ResearchResearch paperTraining & Scaling · Large Language Models1 source · Oct 9, 2026

Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks

In this paper, we show that standard (post-hoc) calibrators can be trained end-to-end with the backbone via a bilevel Stackelberg formulation.

Key points

  • Neural networks (NNs), while highly flexible and versatile, are often poorly calibrated.
  • Post-hoc calibration methods adjust the outputs of an already trained model using a separate calibration dataset and additional calibration parameters.
  • This formulation eliminates the need for a separate calibration set or a dedicated calibration loss by jointly optimizing accuracy and calibration using cross-entropy, introducing only one additional hyperparameter: the calibrator learning rate.
  • Although our framework supports calibrators ranging from temperature and matrix scaling to NN layers, our results show that using the final classification layer itself as the calibrator yields accurate, well-calibrated models with no additional parameters.

Sources (1)

Extractive summary: sentences quoted from the sources.

Related