Aryama/qwen3.5-2b-grpo-solve
Text Generation • Updated
Datasets:
task stringclasses 1
value | split stringclasses 1
value | uid stringlengths 7 12 | dataset_row_index int64 5 102k | source_group_id stringlengths 16 16 | topic stringclasses 41
values | broad_topic stringclasses 4
values | difficulty float64 5 8 | difficulty_band stringclasses 2
values | question stringlengths 28 1.38k | final_answer stringlengths 1 81 | reference_solutions listlengths 3 3 | steps int64 6 8 | label stringclasses 2
values | error_position stringclasses 3
values | public dict | private dict | friend dict | source dict | answer_normalization null | training dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
judge | train | judge-5 | 5 | 78f8cb0ed7b859f1 | Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals | Calculus | 5 | lower | Find the length of the polar curve given by \( r = \sqrt{1 + \cos(2\theta)} \) for \( 0 \leq \theta \leq \frac{\pi\sqrt{2}}{4} \). | \dfrac{\pi}{2} | [
"Okay, so I need to find the length of the polar curve given by \\( r = \\sqrt{1 + \\cos(2\\theta)} \\) from \\( \\theta = 0 \\) to \\( \\theta = \\frac{\\pi\\sqrt{2}}{4} \\). Hmm, polar curves, arc length... I remember there's a formula for the arc length of a polar curve. Let me try to recall.\n\nI think the form... | 6 | correct | null | {
"problem": "Find the length of the polar curve given by \\( r = \\sqrt{1 + \\cos(2\\theta)} \\) for \\( 0 \\leq \\theta \\leq \\frac{\\pi\\sqrt{2}}{4} \\).",
"proposed_solution": [
{
"step_id": "S1",
"text": "Use the polar arc length formula: \\(L = \\int_a^b \\sqrt{r^2 + (dr/d\\theta)^2}\\,d\\the... | {
"label": "correct",
"first_error_step_id": null,
"first_error_explanation": null,
"error_type": null,
"error_position": null,
"teacher_target_response": "Decision: correct\nFirst wrong step: none\nExplanation: The solution correctly applies the polar arc length formula, simplifies r using the identity, an... | {
"assignment_id": "judge-test-5",
"split": "test",
"source_id": "deepmath-row-5",
"replacement_generation": 0,
"generation_record_sha256": "5958ec9e8b2ea115602f1edfa3bc91450d0720d83732b46e0085c3ba3b0ea1ad"
} | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {
"input": "Problem:\nFind the length of the polar curve given by \\( r = \\sqrt{1 + \\cos(2\\theta)} \\) for \\( 0 \\leq \\theta \\leq \\frac{\\pi\\sqrt{2}}{4} \\).\n\nProposed solution:\nS1: Use the polar arc length formula: \\(L = \\int_a^b \\sqrt{r^2 + (dr/d\\theta)^2}\\,d\\theta\\).\nS2: Simplify \\(r = \\sqrt{1... |
judge | train | judge-15 | 15 | 142bb2ab8c9c5d70 | Mathematics -> Algebra -> Intermediate Algebra -> Exponential Functions | Algebra | 7 | upper | Let $a, b, c, d$ be a permutation of the numbers $1, 9, 8, 4$. Define $n = (10a + b)^{10c + d}$. Calculate the probability that $1984!$ is divisible by $n$. Use Fermat's Little Theorem to assist in your calculations. | \dfrac{5}{6} | [
"Alright, so I need to solve this problem where we have a permutation of the numbers 1, 9, 8, 4 assigned to a, b, c, d. Then, we form the number n = (10a + b)^{10c + d}. The question is asking for the probability that 1984! is divisible by n. They also mention using Fermat's Little Theorem to assist in the calculat... | 7 | correct | null | {
"problem": "Let $a, b, c, d$ be a permutation of the numbers $1, 9, 8, 4$. Define $n = (10a + b)^{10c + d}$. Calculate the probability that $1984!$ is divisible by $n$. Use Fermat's Little Theorem to assist in your calculations.",
"proposed_solution": [
{
"step_id": "S1",
"text": "There are 4! = 2... | {
"label": "correct",
"first_error_step_id": null,
"first_error_explanation": null,
"error_type": null,
"error_position": null,
"teacher_target_response": "Decision: correct\nFirst wrong step: none\nExplanation: The solution correctly counts the valid permutations and obtains 5/6."
