<?xml version="1.0" encoding="UTF-8"?>
<modsCollection xmlns="http://www.loc.gov/mods/v3">
<mods ID="peng-etal-2026-beyond-sampled">
    <titleInfo>
        <title>Beyond the Sampled Token: Preserving Candidate Support in RLVR</title>
    </titleInfo>
    <name type="personal">
        <namePart type="given">Ruotian</namePart>
        <namePart type="family">Peng</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <name type="personal">
        <namePart type="given">Yi</namePart>
        <namePart type="family">Ren</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <name type="personal">
        <namePart type="given">Zhouliang</namePart>
        <namePart type="family">Yu</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <name type="personal">
        <namePart type="given">Weiyang</namePart>
        <namePart type="family">Liu</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <name type="personal">
        <namePart type="given">Yandong</namePart>
        <namePart type="family">Wen</namePart>
        <role>
            <roleTerm authority="marcrelator" type="text">author</roleTerm>
        </role>
    </name>
    <originInfo>
        <dateIssued>2026-10</dateIssued>
    </originInfo>
    <typeOfResource>text</typeOfResource>
    <relatedItem type="host">
        <titleInfo>
            <title>Findings of the Association for Computational Linguistics: EMNLP 2026</title>
        </titleInfo>
        <name type="personal">
            <namePart type="given">Hung-Yi</namePart>
            <namePart type="family">Lee</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <name type="personal">
            <namePart type="given">Sunipa</namePart>
            <namePart type="family">Dev</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <name type="personal">
            <namePart type="given">Jessy</namePart>
            <namePart type="family">Li</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <name type="personal">
            <namePart type="given">Desmond</namePart>
            <namePart type="family">Elliott</namePart>
            <role>
                <roleTerm authority="marcrelator" type="text">editor</roleTerm>
            </role>
        </name>
        <originInfo>
            <publisher>Association for Computational Linguistics</publisher>
            <place>
                <placeTerm type="text">Budapest, Hungary</placeTerm>
            </place>
        </originInfo>
        <genre authority="marcgt">conference publication</genre>
        <identifier type="isbn">979-8-89176-462-0</identifier>
    </relatedItem>
    <abstract>We revisit exploration collapse in reinforcement learning with verifiable rewards (RLVR), from the perspective of the candidate distribution for next-token prediction. We formally show that as probability concentrates on the top-1 candidate, the expected number of distinct responses collapses to one regardless of the sampling budget K. This theoretical implication is further verified by our empirical tracking of top-N candidate probabilities during training, where the top-1 candidate progressively dominates while plausible alternatives are suppressed. These findings suggest a key desideratum for effective exploration: preserving non-negligible probability mass on the top-N candidates. To this end, we propose Candidate-aware Support Preservation (CaSP), with two complementary designs. Specifically, CaSP redistributes positive gradients among top-N candidates for correct responses, and applies a stronger penalty to the top-1 candidate for incorrect responses. Unlike many exploration-oriented methods that improve pass@K at the cost of pass@1, CaSP improves pass@K across the full K spectrum. These gains generalize to 6 math, 2 logical-reasoning, and 2 coding benchmarks, and scales to 32B-parameter models and sampling budgets up to K=1024, positioning it as a principled, candidate-level approach for RLVR exploration.</abstract>
    <identifier type="citekey">peng-etal-2026-beyond-sampled</identifier>
    <location>
        <url>https://aclanthology.org/2026.findings-emnlp.635/</url>
    </location>
    <part>
        <date>2026-10</date>
        <extent unit="page">
            <start>13318</start>
            <end>13340</end>
        </extent>
    </part>
</mods>
</modsCollection>

%0 Conference Proceedings
%T Beyond the Sampled Token: Preserving Candidate Support in RLVR
%A Peng, Ruotian
%A Ren, Yi
%A Yu, Zhouliang
%A Liu, Weiyang
%A Wen, Yandong
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F peng-etal-2026-beyond-sampled
%X We revisit exploration collapse in reinforcement learning with verifiable rewards (RLVR), from the perspective of the candidate distribution for next-token prediction. We formally show that as probability concentrates on the top-1 candidate, the expected number of distinct responses collapses to one regardless of the sampling budget K. This theoretical implication is further verified by our empirical tracking of top-N candidate probabilities during training, where the top-1 candidate progressively dominates while plausible alternatives are suppressed. These findings suggest a key desideratum for effective exploration: preserving non-negligible probability mass on the top-N candidates. To this end, we propose Candidate-aware Support Preservation (CaSP), with two complementary designs. Specifically, CaSP redistributes positive gradients among top-N candidates for correct responses, and applies a stronger penalty to the top-1 candidate for incorrect responses. Unlike many exploration-oriented methods that improve pass@K at the cost of pass@1, CaSP improves pass@K across the full K spectrum. These gains generalize to 6 math, 2 logical-reasoning, and 2 coding benchmarks, and scales to 32B-parameter models and sampling budgets up to K=1024, positioning it as a principled, candidate-level approach for RLVR exploration.
%U https://aclanthology.org/2026.findings-emnlp.635/
%P 13318-13340

Markdown (Informal)

[Beyond the Sampled Token: Preserving Candidate Support in RLVR](https://aclanthology.org/2026.findings-emnlp.635/) (Peng et al., Findings 2026)

• Beyond the Sampled Token: Preserving Candidate Support in RLVR (Peng et al., Findings 2026)

ACL

• Ruotian Peng, Yi Ren, Zhouliang Yu, Weiyang Liu, and Yandong Wen. 2026. Beyond the Sampled Token: Preserving Candidate Support in RLVR. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 13318–13340, Budapest, Hungary. Association for Computational Linguistics.