# Confidence is Not Competence

arXiv: https://arxiv.org/abs/2510.24772 · HTML: https://mlsanity.com/paper/2510.24772/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 23 references that are in the map.
- First posted on arXiv 24 Oct 2025.

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

- [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)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Programming Refusal with Conditional Activation Steering](https://mlsanity.com/paper/2409.05907/) (2024)
- [Investigating the Factual Knowledge Boundary of Large Language Models with Retrieval Augmentation](https://mlsanity.com/paper/2307.11019/) (2023)
- [Analyzing the Generalization and Reliability of Steering Vectors](https://mlsanity.com/paper/2407.12404/) (2024)
- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Style Vectors for Steering Generative Large Language Model](https://mlsanity.com/paper/2402.01618/) (2024)
- [Understanding (Un)Reliability of Steering Vectors in Language Models](https://mlsanity.com/paper/2505.22637/) (2025)
- [One-shot Optimized Steering Vectors Mediate Safety-relevant Behaviors in LLMs](https://mlsanity.com/paper/2502.18862/) (2025)
- [Correcting Biased Centered Kernel Alignment Measures in Biological and Artificial Neural Networks](https://mlsanity.com/paper/2405.01012/) (2024)
- [Rethinking Centered Kernel Alignment in Knowledge Distillation](https://mlsanity.com/paper/2401.11824/) (2024)
- [Characterizing Large Language Model Geometry Helps Solve Toxicity Detection and Generation](https://mlsanity.com/paper/2312.01648/) (2023)
- [The Confidence-Competence Gap in Large Language Models: A Cognitive Study](https://mlsanity.com/paper/2309.16145/) (2023)
- [Right Prediction, Wrong Reasoning: Uncovering LLM Misalignment in RA Disease Diagnosis](https://mlsanity.com/paper/2504.06581/) (2025)

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

- [The Cognitive Penalty: Ablating System 1 and System 2 Reasoning in Edge-Native SLMs for Decentralized Consensus](https://mlsanity.com/paper/2604.16913/) (2026)

## Abstract (arXiv)

Large language models (LLMs) often exhibit a puzzling disconnect between their asserted confidence and actual problem-solving competence. We offer a mechanistic account of this decoupling by analyzing the geometry of internal states across two phases - pre-generative assessment and solution execution. A simple linear probe decodes the internal "solvability belief" of a model, revealing a well-ordered belief axis that generalizes across model families and across math, code, planning, and logic tasks. Yet, the geometries diverge - although belief is linearly decodable, the assessment manifold has high linear effective dimensionality as measured from the principal components, while the subsequent reasoning trace evolves on a much lower-dimensional manifold. This sharp reduction in geometric complexity from thought to action mechanistically explains the confidence-competence gap. Causal interventions that steer representations along the belief axis leave final solutions unchanged, indicating that linear nudges in the complex assessment space do not control the constrained dynamics of execution. We thus uncover a two-system architecture - a geometrically complex assessor feeding a geometrically simple executor. These results challenge the assumption that decodable beliefs are actionable levers, instead arguing for interventions that target the procedural dynamics of execution rather than the high-level geometry of assessment.