Datasets:

eltociear
/

bishop-tasks-v1

task_id stringlengths 6 6	category stringclasses 7 values	prompt stringlengths 53 280	api_description stringclasses 1 value	expected_output stringlengths 18 63
bi-000	probability	Give the marginal distribution P(X) over X = 0, 1, 2. Return one row of three rationals, so six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 2, 1, 4, 1, 4]]}
bi-001	probability	Give the marginal distribution P(Y) over Y = 0, 1. Return one row of two rationals, so four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 2, 1, 2]]}
bi-002	probability	Give the conditional distribution P(Y \| X = 0) as two rationals, then P(Y \| X = 1), then P(Y \| X = 2). Return three rows of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 2, 1, 2], [1, 1, 0, 1], [0, 1, 1, 1]]}
bi-003	probability	Are X and Y independent? Answer 1 for yes or 0 for no, then give P(X=1, Y=0) and the product P(X=1)P(Y=0) as two rationals, in that order. Return one row of five integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[0, 1, 4, 1, 8]]}
bi-004	probability	For the diagnostic test, give P(+) and then P(D \| +), as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[297, 10000, 1, 3]]}
bi-005	probability	For the diagnostic test, give P(not D \| +) and P(D \| -), as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[2, 3, 1, 9703]]}
bi-006	information-theory	Give H(X), H(Y) and H(X, Y) in bits, as three rationals. Return one row of six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[3, 2, 1, 1, 2, 1]]}
bi-007	information-theory	Give H(Y \| X) and then H(X \| Y) in bits, each computed as an average of conditional entropies rather than as a difference of entropies. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 2, 1, 1]]}
bi-008	information-theory	Give I(X; Y) in bits. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 2]]}
bi-009	information-theory	Give KL(P \|\| Q) and KL(Q \|\| P) in bits, in that order, as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[11, 16, 5, 8]]}
bi-010	information-theory	Give H(P) and H(Q) in bits, as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[15, 8, 9, 4]]}
bi-011	information-theory	Give the two cross entropies H(P, Q) = -sum_w P(w) log2 Q(w) and H(Q, P) = -sum_w Q(w) log2 P(w), in that order, as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[41, 16, 23, 8]]}
bi-012	regression	Give X^T X for the design matrix XR. Return two rows of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[5, 15], [15, 55]]}
bi-013	regression	Give X^T y for XR and yr. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[20, 69]]}
bi-014	regression	Solve the normal equations for XR and yr. Give the two weights as rationals, intercept first. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[13, 10, 9, 10]]}
bi-015	regression	Give the five residuals y - Xw of the ordinary least-squares fit, as rationals, in order. Return one row of ten integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[-1, 5, -1, 10, 1, 1, -9, 10, 1, 5]]}
bi-016	regression	Give the ridge weights for lambda = 5, solving (X^T X + lambda I) w = X^T y, as two rationals, intercept first. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[11, 25, 26, 25]]}
bi-017	regression	Give the sum of squared residuals of the ordinary least-squares fit, as one rational. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[19, 10]]}
bi-018	regression	Fit the quadratic through XQ and yq exactly. Give the three coefficients as rationals, constant term first. Return one row of six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[2, 1, -2, 1, 1, 1]]}
bi-019	classification	Give the smoothed class priors p(A) and p(B), as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[7, 12, 5, 12]]}
bi-020	classification	Give the smoothed likelihoods p(f=1 \| A) for the three features, then the same for B. Return two rows of six integers each.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[5, 8, 1, 4, 7, 8], [1, 3, 2, 3, 1, 2]]}
bi-021	classification	For the query x = (1, 0, 1), give the unnormalised joint scores p(A) p(x \| A) and p(B) p(x \| B), as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[245, 1024, 5, 216]]}
bi-022	classification	For the query x = (1, 0, 1), give the posterior p(A \| x) and p(B \| x), as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1323, 1451, 128, 1451]]}
bi-023	classification	For the query x = (1, 0, 1), give 0 if naive Bayes predicts class A and 1 if it predicts class B, then give the posterior odds p(A \| x) / p(B \| x) as a rational. Return one row of three integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[0, 1323, 128]]}
bi-024	bayesian-inference	Give the parameters of the Beta posterior after the observed successes and failures, as two integers a and b. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[9, 6]]}
bi-025	bayesian-inference	Give the prior mean of the Bernoulli parameter, then its posterior mean, then the posterior variance ab / ((a+b)^2 (a+b+1)), as three rationals. Return one row of six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[2, 5, 3, 5, 3, 200]]}
