LLMs are Overconfident: Evaluating Confidence Interval Calibration with FermiEval
A Deep Dive into LLM Uncertainty Quantification
This analysis explores the overconfidence observed in Large Language Models when generating confidence intervals for numerical estimations. We introduce FermiEval, a new benchmark, and present methods to improve calibration.
Executive Summary: Bridging the Confidence Gap
Leading LLMs consistently exhibit overconfidence, with nominal 99% confidence intervals covering true values only 65% of the time. This has significant implications for enterprise applications requiring precise uncertainty quantification. Our research outlines a new benchmark, FermiEval, and demonstrates how conformal prediction can restore accurate coverage, halving the Winkler score.
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Actual 99% CI Coverage
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Winkler Score Reduction
New
FermiEval Benchmark
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
LLM Overconfidence Revealed
Our study with FermiEval exposes a systemic issue: LLMs are consistently overconfident in their numerical estimations. Nominal 99% intervals only cover the truth ~65% of the time, highlighting a critical gap in uncertainty calibration.
65%
Average Observed Coverage for Nominal 99% CIs
FermiEval Calibration Process
Elicit Base CIs
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Compute Nonconformity Scores
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Sort Scores
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Select Quantile
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Conformalize Interval
Strategies for Better Calibration
We explore various methods to re-calibrate LLM confidence intervals, including conformal prediction and log-probability elicitation, demonstrating significant improvements in observed coverage and interval sharpness.
| Method | Coverage | Winkler Score |
|---|---|---|
| Baseline LLM | 65% | 321.91 |
| Conformal Prediction | 99% | 122.24 |
| Log-Probability | 90% | 191.03 |
Explaining Overconfidence: The Perception Tunnel
Our novel 'perception-tunnel' theory suggests LLMs reason over a truncated slice of their inferred distribution, neglecting tails. This explains the observed stagnant coverage and motivates new scoring rules.
Impact of Perception Tunnel
The 'perception-tunnel' hypothesis posits that LLMs operate as if sampling from a truncated region of their inferred distribution, leading to systematic overconfidence. This theoretical framework aligns with empirical observations where LLMs struggle to assign appropriate probabilities to extreme outcomes. By understanding this mechanism, we can develop more robust calibration techniques that account for the model's inherent limitations in perceiving the full spectrum of uncertainty. For instance, a model might only 'see' a 50% central region of its true belief, leading to a much narrower reported confidence interval than is actually warranted.
Highlight: Truncated reasoning leads to systematic overconfidence and underestimation of rare events.
Quantify Your AI Efficiency Gains
Use our interactive ROI calculator to estimate the potential efficiency gains and cost savings from implementing advanced AI calibration strategies in your enterprise.
Your Roadmap to Calibrated AI
A structured approach to integrating uncertainty-aware AI, ensuring reliable and trustworthy model outputs for critical decision-making.
Phase 1: Assessment & Benchmarking
Evaluate current LLM performance against FermiEval, identifying key overconfidence patterns.
Phase 2: Calibration Strategy Design
Develop and customize conformal prediction or log-probability elicitation strategies.
Phase 3: Implementation & Integration
Deploy calibrated models into your existing enterprise AI infrastructure.
Phase 4: Continuous Monitoring & Refinement
Establish ongoing monitoring to ensure sustained calibration and performance.
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Don't let overconfident AI undermine your critical decisions. Partner with us to implement robust calibration strategies that ensure your LLMs deliver accurate and trustworthy uncertainty estimates.
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