Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914568695971840 |
|---|---|
| author | Ranard, Daniel |
| author_facet | Ranard, Daniel |
| contents | We introduce an automatically generated benchmark for predicting hidden text in technical papers. A paper supplies visible context $X$ and a hidden continuation $Y$; the evaluated model writes an auxiliary forecast string $Z$, and a separate scorer assigns next-token probability to $Y$ both with and without conditioning on $Z$. This gives a label-free test of whether $Z$ transmits information about the continuation, compared against controls where $Z$ is recent context rather than a forecast. Our main testbed is equation-suffix prediction: the predictor sees context and the first part of a displayed equation, then forecasts the rest. The task mixes surface-level arXiv/TeX text modeling with reasoning-sensitive inference; the suffix is one of many roughly equivalent continuations, so the benchmark is read statistically rather than item-by-item. On 1363 equation continuations from 138 recent physics and mathematics papers, forecasts from GPT-5.5, Opus 4.7, and GPT-5.4 nano all improve clipped likelihood over the context control under both Qwen3-8B and Kimi K2.6 scorers, distinguishing model families and reasoning-effort settings without human labels. To emulate shortcuts where $Z$ further primes the scorer rather than making a useful forecast, we also fine-tune the scorer on context-only prompts and apply it to held-out papers as a stronger control. GPT-5.5 forecasts still beat this fine-tuned control; GPT-5.4 nano forecasts do not. Longer prose/TeX continuations show positive but noisier lift over controls, concentrated near the beginning of the target. These results support cross-model likelihood scoring as a static benchmark and as a setup for probing shortcut vulnerabilities before reinforcement learning or model-selection optimization is applied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10810 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities Ranard, Daniel Machine Learning We introduce an automatically generated benchmark for predicting hidden text in technical papers. A paper supplies visible context $X$ and a hidden continuation $Y$; the evaluated model writes an auxiliary forecast string $Z$, and a separate scorer assigns next-token probability to $Y$ both with and without conditioning on $Z$. This gives a label-free test of whether $Z$ transmits information about the continuation, compared against controls where $Z$ is recent context rather than a forecast. Our main testbed is equation-suffix prediction: the predictor sees context and the first part of a displayed equation, then forecasts the rest. The task mixes surface-level arXiv/TeX text modeling with reasoning-sensitive inference; the suffix is one of many roughly equivalent continuations, so the benchmark is read statistically rather than item-by-item. On 1363 equation continuations from 138 recent physics and mathematics papers, forecasts from GPT-5.5, Opus 4.7, and GPT-5.4 nano all improve clipped likelihood over the context control under both Qwen3-8B and Kimi K2.6 scorers, distinguishing model families and reasoning-effort settings without human labels. To emulate shortcuts where $Z$ further primes the scorer rather than making a useful forecast, we also fine-tune the scorer on context-only prompts and apply it to held-out papers as a stronger control. GPT-5.5 forecasts still beat this fine-tuned control; GPT-5.4 nano forecasts do not. Longer prose/TeX continuations show positive but noisier lift over controls, concentrated near the beginning of the target. These results support cross-model likelihood scoring as a static benchmark and as a setup for probing shortcut vulnerabilities before reinforcement learning or model-selection optimization is applied. |
| title | Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2605.10810 |