# Aletheia: Quantifying Cognitive Conviction in Reasoning Models via Regularized Inverse Confusion Matrix

arXiv: https://arxiv.org/abs/2601.01532 · HTML: https://mlsanity.com/paper/2601.01532/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 13 references that are in the map.
- First posted on arXiv 4 Jan 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 6 of 6)

- [SycEval: Evaluating LLM Sycophancy](https://mlsanity.com/paper/2502.08177/) (2025)
- [OverThink: Slowdown Attacks on Reasoning LLMs](https://mlsanity.com/paper/2502.02542/) (2025)
- [Think Twice: Enhancing LLM Reasoning by Scaling Multi-round Test-time Thinking](https://mlsanity.com/paper/2503.19855/) (2025)
- [Trust Me, I'm Wrong: LLMs Hallucinate with Certainty Despite Knowing the Answer](https://mlsanity.com/paper/2502.12964/) (2025)
- [BrokenMath: A Benchmark for Sycophancy in Theorem Proving with LLMs](https://mlsanity.com/paper/2510.04721/) (2025)
- [Measuring Data Diversity for Instruction Tuning: A Systematic Analysis and A Reliable Metric](https://mlsanity.com/paper/2502.17184/) (2025)

## Abstract (arXiv)

In the progressive journey toward Artificial General Intelligence (AGI), current evaluation paradigms face an epistemological crisis. Static benchmarks measure knowledge breadth but fail to quantify the depth of belief. While Simhi et al. (2025) defined the CHOKE phenomenon in standard QA, we extend this framework to quantify "Cognitive Conviction" in System 2 reasoning models. We propose Project Aletheia, a cognitive physics framework that employs Tikhonov Regularization to invert the judge's confusion matrix. To validate this methodology without relying on opaque private data, we implement a Synthetic Proxy Protocol. Our preliminary pilot study on 2025 baselines (e.g., DeepSeek-R1, OpenAI o1) suggests that while reasoning models act as a "cognitive buffer," they may exhibit "Defensive OverThinking" under adversarial pressure. Furthermore, we introduce the Aligned Conviction Score (S_aligned) to verify that conviction does not compromise safety. This work serves as a blueprint for measuring AI scientific integrity.