Learning from the Gap Between Pass@K and Pass@1

Computer Science > Machine Learning

[Submitted on 17 Sep 2026]

Title:Learning from the Gap Between Pass@K and Pass@1

View PDF HTML (experimental)Abstract:Large language models (LLMs) are increasingly trained with reinforcement learning from verifiable rewards (RLVR). An exact verifier can also support test-time scaling by selecting a passing response from multiple samples, while other deployments use beam search, adaptive sampling, or tools. We study single-sample decoding, where each query receives one response without search, to ask whether search-exposed behavior can be absorbed into the model. Existing verified-response post-training recipes do not generally distinguish problems already solved on the first decode from failures recovered within K samples. Under a fixed budget, this can spend examples repeating behavior the deployed policy already has. We introduce GapFT, which selects training evidence by the source checkpoint's single-sample outcome and fine-tunes on the Pass@K-Pass@1 gap: problems the policy fails on one sample but solves within K samples. We match training examples, processed tokens, and optimizer steps while keeping the objective unchanged. GapFT fills the matched budget with recovered failures and uses an exact decomposition to distinguish corrections of recovered and missed failures from regressions on first-decode successes. On LogiQA 2.0 and ReClor with Llama-3.1-8B, GapFT improves Pass@1 by 14.4 and 13.9 points over the source model, outperforms budget-matched uniform verified RFT at the same learning rate, and matches fine-tuning on the full verified pool using one third of the data. A single decode matches the source model's verifier-selected Pass@4 accuracy. A randomized control attributes gains to covering distinct failures, and our analysis relates available gains to transferable failure support. A three-seed Qwen2.5-7B replication retains positive gains over uniform RFT on both logic tasks.

Current browse context:

cs.LG

References & Citations

Loading...

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)

Connected Papers (What is Connected Papers?)

Litmaps (What is Litmaps?)

scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)

CatalyzeX Code Finder for Papers (What is CatalyzeX?)

DagsHub (What is DagsHub?)

Gotit.pub (What is GotitPub?)

Hugging Face (What is Huggingface?)

ScienceCast (What is ScienceCast?)

Demos

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)

CORE Recommender (What is CORE?)

IArxiv Recommender

(What is IArxiv?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.