On Calibration of Modern Neural Networks

A model is calibrated when its confidence matches how often it is right: among predictions made with 0.8 confidence, about 80% are correct. The authors observe that a 5-layer LeNet from 1998 is close to calibrated on CIFAR-100, while a 110-layer ResNet from 2016 is more accurate but much more confident than it should be.

They measure calibration two ways. A reliability diagram sorts predictions into confidence bins and plots each bin's accuracy against its confidence; a calibrated model follows the diagonal. Expected calibration error (ECE) summarizes the gaps: the average difference between accuracy and confidence across bins, weighted by how many predictions fall in each.

Experiments on CIFAR-100 tie miscalibration to recent training practice. ECE rises with depth and width, rises with batch normalization, and falls as weight decay increases, even past the point where more weight decay hurts accuracy. The explanation offered is that networks keep reducing training loss by growing more confident after they classify the training set correctly; in one training curve, test loss overfits while test error keeps improving.

The authors then compare post-hoc calibration methods, all fitted on a held-out validation set: histogram binning, isotonic regression, Bayesian binning into quantiles, and three versions of Platt scaling (matrix, vector and temperature). Temperature scaling divides every logit by a single number T fitted by minimizing validation log loss. Because dividing by a positive number does not change which class has the largest logit, predictions and accuracy stay the same; only confidence changes. Across 15 image models and 4 text models, temperature scaling was usually the best method or close to it, cut ECE on every vision model, and beat more flexible scaling methods that can overfit.

Thresholds assume calibration. "Auto-approve when confidence is above 0.9" works only if 0.9 means roughly 90% correct. On an overconfident model, that threshold lets through far more errors than the number suggests. Before setting any confidence-based routing, check a reliability diagram on validation data from the customer's distribution.

The fix is cheap and safe. Temperature scaling needs a few thousand labeled validation examples, one parameter and a line of code at inference. It cannot change which answer the model gives, so accuracy metrics and downstream behavior that depend only on the top answer are untouched. That makes it easy to ship.

Calibration lowers coverage. Once confidence is honest, fewer predictions clear a high threshold. In our simulation, the share of predictions above 0.9 dropped from 30% to 1% after calibration, and their accuracy rose from 65% to 97%. Set expectations with the customer: calibrated thresholds mean more cases for review, and the reviewed cases are the right ones.

It applies to language models. Token probabilities and classifier heads on top of LLMs (routers, guardrail classifiers, yes/no judges) are used as confidence all the time. The same check and the same one-parameter fix apply, and routing systems that escalate low-confidence cases depend on it.

Recalibrate after drift. Calibration is fitted to a distribution. When inputs shift, or the model is fine-tuned or replaced, refit the temperature and recheck the reliability diagram.