Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Directional Concentration Uncertainty: A representational approach to uncertainty quantification for generative models

Souradeep Chattopadhyay, Brendan Kennedy, Sai Munikoti, Soumik Sarkar, Karl Pazdernik

TL;DR

Uncertainty quantification for generative models is challenging when relying on task-specific heuristics. The authors introduce Directional Concentration Uncertainty (DCU), an embedding-based, geometry-driven UQ method that models multiple outputs as samples on the unit sphere via a von Mises-Fisher distribution, using the concentration parameter $\kappa$ as the uncertainty score. Across unimodal QA and multimodal visual QA tasks, DCU achieves competitive calibration with, and in some cases exceeds, semantic entropy (SE), demonstrating strong generalization across modalities without relying on semantic clustering. While DCU shows promise as a generalizable UQ framework for multi-modal and agentic systems, it requires multiple samples and depends on the quality of the embedding encoders, indicating avenues for future improvement.

Abstract

In the critical task of making generative models trustworthy and robust, methods for Uncertainty Quantification (UQ) have begun to show encouraging potential. However, many of these methods rely on rigid heuristics that fail to generalize across tasks and modalities. Here, we propose a novel framework for UQ that is highly flexible and approaches or surpasses the performance of prior heuristic methods. We introduce Directional Concentration Uncertainty (DCU), a novel statistical procedure for quantifying the concentration of embeddings based on the von Mises-Fisher (vMF) distribution. Our method captures uncertainty by measuring the geometric dispersion of multiple generated outputs from a language model using continuous embeddings of the generated outputs without any task specific heuristics. In our experiments, we show that DCU matches or exceeds calibration levels of prior works like semantic entropy (Kuhn et al., 2023) and also generalizes well to more complex tasks in multi-modal domains. We present a framework for the wider potential of DCU and its implications for integration into UQ for multi-modal and agentic frameworks.

Directional Concentration Uncertainty: A representational approach to uncertainty quantification for generative models

TL;DR

Uncertainty quantification for generative models is challenging when relying on task-specific heuristics. The authors introduce Directional Concentration Uncertainty (DCU), an embedding-based, geometry-driven UQ method that models multiple outputs as samples on the unit sphere via a von Mises-Fisher distribution, using the concentration parameter as the uncertainty score. Across unimodal QA and multimodal visual QA tasks, DCU achieves competitive calibration with, and in some cases exceeds, semantic entropy (SE), demonstrating strong generalization across modalities without relying on semantic clustering. While DCU shows promise as a generalizable UQ framework for multi-modal and agentic systems, it requires multiple samples and depends on the quality of the embedding encoders, indicating avenues for future improvement.

Abstract

In the critical task of making generative models trustworthy and robust, methods for Uncertainty Quantification (UQ) have begun to show encouraging potential. However, many of these methods rely on rigid heuristics that fail to generalize across tasks and modalities. Here, we propose a novel framework for UQ that is highly flexible and approaches or surpasses the performance of prior heuristic methods. We introduce Directional Concentration Uncertainty (DCU), a novel statistical procedure for quantifying the concentration of embeddings based on the von Mises-Fisher (vMF) distribution. Our method captures uncertainty by measuring the geometric dispersion of multiple generated outputs from a language model using continuous embeddings of the generated outputs without any task specific heuristics. In our experiments, we show that DCU matches or exceeds calibration levels of prior works like semantic entropy (Kuhn et al., 2023) and also generalizes well to more complex tasks in multi-modal domains. We present a framework for the wider potential of DCU and its implications for integration into UQ for multi-modal and agentic frameworks.
Paper Structure (24 sections, 24 equations, 1 figure, 2 tables)

This paper contains 24 sections, 24 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Problem Formulation
  5. Differentiation with Semantic Entropy
  6. The Directional Concentration Measure
  7. Experiments and Results
  8. Datasets and Sampling Strategy
  9. Implementation Details
  10. Models
  11. Prompting and Generation
  12. Performance Evaluation and Baseline
  13. Results and Discussion
  14. Application to Simple QA Tasks
  15. Application to visual QA tasks
  16. ...and 9 more sections

Figures (1)

  • Figure 1: A schematic representation of the directional consistency measure using two LLM queries from TriviaQA evaluated with LLaMA-2. For each query, 10 generations were sampled and encoded using the e5-large-v2 model to obtain embeddings. The radial plots illustrate the angular dispersion of the embeddings relative to the estimated mean direction.