# Quantisation Reshapes the Metacognitive Geometry of Language Models

arXiv: https://arxiv.org/abs/2604.08976 · HTML: https://mlsanity.com/paper/2604.08976/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 11 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [When Quantization Affects Confidence of Large Language Models?](https://mlsanity.com/paper/2405.00632/) (2024)
- [Generalization of Fine-Tuned Uncertainty Communication and Metacognition in Large Language Models](https://mlsanity.com/paper/2510.05126/) (2025)
- [CATTO: Balancing Preferences and Confidence in Language Models](https://mlsanity.com/paper/2601.23096/) (2026)

## Built on by (most cited first, 1 of 1)

- [Distilling Self-Consistency into Verbal Confidence: A Pre-Registered Negative Result and Post-Hoc Rescue on Gemma 3 4B](https://mlsanity.com/paper/2604.24070/) (2026)

## Abstract (arXiv)

We report that model quantisation restructures domain-level metacognitive efficiency in LLMs rather than degrading it uniformly. Evaluating Llama-3-8B-Instruct on the same 3,000 questions at Q5_K_M and f16 precision, we find that M-ratio profiles across four knowledge domains are uncorrelated between formats (Spearman rho = 0.00). Arts & Literature moves from worst-monitored (M-ratio = 0.606 at Q5_K_M) to best-monitored (1.542 at f16). Geography moves from well-monitored (1.210) to under-monitored (0.798). However, Type-2 AUROC profiles are perfectly stable across formats (rho = 1.00), localising the restructuring to the M-ratio normalisation rather than the underlying discrimination signal. This finding emerged from a pre-registered attempt to improve metacognition through domain-conditional training. We prescribed confidence-amplification SFT for the diagnosed weak domain, with matched-budget agnostic and wrong-prescription controls. All four confirmatory hypotheses were null (10,000 bootstrap resamples, seed = 42). The training successfully reshaped confidence distributions, doubling the NLP gap in Science from 0.076 to 0.152, but did not improve meta-d' because the diagnostic profile did not transfer across formats. Any system relying on domain-level M-ratio profiles has an unexamined dependency on inference format. Systems using AUROC_2 are safer. We release all code, pre-registrations, and trial-level data.