bi-026	bayesian-inference	Give the maximum a posteriori estimate of the Bernoulli parameter, that is (a-1)/(a+b-2) for the posterior Beta(a, b), and then the maximum likelihood estimate from the data alone. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[8, 13, 7, 10]]}
bi-027	bayesian-inference	Give the three parameters of the Dirichlet posterior as integers, then the posterior predictive distribution over the three outcomes as three rationals. Return one row of three integers and then one row of six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[5, 2, 5], [5, 12, 1, 6, 5, 12]]}
bi-028	bayesian-inference	For the Gaussian with known variance, give the posterior precision and the posterior variance, as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[7, 4, 4, 7]]}
bi-029	bayesian-inference	For the Gaussian with known variance, give the posterior mean as a rational. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[22, 7]]}
bi-030	mixtures-em	For each of the three data points in order, give the two responsibilities as rationals. Return three rows of four integers each.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 19, 18, 19], [9, 11, 2, 11], [1, 163, 162, 163]]}
bi-031	mixtures-em	Give the likelihood of x1 = (1,1,0,1) under component 1, then under component 2, as two rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[3, 256, 27, 256]]}
bi-032	mixtures-em	Give the mixture probability p(x) for each of the three data points in order, as three rationals. Return one row of six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[19, 256, 11, 256, 163, 768]]}
bi-033	mixtures-em	Perform one M-step from those responsibilities. Give the two updated mixing coefficients as rationals. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[29875, 102201, 72326, 102201]]}
bi-034	mixtures-em	Perform one M-step from those responsibilities. Give the two updated component parameters as rationals, where each is the responsibility-weighted fraction of bits equal to 1. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[8522, 29875, 29806, 36163]]}
bi-035	mixtures-em	Run one k-means iteration from the given centroids. Give the six cluster assignments as 0 or 1, in point order. Return one row of six integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[0, 0, 0, 1, 1, 1]]}
bi-036	mixtures-em	Run one k-means iteration from the given centroids and give the two updated centroids, each as two rationals. Return two rows of four integers each.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 1, 4, 3], [28, 3, 8, 1]]}
bi-037	mixtures-em	Give the k-means distortion J after one iteration, that is the sum of squared distances from each point to its updated centroid under the updated assignment, as one rational. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[40, 3]]}
bi-038	graphical-models	For the directed graph, answer each of these d-separation questions with 1 for d-separated and 0 for not, in order: A ⊥ B \| {}; A ⊥ B \| {C}; A ⊥ B \| {D}; A ⊥ B \| {F}. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 0, 0, 0]]}
bi-039	graphical-models	Same question for: A ⊥ E \| {C, B}; D ⊥ E \| {C}; D ⊥ E \| {}; A ⊥ F \| {E}. Return one row of four integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[1, 1, 0, 1]]}
bi-040	graphical-models	Give the number of nodes, the number of directed edges, and the number of colliders — nodes with two or more parents. Return one row of three integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[6, 6, 2]]}
bi-041	graphical-models	Give the descendants of C and then the descendants of B, each as a count. Then give the size of the Markov blanket of C, that is its parents, its children and its children's other parents. Return one row of three integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[3, 4, 4]]}
bi-042	graphical-models	Take every variable to be binary. Give the number of free parameters of the factorised distribution — the sum over nodes of 2 raised to the number of parents — and then the number of free parameters of an unrestricted joint over the same variables. Return one row of two integers.	The tasks refer to these fixed objects. Every number here is exact. JOINT DISTRIBUTION P(X, Y), with X in {0,1,2} and Y in {0,1}: Y=0 Y=1 X=0 1/4 1/4 X=1 1/4 0 X=2 0 1/4 Every cell, every marginal and every conditional of this table is a power of two. Th...	{"rows": [[14, 63]]}

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.

field	meaning
`task_id`	`bi-000` … `bi-042`
`category`	probability / information-theory / regression / classification / bayesian-inference / mixtures-em / graphical-models
`prompt`	the question and the exact shape of the answer
`api_description`	the fixed distributions, matrices, counts and graph, plus the exact-arithmetic rules
`expected_output`	JSON `{"rows": [[int, ...], ...]}` — the executed reference answer

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

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