# Optimizing Chain-of-Thought Confidence via Topological and Dirichlet Risk Analysis

arXiv: https://arxiv.org/abs/2511.06437 · HTML: https://mlsanity.com/paper/2511.06437/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 12 of its 23 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## 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, 12 of 12)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [Maximizing Confidence Alone Improves Reasoning](https://mlsanity.com/paper/2505.22660/) (2025)
- [Chain of Preference Optimization: Improving Chain-of-Thought Reasoning in LLMs](https://mlsanity.com/paper/2406.09136/) (2024)
- [Think Twice Before Trusting: Self-Detection for Large Language Models through Comprehensive Answer Reflection](https://mlsanity.com/paper/2403.09972/) (2024)
- [Quantifying Uncertainty in Natural Language Explanations of Large Language Models](https://mlsanity.com/paper/2311.03533/) (2023)
- [FRIT: Using Causal Importance to Improve Chain-of-Thought Faithfulness](https://mlsanity.com/paper/2509.13334/) (2025)
- [NGAT: A Node-level Graph Attention Network for Long-term Stock Prediction](https://mlsanity.com/paper/2507.02018/) (2025)
- [GrACE: A Generative Approach to Better Confidence Elicitation and Efficient Test-Time Scaling in Large Language Models](https://mlsanity.com/paper/2509.09438/) (2025)
- [REHEARSE: Experiential Rehearsal for Verbal Confidence Calibration in Large Language Models](https://mlsanity.com/paper/2508.14390/) (2025)

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

- [Broken Chains: The Cost of Incomplete Reasoning in LLMs](https://mlsanity.com/paper/2602.14444/) (2026)

## Abstract (arXiv)

Chain-of-thought (CoT) prompting enables Large Language Models to solve complex problems, but deploying these models safely requires reliable confidence estimates, a capability where existing methods suffer from poor calibration and severe overconfidence on incorrect predictions. We propose Enhanced Dirichlet and Topology Risk (EDTR), a novel decoding strategy that combines topological analysis with Dirichlet-based uncertainty quantification to measure LLM confidence across multiple reasoning paths. EDTR treats each CoT as a vector in high-dimensional space and extracts eight topological risk features capturing the geometric structure of reasoning distributions: tighter, more coherent clusters indicate higher confidence while dispersed, inconsistent paths signal uncertainty. We evaluate EDTR against three state-of-the-art calibration methods across four diverse reasoning benchmarks spanning olympiad-level mathematics (AIME), grade school math (GSM8K), commonsense reasoning, and stock price prediction citezhang2025aime, cobbe2021training, talmor-etal-2019-commonsenseqa, yahoofinance. EDTR achieves 41% better calibration than competing methods with an average ECE of 0.287 and the best overall composite score of 0.672, while notably achieving perfect accuracy on AIME and exceptional calibration on GSM8K with an ECE of 0.107, domains where baselines exhibit severe overconfidence. Our work provides a geometric framework for understanding and quantifying uncertainty in multi-step LLM reasoning, enabling more reliable deployment where calibrated confidence estimates are essential.