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Class Adaptive Conformal Training

NeurIPS 2026 · Learning theory and algorithms › Prediction and decision losses · approach: Conformal prediction sets · 0 citations (OpenAlex)

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Proposes Class Adaptive Conformal Training (CaCT), which learns per-class penalty multipliers via an augmented Lagrangian method (with PHR penalty) to shape class-conditional prediction sets during conformal training.

Problem

Conformal training with a single global size penalty produces inefficient, class-imbalanced prediction sets, especially with many classes or long-tailed label distributions.

Approach

Replace the single size-penalty weight with K class-wise constraints on average set size, solved by an augmented Lagrangian method that adaptively updates per-class multipliers and penalty parameters using a validation split, with a PHR penalty and differentiable smoothing of the conformal objective.

Key results

• On CIFAR100-LT with THR score, CaCT+ALM reduces set size to 3.03 vs 4.21 for the best prior baseline DPSM at alpha=0.1.
• On ImageNet-LT with THR, CaCT+ALM achieves set size 4.99 and coverage gap 4.40, vs ConfTr 6.60 and DPSM 5.78 set size.
• On balanced benchmarks, CaCT+ALM ranks first or second across datasets and scores, e.g. CIFAR100 set size 2.56 under THR versus 2.81 for DPSM.

Surprising findings

• The simple heuristic multiplier update (CaCT+HR) is competitive and often second-best to the ALM version.

Limitations

• Relies on a validation split for multiplier updates, which reduces data available for training and calibration.
• Smoothed differentiable approximations lose the formal marginal coverage guarantee during training, relying on test-time non-smooth calibration.
• Theoretical convergence guarantees for ALM are mainly in convex settings; the nonconvex deep learning case is empirical.

Experimental setup

Datasets: MNIST CIFAR-10 CIFAR-100 ImageNet ImageNet-LT 20 Newsgroups long-tailed MNIST/CIFAR10/CIFAR100 (gamma=0.1)

Benchmarks: MNIST-LT CIFAR10-LT CIFAR100-LT ImageNet-LT MNIST CIFAR10 CIFAR100 ImageNet 20 Newsgroups

Metrics: average set size marginal coverage coverage gap top-k accuracy

Baselines: CE Focal loss ConfTr CUT InfoCTr DPSM

Builds on: ConfTr Split conformal prediction augmented Lagrangian method CUT InfoCTr

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