Energy-Based Open-World Uncertainty Modeling for Confidence Calibration

TL;DR

This paper introduces a novel energy-based open-world softmax model that enhances confidence calibration in neural networks by explicitly modeling uncertainty through an additional dimension, addressing overconfidence issues.

Contribution

It proposes a $K$+1-way softmax with an energy-based objective to better model open-world uncertainty, a novel approach in confidence calibration.

Findings

Outperforms existing methods in confidence calibration tasks

Effectively models open-world uncertainty with the extra dimension

Theoretically links the energy-based objective to data distribution

Abstract

Confidence calibration is of great importance to the reliability of decisions made by machine learning systems. However, discriminative classifiers based on deep neural networks are often criticized for producing overconfident predictions that fail to reflect the true correctness likelihood of classification accuracy. We argue that such an inability to model uncertainty is mainly caused by the closed-world nature in softmax: a model trained by the cross-entropy loss will be forced to classify input into one of $K$ pre-defined categories with high probability. To address this problem, we for the first time propose a novel $K$+1-way softmax formulation, which incorporates the modeling of open-world uncertainty as the extra dimension. To unify the learning of the original $K$-way classification task and the extra dimension that models uncertainty, we propose a novel energy-based objective function, and moreover, theoretically prove that optimizing such an objective essentially forces the extra dimension to capture the marginal data distribution. Extensive experiments show that our approach, Energy-based Open-World Softmax (EOW-Softmax), is superior to existing state-of-the-art methods in improving confidence calibration.