} | {
"assignment_id": "judge-train-15",
"split": "train",
"source_id": "deepmath-row-15",
"replacement_generation": 0,
"generation_record_sha256": "b2847b9736a00c4391b08a89db94c2176e00ce9bfa7d97afe9cee7106c182cc0"
} | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {
"input": "Problem:\nLet $a, b, c, d$ be a permutation of the numbers $1, 9, 8, 4$. Define $n = (10a + b)^{10c + d}$. Calculate the probability that $1984!$ is divisible by $n$. Use Fermat's Little Theorem to assist in your calculations.\n\nProposed solution:\nS1: There are 4! = 24 permutations of the digits 1, 9, 8... |
judge | train | judge-18 | 18 | b96f93d627107c5b | Mathematics -> Number Theory -> Prime Numbers | Number Theory | 8 | upper | Determine the limit of \( \frac{\pi(x)}{x} \) as \( x \to \infty \), where \( \pi(x) \) is the prime counting function. | 0 | [
"Okay, so I need to figure out the limit of π(x)/x as x approaches infinity. π(x) is the prime counting function, which means it gives the number of primes less than or equal to x. Alright, let me start by recalling what I know about prime numbers and their distribution.\n\nFirst off, primes are numbers greater tha... | 7 | incorrect | middle | {
"problem": "Determine the limit of \\( \\frac{\\pi(x)}{x} \\) as \\( x \\to \\infty \\), where \\( \\pi(x) \\) is the prime counting function.",
"proposed_solution": [
{
"step_id": "S1",
"text": "The prime counting function \\(\\pi(x)\\) counts the number of primes less than or equal to \\(x\\), s... | {
"label": "incorrect",
"first_error_step_id": "S4",
"first_error_explanation": "Dividing \\(\\pi(x) \\sim x/\\ln x\\) by \\(x\\) gives \\(\\pi(x)/x \\sim 1/\\ln x\\), not \\(1\\). The factor \\(1/\\ln x\\) cannot be dropped; since \\(\\ln x \\to \\infty\\), the ratio tends to \\(0\\), not \\(1\\).",
"error_typ... | {
"assignment_id": "judge-train-18",
"split": "train",
"source_id": "deepmath-row-18",
"replacement_generation": 0,
"generation_record_sha256": "9328cfcdb3d4cfff93675d54a900e1eeae66c7e33b4d1317c58e6a84970a1720"
} | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {
"input": "Problem:\nDetermine the limit of \\( \\frac{\\pi(x)}{x} \\) as \\( x \\to \\infty \\), where \\( \\pi(x) \\) is the prime counting function.\n\nProposed solution:\nS1: The prime counting function \\(\\pi(x)\\) counts the number of primes less than or equal to \\(x\\), so \\(\\pi(x)/x\\) is the proportion ... |
judge | train | judge-21 | 21 | 20b54484a90c0212 | Mathematics -> Calculus -> Differential Calculus -> Applications of Derivatives | Calculus | 5 | lower | "Find parametric equations for a unit circle with a speed of \\( e^t \\), starting from \\( x=1 \\),(...TRUNCATED) | \ln(2\pi + 1) | ["Okay, so I need to find parametric equations for a unit circle that starts at (1,0) and has a spee(...TRUNCATED) | 6 | incorrect | early | {"problem":"Find parametric equations for a unit circle with a speed of \\( e^t \\), starting from \(...TRUNCATED) | {"label":"incorrect","first_error_step_id":"S2","first_error_explanation":"At t=0, the point (1,0) c(...TRUNCATED) | {"assignment_id":"judge-train-21","split":"train","source_id":"deepmath-row-21","replacement_generat(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nFind parametric equations for a unit circle with a speed of \\( e^t \\), startin(...TRUNCATED) |
judge | train | judge-22 | 22 | 1ba30d6f74824494 | Mathematics -> Algebra -> Intermediate Algebra -> Other | Algebra | 6.5 | lower | "Using the generating function \\( \\sum_{n=0}^{\\infty}P_n(x)r^n=(1-2rx+r^2)^{-\\frac{1}{2}} \\), f(...TRUNCATED) | 1 | ["Okay, so I need to find the value of \\( P_n(1) \\) using the generating function provided. The ge(...TRUNCATED) | 6 | correct | null | {"problem":"Using the generating function \\( \\sum_{n=0}^{\\infty}P_n(x)r^n=(1-2rx+r^2)^{-\\frac{1}(...TRUNCATED) | {"label":"correct","first_error_step_id":null,"first_error_explanation":null,"error_type":null,"erro(...TRUNCATED) | {"assignment_id":"judge-test-22","split":"test","source_id":"deepmath-row-22","replacement_generatio(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nUsing the generating function \\( \\sum_{n=0}^{\\infty}P_n(x)r^n=(1-2rx+r^2)^{-\(...TRUNCATED) |
