# False Fixed Points: Kantian Feedback, Stable Miscalibration, and Representational Compression in LLMs

arXiv: https://arxiv.org/abs/2510.14925 · HTML: https://mlsanity.com/paper/2510.14925/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 41 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (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)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [ChatEval: Towards Better LLM-based Evaluators through Multi-Agent Debate](https://mlsanity.com/paper/2308.07201/) (2023)
- [Representation Degeneration Problem in Training Natural Language Generation Models](https://mlsanity.com/paper/1907.12009/) (2019)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [RankMe: Assessing the downstream performance of pretrained self-supervised representations by their rank](https://mlsanity.com/paper/2210.02885/) (2022)
- [Know Your Limits: A Survey of Abstention in Large Language Models](https://mlsanity.com/paper/2407.18418/) (2024)
- [LLM Internal States Reveal Hallucination Risk Faced With a Query](https://mlsanity.com/paper/2407.03282/) (2024)
- [Reasoning Models Better Express Their Confidence](https://mlsanity.com/paper/2505.14489/) (2025)
- [Anisotropy Is Inherent to Self-Attention in Transformers](https://mlsanity.com/paper/2401.12143/) (2024)
- [Tracing the Representation Geometry of Language Models from Pretraining to Post-training](https://mlsanity.com/paper/2509.23024/) (2025)
- [The Illusion of Progress: Re-evaluating Hallucination Detection in LLMs](https://mlsanity.com/paper/2508.08285/) (2025)
- [Probing the Critical Point (CritPt) of AI Reasoning: a Frontier Physics Research Benchmark](https://mlsanity.com/paper/2509.26574/) (2025)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [How to Detect and Defeat Molecular Mirage: A Metric-Driven Benchmark for Hallucination in LLM-based Molecular Comprehension](https://mlsanity.com/paper/2504.12314/) (2025)
- [Black-Box Hallucination Detection via Consistency Under the Uncertain Expression](https://mlsanity.com/paper/2509.21999/) (2025)

## Abstract (arXiv)

High-confidence errors in large language models are often treated as fragile failures. We study an alternative: some errors may be false fixed points, locally stable, internally coherent, and confidently wrong. This separates robustness from truth-tracking. We develop the separation through a Kantian commitment-gate framing and a minimal linear feedback model in which stability and correctness can diverge. Across three open-weight models, overconfident wrong items are not systematically more locally fragile than confidently correct items under our hidden-state sensitivity probes. Abstention-aware self-critique reduces overconfident wrong commitments by sacrificing coverage, and C3-R, a rule-based explicit feedback gate, sharpens that tradeoff rather than eliminating it. These results motivate, but do not establish, high signal-to-noise (high-SNR) inertia and representational compression as possible mechanisms for stable miscalibration.