Different open-ended generation tasks require different degrees of output diversity. However, current LLMs are often miscalibrated. They collapse to overly homogeneous outputs for creative tasks and hallucinate diverse but incorrect responses for factual tasks. We argue that these two failure modes are unified by, and can both be addressed by, the notion of effective generation space size (GSS) -- the set of semantically distinct outputs a model considers for a prompt. We present GSSBench, a task suite of prompt pairs with ground-truth GSS relationships to assess different metrics and understand where models diverge from desired behavior. We find that hallucination detection metrics, particularly EigenScore, consistently outperform standard diversity and uncertainty quantification metrics, while using only model internals, providing interpretable insights into a model's internal task representations. We demonstrate three applications of GSS: (1) detecting prompt ambiguity and predicting clarification questions for better grounding, (2) interpreting overthinking and underthinking in reasoning models, and (3) steering models to expand their generation space to yield high-quality and diverse outputs.

Detecting hallucinations in large language models (LLMs) remains a fundamental challenge for their trustworthy deployment. Going beyond basic uncertainty-driven hallucination detection frameworks, we propose a simple yet powerful method that quantifies uncertainty by measuring the effective rank of hidden states derived from multiple model outputs and different layers. Grounded in the spectral analysis of representations, our approach provides interpretable insights into the model's internal reasoning process through semantic variations, while requiring no extra knowledge or additional modules, thus offering a combination of theoretical elegance and practical efficiency. Meanwhile, we theoretically demonstrate the necessity of quantifying uncertainty both internally (representations of a single response) and externally (different responses), providing a justification for using representations among different layers and responses from LLMs to detect hallucinations. Extensive experiments demonstrate that our method effectively detects hallucinations and generalizes robustly across various scenarios, contributing to a new paradigm of hallucination detection for LLM truthfulness.

As large language models (LLMs) are increasingly deployed across various industries, concerns regarding their reliability, particularly due to hallucinations - outputs that are factually inaccurate or irrelevant to user input - have grown. Our research investigates the relationship between the training process and the emergence of hallucinations to address a key gap in existing research that focuses primarily on post hoc detection and mitigation strategies. Using models from the Pythia suite (70M - 12B parameters) and several hallucination detection metrics, we analyze hallucination trends throughout training and explore LLM internal dynamics. We introduce Sensitivity Dropout (SenD), a novel training protocol designed to mitigate hallucinations by reducing variance during training. SenD achieves this by deterministically dropping embedding indices with significant variability, referred to as Sensitive Embedding Indices. In addition, we develop an unsupervised hallucination detection metric, Efficient EigenScore (EES), which approximates the traditional EigenScore at 2x speed. This efficient metric is integrated into our protocol, allowing SenD to be both computationally scalable and effective at reducing hallucinations. Our empirical evaluation demonstrates that our approach improves LLM reliability at test time by up to 40% compared to normal training while also providing an efficient method to improve factual accuracy when adapting LLMs to Wikipedia, Medical, and LegalBench domains.

Knowledge hallucination have raised widespread concerns for the security and reliability of deployed LLMs. Previous efforts in detecting hallucinations have been employed at logit-level uncertainty estimation or language-level self-consistency evaluation, where the semantic information is inevitably lost during the tokendecoding procedure. Thus, we propose to explore the dense semantic information retained within LLMs' INternal States for hallucInation DEtection (INSIDE). In particular, a simple yet effective EigenScore metric is proposed to better evaluate responses' self-consistency, which exploits the eigenvalues of responses' covariance matrix to measure the semantic consistency/diversity in the dense embedding space. Furthermore, from the perspective of self-consistent hallucination detection, a test time feature clipping approach is explored to truncate extreme activations in the internal states, which reduces overconfident generations and potentially benefits the detection of overconfident hallucinations. Extensive experiments and ablation studies are performed on several popular LLMs and questionanswering (QA) benchmarks, showing the effectiveness of our proposal. Large Language Models (LLMs) have recently achieved a milestone breakthrough and demonstrated impressive abilities in various applications (Ouyang et al., 2022; OpenAI, 2023). However, it has been widely observed that even the state-of-the-art LLMs often make factually incorrect or nonsense generations (Cohen et al., 2023; Ren et al., 2022; Kuhn et al., 2022), which is also known as knowledge hallucination (Ji et al., 2023). The potentially unreliable generations make it risky to deploy LLMs in practical scenarios.

Dimension reduction and data visualization aim to project a high-dimensional dataset to a low-dimensional space while capturing the intrinsic structures in the data. It is an indispensable part of modern data science, and many dimensional reduction and visualization algorithms have been developed. However, different algorithms have their own strengths and weaknesses, making it critically important to evaluate their relative performance for a given dataset, and to leverage and combine their individual strengths. In this paper, we propose an efficient spectral method for assessing and combining multiple visualizations of a given dataset produced by diverse algorithms. The proposed method provides a quantitative measure -- the visualization eigenscore -- of the relative performance of the visualizations for preserving the structure around each data point. Then it leverages the eigenscores to obtain a consensus visualization, which has much improved { quality over the individual visualizations in capturing the underlying true data structure.} Our approach is flexible and works as a wrapper around any visualizations. We analyze multiple simulated and real-world datasets from diverse applications to demonstrate the effectiveness of the eigenscores for evaluating visualizations and the superiority of the proposed consensus visualization. Furthermore, we establish rigorous theoretical justification of our method based on a general statistical framework, yielding fundamental principles behind the empirical success of consensus visualization along with practical guidance.