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Correctness Is a Direction: Geometric Answer Selection in Language Models — arXiv:2610.04512

Source: arXiv
Original: https://arxiv.org/abs/2610.04512
License (as archived): CC0-1.0
Archived: 2026-10-06T05:28:05.431Z
SHA-256 of the archived text: 2844204718207c1715d39215aeed36f6f7fe02d892270bf45874fc0baa0b8f15
Stable URL of this page: https://metraipolis.com/documento/dc_adcdadafd693

How to cite

Correctness Is a Direction: Geometric Answer Selection in Language Models — arXiv:2610.04512 — arXiv, https://arxiv.org/abs/2610.04512 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_adcdadafd693 (Metraipolis archive dc_adcdadafd693, sha256 2844204718207c1715d39215aeed36f6f7fe02d892270bf45874fc0baa0b8f15)

BibTeX

@misc{dcadcdadafd693,
  title = {Correctness Is a Direction: Geometric Answer Selection in Language Models — arXiv:2610.04512},
  howpublished = {arXiv},
  url = {https://arxiv.org/abs/2610.04512},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_adcdadafd693; sha256 2844204718207c1715d39215aeed36f6f7fe02d892270bf45874fc0baa0b8f15},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv, https://arxiv.org/abs/2610.04512. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Answer correctness is encoded as a recoverable geometric direction in the hidden states of language models. We show that the mean displacement from incorrect to correct answer representations, computed at approximately 70\% of model depth from fifty labeled examples with no parameter updates, yields a scoring direction that outperforms zero-shot log-probability scoring by up to +32.0 percentage points on factual benchmarks (ARC-Challenge and MMLU) and by +38.1 to +51.8 percentage points on TruthfulQA, across five models spanning 1B to 8B parameters in three architecture families (Llama, Qwen, Gemma). The method requires one forward pass and one dot product per candidate; no generation is performed at inference. Applied as a hallucination detector on individual (question, answer) pairs, the recovered direction achieves 0.693~AUROC versus 0.578 for log-probability scoring. We additionally find that correctness directions for factual reasoning, domain knowledge, and calibrated truthfulness are near-orthogonal in representation space, revealing that language models allocate geometrically independent subspaces to qualitatively distinct notions of correct answer, with architecture-dependent variation in the degree of separation. This structure explains the observed transfer pattern---the direction calibrated on factual questions transfers within task type but not across it---and suggests that LLM calibration failures may reflect a routing problem: the model's internal representation contains more correctness signal than its output behaviour exploits.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.CL, nuovi lavori del giorno).
Categorie arXiv: Computation and Language (cs.CL).
Pagina del lavoro: https://arxiv.org/abs/2610.04512 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-06T05:24:20.266Z dalla pagina https://arxiv.org/list/cs.CL/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).