arxiv: 2510.24832 · v2 · submitted 2025-10-28 · 💻 cs.AI

Scheduling Your LLM Reinforcement Learning with Reasoning Trees

Hong Wang , Zhezheng Hao , Jian Luo , Chenxing Wei , Yao Shu , Lei Liu , Qiang Lin , Hande Dong

show 1 more author

Jiawei Chen

This is my paper

Pith reviewed 2026-05-18 02:38 UTC · model grok-4.3

classification 💻 cs.AI

keywords reasoning treer-scoreRe-ScheduleRLVRcurriculum learningLLM reinforcement learningmath reasoningdata scheduling

0 comments

The pith

A reasoning score based on tree structure creates an effective curriculum for RLVR, improving LLM accuracy by up to 3.2%.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that the structure of a query's reasoning tree can measure its difficulty for reinforcement learning with verifiable rewards in LLMs. They define a Reasoning Score (r-score) from this structure and use it to schedule training from high-score simple queries to low-score complex ones. This Re-Schedule method yields better average accuracy on math benchmarks compared to existing path-based scheduling. A reader would care because it suggests a more principled, structure-aware way to order data for efficient model improvement without custom tuning per task.

Core claim

The authors conceptualize RLVR as editing a query's Reasoning Tree and introduce the r-score to measure learning difficulty based on its structure. The Re-Schedule algorithm then orders queries from structurally simple (high r-score) to complex (low r-score), resulting in gains of up to 3.2% accuracy on six math-reasoning benchmarks and validating that structural understanding offers a powerful foundation for data scheduling.

What carries the argument

The Reasoning Score (r-score), a metric that assesses query learning difficulty from the structure of its reasoning tree, which is then used to build the curriculum in the Reasoning Tree Schedule (Re-Schedule) algorithm.

If this is right

Re-Schedule leads to improved data efficiency and higher accuracy in RLVR for LLMs.
The method works across six different math-reasoning benchmarks.
Structural metrics outperform path-based ones for ranking query difficulty.
Ordering from simple to complex structures creates an effective learning curriculum.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This approach might generalize to non-math tasks if reasoning trees can be constructed similarly.
Future work could explore combining r-score with other difficulty metrics for hybrid scheduling.
Validating the r-score on different model sizes or RL algorithms would test its robustness.

Load-bearing premise

The structure of a query's reasoning tree provides a reliable measure of its difficulty for learning under RLVR.

What would settle it

Running the Re-Schedule on the benchmarks but observing no significant accuracy gains or seeing better results from random or reverse ordering would challenge the claim.

read the original abstract

Using Reinforcement Learning with Verifiable Rewards (RLVR) to optimize Large Language Models (LLMs) can be conceptualized as progressively editing a query's `Reasoning Tree'. This process involves exploring nodes (tokens) and dynamically modifying the model's policy at each node. When combined with data scheduling, this process yields further gains in data efficiency and accuracy. However, existing RLVR data scheduling methods typically rely on path-based metrics to rank queries, overlooking the reasoning tree structures of these queries. In this paper, we introduce a novel metric, namely Reasoning Score (r-score), which measures the query's learning difficulty based on the structure of its reasoning tree. Based on the r-score, we propose the Reasoning Tree Schedule (Re-Schedule), a scheduling algorithm that constructs a curriculum progressing from structurally simple (high r-score) to complex (low r-score) queries. Experiments on six math-reasoning benchmarks show that Re-Schedule significantly improves average accuracy, achieving gains of up to 3.2%. These strong results validate our approach and demonstrate that a structural understanding of the reasoning tree provides a more powerful and principled foundation for RLVR data scheduling.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper conceptualizes RLVR as progressively editing a query's Reasoning Tree and introduces the Reasoning Score (r-score) as a structural measure of query learning difficulty. It proposes Re-Schedule, a curriculum that orders queries from high r-score (structurally simple) to low r-score (complex), and reports that this yields accuracy gains of up to 3.2% on six math-reasoning benchmarks.

Significance. If the r-score is shown to be a reproducible, non-circular structural metric that reliably predicts learning difficulty and the curriculum produces consistent gains over standard schedulers, the work could provide a more principled alternative to path-based scheduling in LLM reinforcement learning, improving data efficiency for reasoning tasks.

major comments (1)

[Abstract] Abstract: The central claim of up to 3.2% accuracy improvement cannot be evaluated because the abstract supplies no definition or computation method for the r-score, no description of how reasoning trees are constructed or analyzed, no baseline schedulers, no details on the six benchmarks or RLVR training protocol, and no statistical significance tests or error bars.

minor comments (1)

[Abstract] Abstract: The parenthetical gloss 'structurally simple (high r-score)' to 'complex (low r-score)' leaves unclear whether r-score is monotonically related to structural complexity or whether this ordering was validated against any external difficulty measure.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address the major comment regarding the abstract below.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim of up to 3.2% accuracy improvement cannot be evaluated because the abstract supplies no definition or computation method for the r-score, no description of how reasoning trees are constructed or analyzed, no baseline schedulers, no details on the six benchmarks or RLVR training protocol, and no statistical significance tests or error bars.

Authors: We agree that the abstract is a concise summary and therefore omits the detailed definitions, methods, and experimental protocols that are necessary for full evaluation. The full manuscript defines the r-score as a structural metric of query difficulty derived from the reasoning tree, explains tree construction and analysis within the RLVR editing process, compares Re-Schedule against path-based baselines, specifies the six math-reasoning benchmarks and RLVR training protocol, and reports results with error bars and statistical significance tests. To address the concern, we will revise the abstract to include a brief definition of the r-score and to indicate that the reported gains are obtained relative to standard schedulers. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

Only the abstract is available, which introduces the r-score as a novel metric measuring learning difficulty from reasoning tree structure and proposes Re-Schedule as a curriculum ordering from high to low r-score. No equations, explicit definitions of r-score computation, derivation steps, or self-citations appear in the provided text. Without these elements, no load-bearing step can be quoted that reduces by construction to fitted inputs, self-definitions, or prior author work. The accuracy gains are presented as experimental outcomes on six benchmarks rather than a derived result forced by the metric itself. This is the most common honest finding when the derivation chain is not inspectable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on the domain assumption that reasoning trees capture learning difficulty in RLVR and introduces the r-score as a new metric without external grounding shown in the abstract.

axioms (1)

domain assumption Reasoning trees represent the token-level exploration process in RLVR for a given query.
Stated in the opening conceptualization of the abstract.

invented entities (1)

Reasoning Score (r-score) no independent evidence
purpose: Quantifies a query's learning difficulty from the structure of its reasoning tree.
Newly defined metric introduced to replace path-based ranking; no independent evidence or external validation supplied in the abstract.

pith-pipeline@v0.9.0 · 5717 in / 1377 out tokens · 24580 ms · 2026-05-18T02:38:16.607796+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce the Reasoning Score (r-score), a novel metric that quantifies a query’s learning potential based on its reasoning tree structure... R(q) = max sum of r-scores from any set of M non-conflicting nodes
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

constructs a curriculum progressing from structurally simple (high r-score) to complex (low r-score) queries

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

SCALER:Synthetic Scalable Adaptive Learning Environment for Reasoning
cs.AI 2026-01 unverdicted novelty 6.0

SCALER creates adaptive synthetic environments for RL-based LLM reasoning training that outperforms fixed-dataset baselines with more stable long-term progress.