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 a 20% test split of the UCI digits, 360 images, logistic regression, an RBF SVM and 3-NN score 0.967, 0.986 and 0.986, and one test set’s 95% binomial interval is about +-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. Two character transformers, identical in architecture, parameters, seed, steps, schedule and training problems. The one manipulated variable is the order of the lines in the training file. Packed in generation order, every reversed sum lands directly beneath the forward form of the same sum - 5,076 of 5,076, which is all of them - and ‘reverse the line above’ answers the question with no arithmetic....
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. relu, abs, clamp, hardtanh and a vector norm all return 0 at their kinks; maximum, minimum and max split the tie and return 0.5; and sqrt(x·x), which is abs(x), returns nan where abs returns 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. Persistent homology arrives with a large vocabulary and, in dimension zero, a very small computation: walk the edges shortest first and record the length of each one that joins two components. That is the single-linkage dendrogram’s merge heights, and not approximately — the two return arrays that are equal float for float, on four designs from 12 to 60 points and 1 to 30 dimensions....
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. The optimiser everyone uses is an ODE solver, and that is an identity rather than an analogy: gradient descent is forward Euler on the gradient flow. So the learning rate is a step size, and step sizes have stability limits....
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 2,000 simulated least-squares datasets of 100 rows, where the exact test error of each fitted model is known, the correlation between the 10-fold CV estimate and that error is -0.01. The CV estimates spread 2....
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. The softmax Jacobian is diag(p) minus p pᵀ, its quadratic form is exactly a variance under p, and so its spectral norm is trapped between m(1 - m) and 2m(1 - m) where m is the largest probability - checked on 25,443 random distributions with no violations and the upper end attained to nine digits....
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 measurements, and the third one reversed the plan. First: the H0 death spread, as a fraction of its own mean, falls from 4.87 at two dimensions to 0.078 at 768 on pure noise....