# Likelihood scoring for continuations of mathematical text: a self-supervised benchmark with tests for shortcut vulnerabilities

arXiv: https://arxiv.org/abs/2605.10810 · HTML: https://mlsanity.com/paper/2605.10810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 50 of its 64 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 30 of 50)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [The LAMBADA dataset: Word prediction requiring a broad discourse context](https://mlsanity.com/paper/1606.06031/) (2016)
- [BARTScore: Evaluating Generated Text as Text Generation](https://mlsanity.com/paper/2106.11520/) (2021)
- [LLM Evaluators Recognize and Favor Their Own Generations](https://mlsanity.com/paper/2404.13076/) (2024)
- [Prometheus: Inducing Fine-grained Evaluation Capability in Language Models](https://mlsanity.com/paper/2310.08491/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Generative Verifiers: Reward Modeling as Next-Token Prediction](https://mlsanity.com/paper/2408.15240/) (2024)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [LiveBench: A Challenging, Contamination-Limited LLM Benchmark](https://mlsanity.com/paper/2406.19314/) (2024)
- [Logic-RL: Unleashing LLM Reasoning with Rule-Based Reinforcement Learning](https://mlsanity.com/paper/2502.14768/) (2025)
- [Scaling Laws for Reward Model Overoptimization in Direct Alignment Algorithms](https://mlsanity.com/paper/2406.02900/) (2024)
- [Amortizing intractable inference in large language models](https://mlsanity.com/paper/2310.04363/) (2023)
- [LLMs as Narcissistic Evaluators: When Ego Inflates Evaluation Scores](https://mlsanity.com/paper/2311.09766/) (2023)
- [Prover-Verifier Games improve legibility of LLM outputs](https://mlsanity.com/paper/2407.13692/) (2024)
- [RLPR: Extrapolating RLVR to General Domains without Verifiers](https://mlsanity.com/paper/2506.18254/) (2025)
- [Reinforcing General Reasoning without Verifiers](https://mlsanity.com/paper/2505.21493/) (2025)
- [One Token to Fool LLM-as-a-Judge](https://mlsanity.com/paper/2507.08794/) (2025)
- [Training Chain-of-Thought via Latent-Variable Inference](https://mlsanity.com/paper/2312.02179/) (2023)

## Abstract (arXiv)

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.