Uncertainty

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Split conformal at alpha = 0.1 on 24,576 held-out predictions split in half delivers 0.8961 coverage against a finite-sample guarantee of 0.9001, and over 200 calibration splits a mean of 0.8999. Exactly what was promised....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. A model calibrated by construction - labels drawn from its own probabilities - scores an ECE of 0.085 on 200 predictions, 0.035 on 1,000 and 0.008 on 20,000 at 15 bins, and the fitted slope against bins/n is 0....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. On 10,240 next-character predictions from the committed model, accuracy is 0.5466 at all seven temperatures from 0.5 to 3, identical to the bit, while ECE runs from 0.026 to 0.375. Between predictions the confidence order moves: at T = 2 Kendall’s tau against T = 1 is 0....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Three training runs of the same 816,128-parameter model, evaluated at every checkpoint on 10,240 held-out predictions. Every run starts slightly underconfident; overconfidence begins after one to ten passes over the training text and grows as training loss pulls away from validation loss....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Over 200 random row splits of 24,576 predictions, realised conformal coverage at alpha = 0.1 has an SD of 0.0040, 1.49 times the Beta spread episode 1 compared it with. That comparison was short a term: the coverage is measured on a finite test half, and with the test half’s binomial variance added the excess is 1....

Disclosure: this post was written with the assistance of an AI system (Claude), which wrote the analysis code, ran the experiments and drafted the text. The topic, the constraints, the data choices and the final review are the author’s. Networks trained with dropout 0.5 were evaluated two ways: with dropout off and the weights scaled, and by averaging up to 300 sampled masks. On the digits the two agreed on 99....