README.md

metadata

pretty_name: PRM-SFT Polaris MC (Monte-Carlo value, unfiltered)
language:
  - en
tags:
  - process-reward-model
  - prm
  - monte-carlo
  - value-function
  - math
  - reasoning
size_categories:
  - 100K<n<1M
configs:
  - config_name: default
    data_files:
      - split: train
        path: train.parquet
      - split: validation
        path: val.parquet

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

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

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loss_weight	float	1.0 (unused; superseded by soft-target reward)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,

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

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).