judge | train | judge-26 | 26 | 17ba09fb453f2688 | Mathematics -> Algebra -> Intermediate Algebra -> Quadratic Functions | Algebra | 5.5 | lower | "Find the minimum value of the product \\(abc\\) if the quadratic equation \\(ax^2 - bx + c = 0\\) h(...TRUNCATED) | 25 | ["Alright, so I need to find the minimum value of the product \\(abc\\) where \\(a\\), \\(b\\), and (...TRUNCATED) | 7 | incorrect | late | {"problem":"Find the minimum value of the product \\(abc\\) if the quadratic equation \\(ax^2 - bx +(...TRUNCATED) | {"label":"incorrect","first_error_step_id":"S6","first_error_explanation":"For 5x^2-5x+1=0, the root(...TRUNCATED) | {"assignment_id":"judge-train-26","split":"train","source_id":"deepmath-row-26","replacement_generat(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nFind the minimum value of the product \\(abc\\) if the quadratic equation \\(ax^(...TRUNCATED) |
judge | train | judge-27 | 27 | d746d51c63512715 | Mathematics -> Algebra -> Intermediate Algebra -> Quadratic Functions | Algebra | 5.5 | lower | "Find the maximum value of $x^2 + y^2$ given that $(x, y)$ satisfy the following equations:\n\\[ 2x^(...TRUNCATED) | \dfrac{5}{2} | ["Okay, so I need to find the maximum value of \\( x^2 + y^2 \\) given that the point \\( (x, y) \\)(...TRUNCATED) | 7 | incorrect | middle | {"problem":"Find the maximum value of $x^2 + y^2$ given that $(x, y)$ satisfy the following equation(...TRUNCATED) | {"label":"incorrect","first_error_step_id":"S5","first_error_explanation":"From \\(xy=-1\\) and \\(y(...TRUNCATED) | {"assignment_id":"judge-train-27","split":"train","source_id":"deepmath-row-27","replacement_generat(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nFind the maximum value of $x^2 + y^2$ given that $(x, y)$ satisfy the following (...TRUNCATED) |
judge | train | judge-28 | 28 | 55dacca098e40de6 | Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals | Calculus | 8 | upper | "Determine whether the following statement is true or false: \"Any bounded sequence in $L^4[0,1]$ ha(...TRUNCATED) | B | ["Okay, so I need to figure out if the statement \"Any bounded sequence in \\( L^4[0,1] \\) has a co(...TRUNCATED) | 6 | correct | null | {"problem":"Determine whether the following statement is true or false: \"Any bounded sequence in $L(...TRUNCATED) | {"label":"correct","first_error_step_id":null,"first_error_explanation":null,"error_type":null,"erro(...TRUNCATED) | {"assignment_id":"judge-train-28","split":"train","source_id":"deepmath-row-28","replacement_generat(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nDetermine whether the following statement is true or false: \"Any bounded sequen(...TRUNCATED) |
judge | train | judge-30 | 30 | 3100c08bfd04ebe5 | Mathematics -> Calculus -> Integral Calculus -> Integrals | Calculus | 6.5 | lower | "Determine whether the following inequality is true for all real numbers $0 < r < 1$ and $t \\geq 0$(...TRUNCATED) | True | ["Okay, so I need to figure out if the inequality\n\n\\[\n\\int_t^{t+r} \\sin(x)\\, dx \\leq \\int_{(...TRUNCATED) | 6 | correct | null | {"problem":"Determine whether the following inequality is true for all real numbers $0 < r < 1$ and (...TRUNCATED) | {"label":"correct","first_error_step_id":null,"first_error_explanation":null,"error_type":null,"erro(...TRUNCATED) | {"assignment_id":"judge-train-30","split":"train","source_id":"deepmath-row-30","replacement_generat(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nDetermine whether the following inequality is true for all real numbers $0 < r <(...TRUNCATED) |
judge | train | judge-31 | 31 | cf0bbd3086f1a3da | Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers | Algebra | 8 | upper | "Let $E \\subset \\mathbb{C}$ be a set such that for any sequence of distinct elements $(e_n)_{n \\i(...TRUNCATED) | Yes | ["Okay, let me try to figure out this problem. So, the question is: If a set E in the complex number(...TRUNCATED) | 6 | correct | null | {"problem":"Let $E \\subset \\mathbb{C}$ be a set such that for any sequence of distinct elements $((...TRUNCATED) | {"label":"correct","first_error_step_id":null,"first_error_explanation":null,"error_type":null,"erro(...TRUNCATED) | {"assignment_id":"judge-train-31","split":"train","source_id":"deepmath-row-31","replacement_generat(...TRUNCATED) | {
"dataset": "zwhe99/DeepMath-103K",
"selection": "judge_data/judge-final-4604"
} | null | {"input":"Problem:\nLet $E \\subset \\mathbb{C}$ be a set such that for any sequence of distinct ele(...TRUNCATED) |
End of preview. Expand in Data Studio
FINAL-v3: SOLVE, JUDGE and RECONSTRUCT
Three mathematical tasks built from DeepMath-103K, for studying how training on one task transfers to the others. 4,000 questions per task, 3,600 train / 400 test. No question appears in two tasks or in both splits; the tasks are matched by topic and difficulty distribution, not item by item.
