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This paper introduces Invertible Logits Transformation (InvLT), a novel method for post-hoc calibration that aligns predicted confidences with empirical accuracy without the need for retraining. InvLT employs a learned scalar MLP to transform pre-softmax logits while maintaining a constant parameter count independent of the number of classes, and it preserves the original classification predictions through a soft encouragement of monotonicity. Experimental results across various image classification benchmarks demonstrate that InvLT consistently outperforms existing calibration methods on standard metrics, highlighting its effectiveness in addressing nonlinear miscalibration and scalability issues.
InvLT achieves superior calibration performance without compromising classification accuracy or increasing parameter complexity, setting a new standard for post-hoc uncertainty calibration.
Post-hoc calibration aligns a classifier's predicted confidences with its empirical accuracy without retraining. An ideal calibrator should correct nonlinear miscalibration, scale gracefully to large label spaces, and preserve the original predictions; existing methods typically violate at least one of these properties---temperature scaling lacks expressivity, more flexible parametric alternatives introduce parameters that grow with the number of classes $C$, and other expressive methods do not preserve the rank ordering of class scores and may alter the predicted class. We propose \textbf{Invertible Logits Transformation (InvLT)}, which applies a learned scalar MLP $f:\mathbb{R}\to\mathbb{R}$ element-wise to the pre-softmax logits. Sharing $f$ across all logit dimensions makes the parameter count independent of $C$. Monotonicity of $f$---and hence preservation of the argmax prediction---is softly encouraged via a paired inverse network rather than enforced through the numerical integration required by prior monotone calibrators; this avoids their computational overhead while empirically preserving the original classification accuracy in every setting we evaluate. Across standard image classification benchmarks and a range of architectures, InvLT consistently outperforms a broad set of post-hoc baselines on standard calibration metrics.
