README.md

metadata

license: apache-2.0
pretty_name: ultraviolet param-object pools
tags:
  - math
  - reinforcement-learning
  - synthetic
  - verifiable
configs:
  - config_name: default
    data_files:
      - split: train
        path: train.jsonl
      - split: eval
        path: eval.jsonl
      - split: eval_tier0
        path: eval_tier0.jsonl

ultraviolet param-object pools

Synthetic, exactly verifiable math construction problems for RL. Each item asks for a short integer tuple that parameterises a mathematical object (polynomial coefficients, matrix entries, a lattice point, a permutation, ...) with stated properties. Every item has a finite answer box, so all of its valid answers are enumerated exactly and stored in the row; any one valid answer is correct. Each item has 2-64 valid answers and a blind-guess success rate of at most 0.02.

split	file	rows	md5
train	train.jsonl	239,584	d59f16328d437c68d6b96caf0b0c44a8
eval	eval.jsonl	2,241	6a8c2cf0f50a53ac5ba0223ca74da4c8
eval_tier0 (tier 0 only)	eval_tier0.jsonl	324	d4fb551a4c6afd10198c78f0f1460f76

The eval splits share no problems with train.

Example

Find integers a, d with -10 <= a, d <= 10 such that the arithmetic progression a, a + d, a + 2d, ... has sum of its first 6 terms equal to 81. Several answers are possible; any one correct answer is accepted. Give one solution. End with the answer in the form \boxed{a = ..., d = ...}, with the dots replaced by the values.

Valid answers (meta.valid_answers): -9, 9, -4, 7, 1, 5, 6, 3.

Fields

problem (statement), prompt (Problem:\n{problem}\n\n<think>\n), answer (one valid answer), family, domain, tier (0-3, difficulty), n_valid, guess_rate, meta.params / meta.seed (the generator's inputs) and meta.valid_answers.

Usage

from datasets import load_dataset
ds = load_dataset("harribo11/ultraviolet-paramobj-pools", split="train")

Generator, verifier and scorer: workbench/envs/paramobj/ in github.com/hliuson/ultraviolet. There the tasks are registered as wb_po_<name>, and the rows here say cx_po_<name>, so rename the task field before scoring:

from ultraviolet.tasks.score import score
row = dict(row, task="wb_" + row["task"][3:])     # cx_po_ap_sum -> wb_po_ap_sum
score(row["task"], completion, row)               # 1.0 if the last \boxed{} after </think> is a valid answer

Families (53) and tiers

Train rows per tier, and eval rows per family:

family	domain	t0	t1	t2	t3	eval
po_ap_sum	sequence	186	842	1,979	1,998	48
po_binary_runs	combinatorics	15	43	73	64	32
po_circle_through	geometry	498	1,853	2,015	2,002	48
po_consecutive_sum	number	18	117	211	1,471	35
po_crt_range	number	1,987	2,037	1,989	2,033	48
po_diff_squares	number	26	30	52	119	14
po_egyptian	number	23	97	74	141	29
po_fraction_between	number	1,564	1,971	1,985	2,014	48
po_gauss_factor	number	33	166	453	1,926	36
po_gcd_lcm	number	280	774	1,170	91	48
po_gp_term	sequence	110	113	433	191	48
po_int_triangle	geometry	118	503	1,981	1,988	48
po_lattice_tri_area	geometry	1,611	1,956	2,001	2,009	48
po_lin2_box	number	1,995	2,011	2,029	2,008	48
po_lin_commute	function	756	1,599	2,008	2,018	48
po_lin_congruence	number	1,997	1,995	2,012	1,971	48
po_magic3	combinatorics	1,990	2,007	2,002	2,013	48
po_mat2_commute	linalg	2,017	2,032	1,999	2,014	48
po_mat2_eigvec	linalg	679	963	1,149	1,293	48
po_mat2_idempotent	linalg	47	715	1,364	2,023	37
po_mat2_involution	linalg	42	609	1,318	1,999	44
po_mat2_nilpotent	linalg	48	456	846	2,011	36
po_mat2_trdet	linalg	181	735	1,887	2,032	48
po_mat3_det	linalg	2,027	1,990	1,993	2,043	48
po_mobius	function	1,014	1,466	2,000	2,007	48
po_moment_weights	combinatorics	107	328	675	928	48
po_order_mod	number	22	154	528	1,680	36
po_parallelogram	geometry	1,987	2,021	1,987	2,007	48
po_partition_sq	combinatorics	366	1,623	2,004	1,981	48
po_perm_cycles	combinatorics	19	45	45	517	35
po_perm_descents	combinatorics	76	248	248	424	48
po_perm_inversions	combinatorics	15	40	40	354	45
po_poly_critical	polynomial	258	1,998	1,997	1,942	48
po_poly_integral	polynomial	1,993	2,002	2,016	1,999	48
po_poly_mixed	polynomial	2,006	2,020	1,987	1,977	48
po_poly_roots	polynomial	32	62	143	68	19
po_poly_slope	polynomial	767	1,963	2,007	2,015	48
po_poly_values	polynomial	1,003	2,018	2,000	1,994	48
po_pyth_leg	number	25	80	242	867	29
po_pyth_perim	geometry	28	68	189	491	41
po_quad_rootdiff	polynomial	52	294	518	882	37
po_recur_coef	sequence	338	1,829	700	394	48
po_recur_init	sequence	1,008	1,915	2,019	1,982	48
po_sfft	number	1,461	1,987	1,986	1,991	48
po_sigma_inv	number	25	126	357	1,248	36
po_sqrt_mod	number	414	2,029	2,018	1,988	48
po_stats_multiset	combinatorics	32	103	193	1,610	36
po_tau_range	number	2,005	1,975	2,052	1,980	48
po_totient_inv	number	14	25	48	88	4
po_two_sq_comp	number	87	727	1,997	2,039	48
po_vec_cross	linalg	2,007	1,980	2,002	1,991	48
po_vec_dot	linalg	989	1,980	1,992	1,997	48
po_vieta3	polynomial	14	84	467	1,975	28
total		36,412	56,804	67,480	78,888