Datasets:

asingh15
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prm-sft-polaris-mc

messages listlengths 2 2	enable_thinking bool 1 class	id stringlengths 16 16	source stringclasses 1 value	sample_index int64 0 7	step_idx int64 0 2.26k	num_steps int64 1 2.26k	label stringclasses 1 value	correct bool 2 classes	loss_weight float64 1 1	reward float64 0 1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	1	0	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	1	4	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	1	8	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	1	12	12	yes	true	1	0.9375
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	0	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	4	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	8	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	12	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	16	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	20	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	8754a7c9a035fd12	polaris	0	23	23	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	0	0	18	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	0	4	18	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	0	8	18	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	0	12	18	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	0	16	18	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	0	18	18	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	0	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	4	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	8	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	12	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	16	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	20	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	24	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	16c10074af3b3015	polaris	1	28	28	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	6	0	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	6	4	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	6	8	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	6	12	12	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	0	0	15	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	0	4	15	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	0	8	15	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	0	12	15	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	217443ef5fd5c764	polaris	0	15	15	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	05a0b46b26de4904	polaris	0	0	48	yes	true	1	1
[ { "role": "user", "content": "# Role\nYou are an expert evaluator acting as a process reward model (PRM). You are given a\nproblem and a step-by-step solution that may be only a partial trace -- a prefix\nof a longer reasoning chain that can stop in the middle of a step. Judge whether the\nreasoning sho...	false	05a0b46b26de4904	polaris	0	4	48	yes	true	1	1

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PRM-SFT Polaris MC — Monte-Carlo value (unfiltered)

Soft-target process reward model (PRM) training data with per-prefix Monte-Carlo values, in the style of Math-Shepherd. Each row is one prefix of a reasoning trace on a Polaris math problem, labeled with

$V(\text{prefix}) = P(\text{correct} \mid \text{prefix}) = \frac{\#\text{correct continuations}}{\#\text{continuations}}$

estimated from N shared-prefix continuations sampled by Qwen3.5-4B.

This is the unfiltered set: every prefix is kept, including the fully-collapsed V=0 and V=1 prefixes. It is not filtered to mid-difficulty problems or to the uncertain V∈[0.1,0.9] band.

Splits

split	rows	notes
`train`	126,987
`validation`	2,471	128 problems held out by problem `id`

Value distribution (train)

bucket	fraction
`V == 0`	16.6%
`V == 1`	53.9%
`0 < V < 1`	29.4%
`V ∈ [0.1, 0.9]`	17.4%
`correct` (V ≥ 0.5)	75.5%

Mean V = 0.737. The mass at 0/1 reflects label collapse on problems the base model reliably solves or reliably fails — the reason value-filtered variants exist.

Columns

column	type	meaning
`messages`	list[dict]	chat turns: a `user` judge prompt (question + prefix) and a placeholder `assistant` `"yes"` verdict token
`reward`	float	the Monte-Carlo value `V` — the training target
`correct`	bool	`V ≥ 0.5`
`label`	str	placeholder verdict string (`"yes"`)
`id`	str	problem id (splits are disjoint by this)
`source`	str	`"polaris"`
`sample_index`	int	base-trace index the prefix came from
`step_idx`	int	prefix position within the base trace
`num_steps`	int	number of steps in the base trace
`loss_weight`	float	`1.0` (unused; superseded by soft-target `reward`)
`enable_thinking`	bool	`false`

Intended training use

One row per prefix with a placeholder yes verdict token. The soft-target PRM loss reads reward as V and minimizes soft cross-entropy at the verdict position,

$-\big[\,V \log P(\text{yes}) + (1-V)\log P(\text{no})\,\big],$

so P(yes) regresses to V. Same schema as the outcome-PRM sets, so it is concatenable.

Provenance

Branched-rollout pipeline: build branch set (prefixes) → sample N shared-prefix continuations → grade (math_verify + LLM-judge relabel) → aggregate to per-prefix V. Correctness comes from the relabeled grades (the raw branch shard is largely ungraded).

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Paper for asingh15/prm-sft-polaris-mc

Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations

Paper • 2312.08935 • Published Dec 14, 2023 • 4