# Intention Collapse: Intention-Level Metrics for Reasoning in Language Models

arXiv: https://arxiv.org/abs/2601.01011 · HTML: https://mlsanity.com/paper/2601.01011/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 27 of its 40 references that are in the map.
- First posted on arXiv 3 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 27 of 27)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Qwen2 Technical Report](https://mlsanity.com/paper/2407.10671/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Discovering Latent Knowledge in Language Models Without Supervision](https://mlsanity.com/paper/2212.03827/) (2022)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Quiet-STaR: Language Models Can Teach Themselves to Think Before Speaking](https://mlsanity.com/paper/2403.09629/) (2024)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [Test-Time Training with Masked Autoencoders](https://mlsanity.com/paper/2209.07522/) (2022)
- [Let's reward step by step: Step-Level reward model as the Navigators for Reasoning](https://mlsanity.com/paper/2310.10080/) (2023)
- [The Surprising Effectiveness of Test-Time Training for Few-Shot Learning](https://mlsanity.com/paper/2411.07279/) (2024)
- [SkipDecode: Autoregressive Skip Decoding with Batching and Caching for Efficient LLM Inference](https://mlsanity.com/paper/2307.02628/) (2023)
- [Eliciting Latent Knowledge from Quirky Language Models](https://mlsanity.com/paper/2312.01037/) (2023)
- [Can language models handle recursively nested grammatical structures? A case study on comparing models and humans](https://mlsanity.com/paper/2210.15303/) (2022)
- [Improving Complex Reasoning over Knowledge Graph with Logic-Aware Curriculum Tuning](https://mlsanity.com/paper/2405.01649/) (2024)

## Abstract (arXiv)

Language generation maps a rich, high-dimensional internal state to a single token sequence. We study this many-to-one mapping through the lens of intention collapse: the projection from an internal intention space I to an external language space L. We introduce three cheap, model-agnostic metrics computed on a pre-collapse state I: (i) intention entropy Hint(I), (ii) effective dimensionality deff(I), and (iii) recoverability Recov(I), operationalized as probe AUROC for predicting eventual success. We evaluate these metrics in a 3x3 study across models (Mistral-7B, LLaMA-3.1-8B, Qwen-2.5-7B) and benchmarks (GSM8K, ARC-Challenge, AQUA-RAT), comparing baseline, chain-of-thought (CoT), and a babble control (n=200 items per cell). CoT increases average accuracy from 34.2% to 47.3% (+13.1 pp), driven by large gains on GSM8K but consistent degradations on ARC-Challenge. Across models, CoT induces distinct entropy regimes relative to baseline, dH = Hint(CoT) - Hint(Base): Mistral shows dH < 0 (lower-entropy CoT), whereas LLaMA shows dH > 0 (higher-entropy CoT), highlighting heterogeneity in CoT-induced internal uncertainty. Finally, probe AUROC is significantly above chance in a subset of settings and can dissociate from behavioral accuracy (e.g., high AUROC alongside lower CoT accuracy on ARC-Challenge for Qwen), suggesting that informative internal signal is not always reliably converted into a final discrete decision under constrained response formats.