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Invertible Logits Transformation for Accuracy-Preserving Post-Hoc Uncertainty Calibration

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Confidence calibration objectives · 0 citations (OpenAlex)

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Proposes InvLT, a post-hoc calibrator that applies a shared scalar MLP element-wise to logits, with monotonicity softly enforced by a jointly trained inverse network reconstruction loss instead of UMNN-style numerical integration.

Problem

Post-hoc calibration of classifiers that is expressive enough to correct nonlinear miscalibration, scales to many classes, and preserves the argmax prediction, without the overhead of monotone calibrators that rely on numerical integration.

Approach

Train a shared scalar MLP f element-wise on logits jointly with an auxiliary inverse network g, using a reconstruction loss g(f(u)) ≈ u to softly encourage injectivity and hence strict monotonicity, avoiding UMNN's numerical quadrature; the parameter count is independent of the number of classes.

Key results

• On ImageNet ResNet-152 (val 5,000), InvLT reaches ECE 0.39% vs 0.56% for UMNN and 1.10% for the best non-preserving baseline (Spline).
• On CIFAR-100 (ResNet-50), InvLT achieves ECE 1.67% vs 2.48% for UMNN, and is 3.5x faster to fit than UMNN (22.7 s vs 80.2 s).
• On six CIFAR-100 architectures, InvLT has average ECE 2.41% vs 3.08% for the next-best method (PTS); the ablation shows the reconstruction loss restores classification error to 4.52% on CIFAR-10.

Surprising findings

• Without the reconstruction regularizer, classification error rises from 4.52% to 4.69% on CIFAR-10, showing an unregularized scalar map can alter argmax predictions.

Limitations

• Soft monotonicity via reconstruction loss gives no formal guarantee of global monotonicity or argmax preservation.
• Element-wise design cannot capture cross-class dependencies in miscalibration.
• Several non-InvLT architecture results are single-seed at default hyperparameters without grid search.

Experimental setup

Datasets: CIFAR-10 CIFAR-100 ImageNet

Benchmarks: CIFAR-10 CIFAR-100 ImageNet

Metrics: ECE AdaECE KDE-ECE NLL wall-clock fit and inference time

Baselines: Temperature Scaling Vector Scaling Matrix Scaling Ensemble Temperature Scaling Parameterized Temperature Scaling Histogram Binning Isotonic Regression Spline Calibration Dirichlet Calibration UMNN

Builds on: temperature scaling UMNN intra order-preserving calibration parameterized temperature scaling Adam

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