Parham Sharafoleslami

arXiv2026

Visualizing and Benchmarking LLM Factual Hallucination Tendencies via Internal State Analysis and Clustering

Large Language Models (LLMs) often hallucinate, generating nonsensical or false information that can be especially harmful in sensitive fields such as medicine or law. To study this phenomenon systematically, we introduce FalseCite, a curated dataset designed to capture and benchmark hallucinated responses induced by misleading or fabricated citations. Running GPT-4o-mini, Falcon-7B, and Mistral 7-B through FalseCite, we observed a noticeable increase in hallucination activity for false claims with deceptive citations, especially in GPT-4o-mini. Using the responses from FalseCite, we can also analyze the internal states of hallucinating models, visualizing and clustering the hidden state vectors. From this analysis, we noticed that the hidden state vectors, regardless of hallucination or non-hallucination, tend to trace out a distinct horn-like shape. Our work underscores FalseCite's potential as a foundation for evaluating and mitigating hallucinations in future LLM research.

cs.CL↗

arXiv2025

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

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 \cite{zhang2025aime, cobbe2021training, talmor-etal-2019-commonsenseqa, yahoo_finance}. 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.

cs.AI↗