| Config | Model sees | Model produces | Items |
|---|---|---|---|
solve |
a maths problem | a solution with one final answer | drawn from DeepMath-103K to match the other tasks cell by cell |
judge |
a problem + a solution split into steps S1…Sn | Decision: correct/incorrect, the first wrong step, why |
2,000 correct / 2,000 incorrect verified items from a teammate's generation pipeline (test: 200 / 200) |
reconstruct |
a final answer + 4 observations (the question is hidden) | the original question | clues written by DeepSeek V4.1 Flash, then audited and corrected so they do not give the question away |
from datasets import load_dataset
solve = load_dataset("Aryama/deepmath-solve-judge-reconstruct", "solve")
judge_test = load_dataset("Aryama/deepmath-solve-judge-reconstruct", "judge", split="test")
Construction
- Topics: Algebra, Calculus, Discrete Mathematics, Number Theory (37 DeepMath topic paths).
- Difficulty: DeepMath 5.0–8.0 in steps of 0.5; about 30% of each task in 7.0–8.0.
- Cells: 28 (topic × difficulty). Test questions are spread over cells in proportion to cell size; JUDGE also balances labels within each cell.
- One question, one task: questions are compared after whitespace and case normalisation, so every DeepMath duplicate counts as the same question.
- JUDGE trimming: all five-step solutions were removed (they were 79% incorrect, a label shortcut).
- Seed 20260928. SHA-256 of the source DeepMath parquet files is in
manifests/summary.json; file checksums inmanifests/CHECKSUMS.txt.
Every row has a training block (input, chain_of_thought, final_answer). JUDGE rows keep the answer key in
private (label, first wrong step, explanation, error type) and the model input in public. RECONSTRUCT rows keep
the model input in public_input and the hidden question in question.
Development slices and training orders (manifests/)
| File | Contents |
|---|---|
opd-trial-{task}.json |
seeded, disjoint train (512) and dev (200) uid slices of each task's train split; the 200-question dev slice is never trained on |
opd-matrix-{task}.json |
the single-task GRPO training order: every train question except the dev slice, shuffled |
grpo-mixed-1134.json |
the mixed-task GRPO order: the first 1,134 questions of each task, interleaved |
Models and results
LoRA adapters trained with Dr. GRPO on these tasks (Qwen3.5-2B): SOLVE · JUDGE · RECONSTRUCT · mixed. Code, scorers (rule-based SOLVE checker, strict format gates) and reports: github.com/MukundHebbar/anlp-project.
Limitations
- Tasks use different questions, so one cannot ask whether a model solves the same question it judges.
- JUDGE errors are injected into otherwise valid solutions; they are shorter and cleaner than real model errors.
- RECONSTRUCT is scored by an LLM rubric; the original question is one of several valid reconstructions.
- DeepMath reference solutions (
reference_solutions,training.chain_of_thought) are long and not verified by us.
Authors
Aryama V Murthy, Mukund Hebbar, Yashas Nataraj Kotre, Anivarth Varma Penumetcha (IIIT Hyderabad, Advanced NLP, Monsoon 2026). Released under MIT, the license of DeepMath-103K.
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