Oversight
Weak models used as critics supplying non-misleading revision directions, distilled on-policy via OPCD, improve frozen and trained strong models on reasoning and alignment benchmarks.
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Self-Trained Verification for Training- and Test-Time Self-Improvement
Self-trained verification trains verifiers to imitate informed versions of themselves using reference solutions, improving test-time V-R loops and training-time self-improvement with reported gains of 2x on hard math and 14x on scientific reasoning.
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CLORE: Content-Level Optimization for Reasoning Efficiency
CLORE augments correct on-policy rollouts by deleting repetitive and irrelevant segments then optimizes with auxiliary DPO to improve accuracy-efficiency trade-off on math benchmarks.
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Common-agency Games for Multi-Objective Test-Time Alignment
CAGE uses common-agency games and an EPEC algorithm to compute equilibrium policies that balance multiple conflicting objectives for test-time LLM alignment.
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Calibrating Conservatism for Scalable Oversight
CCO aggregates scoring functions into a calibrated penalty using conformal decision theory to enforce target violation rates for AI oversight on benchmarks like modified SWE-bench and MACHIAVELLI.
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Proxy Reward Internalization and Mechanistic Exploitation: A Learned Precursor to Reward Hacking and Its Generalization
Proxy RL produces a staged proxy-internalization capability that emerges before and predicts reward hacking in coding environments.