eltociear/bishop-tasks-v1

bishop-tasks-v1

43 exact pattern-recognition tasks for the `bishop-env` RL environment, on the topics of Pattern Recognition and Machine Learning (Bishop): probability and Bayes, information theory, linear regression and ridge, naive Bayes, Bernoulli mixtures and EM, k-means, conjugate priors, and d-separation in directed graphical models.

Everything is exact

Every value is an integer or an exact rational, flattened as [numerator, denominator] in lowest terms. There is no float anywhere and no tolerance in the comparator, so a responsibility of 1/19 computed as 0.05263157894736842 does not pass. numpy is deliberately absent from the environment's sandbox for the same reason.

Every logarithm is base 2 and every argument is a power of two, so every entropy, KL divergence and cross entropy in the dataset is an exact rational. The joint distribution was chosen so that its marginals and conditionals are dyadic too, not just its cells — the failure mode being avoided is a joint of dyadic cells whose marginal comes out 5/8, at which point log2 is irrational and the exactness quietly stops holding. The builder's log2_exact raises on any non-dyadic argument, so the dataset cannot be built if that is ever violated.

How it was built and checked

Answer keys are computed by executing a reference solution, never typed. --verify then re-checks every task for determinism across two fresh runs, integer-only JSON-safe output, an exact serialisation round-trip, no repeated row inside one answer, and no duplicate of another task's answer. Wherever a second independent route to a number exists — the entropy chain rule both ways, all three forms of mutual information, Bayes in both directions, residual orthogonality, the ridge normal equations, exact interpolation, the Beta predictive against the posterior mean, two textbook formulas for the Gaussian posterior mean, monotone k-means distortion, and d-separation computed by both path enumeration and ancestral moralisation — the builder asserts the two agree and refuses to build if they do not.

That process caught seven real defects before publication, all of the same shape: a task asking for two quantities that are provably equal, which hands over half its own answer. They are documented in the environment README.

Original problems, not the book's exercises. Nothing is copied; the distributions, design matrices, counts and graph are invented. Bishop's worked examples are reproduced in thousands of lecture notes, so their numbers are memorisable rather than computable.

Source: <https://github.com/eltociear/my-molt-agent/tree/main/environments/bishop_env>