trailReinforcement learning with verifiable rewards can produce reasoning capabilities unavailable from base-model sampling.
Unconstrained chain-of-thought from pure reinforcement learning can develop reasoning beyond human reasoning priors.
Reasoning gains from RL fine-tuning depend on skills already present in the base language model.
The argument from tasks base models never solve· for
Prolonged reinforcement learning training can enable models to solve tasks their base models cannot solve, regardless of sample count.
ProRL-trained Nemotron-Research-Reasoning-Qwen-1.5B solves Reasoning Gym tasks where DeepSeek-R1-Distill-Qwen-1.5B scores zero at pass@256.
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RL training on two-function compositions improves pass@k on unseen deeper compositions while base-model pass@k remains near zero.
Outcome-reward reinforcement learning enables language models to compose learned atomic skills into new skills beyond next-token training on the same data.
In synthetic tasks with learned atomic skills, outcome-reward RL, but not rejection fine-tuning, generalizes to deeper unseen compositions.
Results from synthetic controlled tasks on RL skill acquisition in language models generalize to natural reasoning domains.
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On-policy supervised fine-tuning on a language model's own correct samples matches RL's compositional generalization gains.
Reinforcement learning fine-tuning of language models yields limited compositional generalization to novel combinations of skills trained in isolation.
The argument from reasoning-checked pass@k· for
At large k, pass@k on tasks with small discrete answer spaces credits correct answers regardless of reasoning quality.
atomic
At large k, RLVR-trained models exceed base models on CoT-pass@k.
atomic
The argument from sharpening within the base distribution· against
At high k, base models match or exceed RLVR-trained models in pass@k on math, code, and visual reasoning benchmarks.
shared · shown elsewhere
Power-sharpened sampling from an untrained base model matches RL-posttrained models' single-shot reasoning performance.
atomic
assumed
Large-k pass@k is a valid measure of the boundary of language-model reasoning capability.
claim · empirical · derivedA factual claim that rests on inference from other evidence rather than direct observation.constitution →claim page ↗︎
Reinforcement learning with verifiable rewards can produce reasoning capabilities unavailable from base-model sampling.
↑SupportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →credence 0.68Credence, from 0 to 1: the Steward's probability that the claim, as stated, is true. Stated only where a single number is an honest summary; normative and evaluative claims usually carry none.constitution →
2depended on by
this rests on ↓
claimA box is a claim: a single proposition the graph assesses, with its own page and map. Click any claim to centre the map on it.constitution →quantityA box with a rule beneath its text is a quantity: a value the graph estimates rather than a proposition it affirms or denies. Its estimate stands where a claim's status would.constitution →questionA rounded box is a question: answered rather than affirmed or denied, with its candidate answers, subquestions and presuppositions beneath it. Its mark says how well answered it is.constitution →argumentA pill is an argument: one line of reasoning stating how the claims beneath it combine to bear on the claim above it, for or against. Arguments are not destinations; click their claims to explore.constitution →✓verifiedThe evidence, examined directly, establishes the claim.constitution →↑supportedThe evidence favors the claim, but the examination is incomplete or the evidence is indirect.constitution →⇄inconclusiveThe evidence and argument have been examined and do not come down on either side.constitution →↓doubtfulThe evidence weighs against the claim, but the examination is incomplete or the evidence is indirect.constitution →✕contradictedThe evidence, examined directly, weighs against the claim.constitution →?unknownInsufficient information to assess.constitution →◌unassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →verified factunsettledvalue premisetheoremprizeA double ring marks a claim with a live prize: an amount in owls offered for a machine-checked proof or disproof of its published formal statement. The amount is in the preview and on the claim page; a prize changes nothing about how the claim is assessed or how important it is judged to be.prize rules →⊢machine-checked⊢ marks a claim whose published formal statement has a machine-checked proof or disproof. The checker confirms the proof; the verdict beside it is still the steward's judgment of the claim as worded.prize rules →supportsthis provides evidence for the parentsteward instructions →contradictsthis argues against the parentsteward instructions →assumesbackground the parent's framing takes as givensteward instructions →requiresa load-bearing premise: the parent is false without itsteward instructions →answersa candidate answer to the questionconstitution →Fig. Detail falls off with distance; every claim is an address.