SPEAR: Order-sensitive process rewards from symbolic reasoning skeletons¶

Core mechanism mini-suite: milestones, order alignment, and dense reward without a neural PRM.

Paper information¶

Field	Details
Paper	arXiv 2608.26550
Institution	University of Pittsburgh (first-listed affiliation of the first author).
First public release	2026-08-27 (arXiv v1)
Author code	zhuochunli/SPEAR.
Local adapter or method key	`spear`
Local reproduction code	`src/auto_research/post_training/latest_20260829.py`

Paper method and evidence¶

Outcome rewards are sparse and neural process reward models are expensive. Project teacher reasoning into domain-specific symbolic milestones and reward student traces with order-sensitive longest-common-subsequence F1.

flowchart LR
  T[Teacher reasoning] --> M[Symbolic milestones]
  S[Student rollout] --> L[LCS-F1 alignment]
  M --> L
  L --> R[Dense process reward]

Original paper figure¶

Figure 2 shows milestone extraction and reward calculation. From the original paper; copyright remains with the authors.

Core equation¶

\[ R_{SPEAR}=\frac{2P_{LCS}R_{LCS}}{P_{LCS}+R_{LCS}}. \]

Reported results¶

The paper reports better student distillation on mathematical, scientific, and commonsense reasoning without an external neural verifier; no industrial A/B.

Local reproduction¶

The 100-step arithmetic smoke test improved from 0.1953 to 0.2812 accuracy with zero neural PRM calls. Metrics and batch results. Local milestones use candidate process/format attributes, not the paper's natural-language symbolic extractor.