Selection, Recombination, or a Fresh Solve? A Candidate-Free Control for Single-Pass Test-Time Aggregation

Title:Selection, Recombination, or a Fresh Solve? A Candidate-Free Control for Single-Pass Test-Time Aggregation

Abstract:When every candidate is wrong, correct-candidate selection is unavailable, yet the aggregation call can still solve the problem afresh. A correct aggregate answer may therefore reflect recombination, fresh solving, or both. For efficient test-time reasoning, the relevant question is whether candidate context adds value beyond the additional generation pass. We introduce the missing candidate-free control under the same maximum output-token allowance and stratify by the number of correct candidates. Across AIME-2025 and HMMT-2025 with Qwen3-4B, candidate conditioning improves accuracy when multiple candidates are correct ($\Delta_{\mathrm{cand}}$(c2+) = +0.290), lowers accuracy when every candidate is wrong ($\Delta_{\mathrm{cand}}$(c0) = -0.123), and remains unresolved in the one-correct regime. The c2+ and c0 conclusions survive a conservative correction for the adaptive two-benchmark procedure. Under this counterfactual, the interpretation of all-wrong recovery reverses at this scale: conditioning on an all-wrong candidate pool lowers accuracy relative to a fresh solve. Original-format matching and placebo results characterize the failures descriptively but leave their mechanism unresolved. Within a separate structured intervention, explicit answer fields causally steer outputs toward their values; masking yields no measurable accuracy improvement, and equivalence with the original format was not established. The evidence is limited to one Qwen3-4B family, two mathematics benchmarks, first-answer-truncated candidate fragments, and single-pass prompted aggregation.

Accepted at the COLM 2026 Workshop on Efficient Reasoning. 18 pages

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL)

arXiv:2608.18379 [cs.LG]

(or arXiv:2608.18379v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.18379 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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