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REVIEW 3 minor 23 references

Reinforcement learning post-training improves reasoning by activating strategy selection via diverse SFT data and strategy improvement via harder RL data.

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2026-06-27 07:13 UTC pith:TCKAWUFM

load-bearing objection Controlled experiments on Qwen-2.5-1.5B separate strategy selection (tied to SFT diversity) from strategy improvement (tied to RL data difficulty) in math reasoning post-training.

arxiv 2606.13125 v1 pith:TCKAWUFM submitted 2026-06-11 cs.LG cs.AI

Select and Improve: Understanding the Mechanics of Post-Training for Reasoning

Akshay Krishnamurthy , Audrey Huang , Nived Rajaraman This is my paper
classification cs.LG cs.AI
keywords reinforcement learningreasoning modelspost-trainingstrategy selectionstrategy improvementmath reasoningSFT dataRL data
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper examines the processes through which reinforcement learning post-training builds or strengthens reasoning skills in models. Controlled experiments on mathematical reasoning with the Qwen-2.5-1.5B model isolate two mechanisms as central. Diverse reasoning strategies in supervised fine-tuning data allow the model to pick effective approaches. Harder problems in the reinforcement learning phase then let the model refine those approaches for better performance. The results tie specific data choices to these mechanisms and point to ways to design training for continued gains.

Core claim

Through controlled math reasoning experiments with Qwen-2.5-1.5B, the work shows that RL post-training enhances capabilities via two mechanisms: strategy selection, enabled by supervising on diverse reasoning strategies in SFT data, and strategy improvement, enabled by increasing difficulty in RL data.

What carries the argument

Strategy selection (choosing among different reasoning approaches) and strategy improvement (refining performance on a chosen approach), activated by choices in SFT and RL data respectively.

Load-bearing premise

The two mechanisms isolated in the controlled experiments on Qwen-2.5-1.5B math tasks are the primary and general drivers of capability gains in RL post-training across models and domains.

What would settle it

An experiment in which RL post-training produces large reasoning gains on math tasks even when SFT data uses only a narrow set of strategies and RL data uses no difficulty increases would falsify the centrality of these mechanisms.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Supervising on diverse reasoning strategies during SFT activates the model's ability to select effective strategies.
  • Increasing problem difficulty during RL training activates the ability to improve on selected strategies.
  • These mechanisms explain observed capability gains and suggest data design choices for scaling reasoning.

Where Pith is reading between the lines

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

  • If the mechanisms prove general, training pipelines could sequence diverse strategy examples first and difficulty ramps later.
  • The same separation of selection and improvement could be tested on coding tasks to check whether the pattern holds beyond math.
  • The results imply that future gains may come more from targeted data curation than from changes to model architecture or algorithm.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The paper investigates the mechanistic processes underlying capability gains from RL post-training in reasoning models. Using controlled math reasoning experiments on Qwen-2.5-1.5B, it identifies two core mechanisms—strategy selection (activated via diversity in SFT data) and strategy improvement (enabled by increasing difficulty in RL data)—and demonstrates how SFT and RL data choices influence these processes.

Significance. If the controlled experiments and interventions hold, the work supplies concrete, testable mechanistic insight into RL post-training for reasoning, with direct suggestions for data curation that could aid scaling. The scoped empirical framing on one model and domain is a strength, as is the focus on falsifiable interventions rather than broad claims.

minor comments (3)
  1. The abstract states that experiments 'reveal the mechanisms' but does not name the specific metrics, controls, or baselines used to isolate strategy selection versus improvement; adding one sentence on these would improve clarity without altering the central claim.
  2. Section 4 (or equivalent results section): the paper should explicitly state the number of runs, variance, and statistical tests supporting the reported differences in strategy selection and improvement to allow readers to assess robustness.
  3. The discussion of generalization beyond Qwen-2.5-1.5B math tasks is appropriately cautious, but a short paragraph clarifying the scope (observations on this model/domain only) would prevent over-reading by future citations.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the supportive summary, positive significance assessment, and recommendation of minor revision. No specific major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper is an empirical study reporting observations from controlled experiments on Qwen-2.5-1.5B math reasoning tasks. It isolates two mechanisms (strategy selection via SFT data diversity; strategy improvement via RL data difficulty) through direct experimentation rather than any mathematical derivation, fitted parameters presented as predictions, or self-citation chains. No equations, ansatzes, uniqueness theorems, or load-bearing self-citations appear in the provided abstract or framing. The central claims are scoped to the specific experimental setup and do not reduce to their own inputs by construction. This is the expected outcome for a well-scoped observational paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no identifiable free parameters, axioms, or invented entities; the central claim rests on the validity of the controlled experiments whose details are not provided.

pith-pipeline@v0.9.1-grok · 5657 in / 1046 out tokens · 28712 ms · 2026-06-27T07:13:19.813904+00:00 · methodology

0 comments
read the original abstract

Reinforcement learning has rapidly emerged as a key component in the training of reasoning and coding models, yet it remains poorly understood from a mechanistic perspective. We study how and through what underlying processes capabilities are acquired or enhanced via reinforcement learning post-training. Our analysis, based on controlled math reasoning experiments with Qwen-2.5-1.5B, reveals two core mechanisms: strategy selection and strategy improvement. Our results highlight the role of SFT data and reinforcement learning data in activating these mechanisms, in particular showing how supervising the model on diverse reasoning strategies can enable strategy selection and how increasing difficulty in reinforcement learning data can enable strategy improvement. Taken together, our results provide mechanistic insight into RL training and suggest practical interventions to continue scaling reasoning capabilities.

Figures

Figures reproduced from arXiv: 2606.13125 by Akshay Krishnamurthy, Audrey Huang, Nived Rajaraman.

Figure 1
Figure 1. Figure 1: Examples of evaluation and inversion problems and forward and backward solutions over GF(11). [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Main results in GF(11) setting, demonstrating both strategy selection and improvement. Left panel shows accuracy on held-out 2-5 step problems over the course of SFT training. Center panel shows accuracy on held-out 6-9 step problems over the course of RL training, with inset showing per step (in-sample) reward curves. Right panel focuses on the learning dynamics of FB models. A simple rule-based classifie… view at source ↗
Figure 3
Figure 3. Figure 3: Pass@k results for the best SFT and RL checkpoints in the main [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Breakdown of RL training dynamics in the main GF [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Results for mixed reasoning models in the skewed setting with GF(11). Left: The (smoothed) reward [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Main results in the GF(11) setting with composition, demonstrating strategy improvement. The red, green and blue curves show accuracy on held-out 3-5 part composition problems over the course of RL training when the SFT mix contains 2-part composition problems. The purple curve tracks the average evaluation performance on 3-5 part problems over the course of RL training, when the SFT dataset only contains … view at source ↗
Figure 7
Figure 7. Figure 7: Main results for GF(13). Left: accuracy (measured via outcome correctness on model rollouts) over [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Pass@k results and per-problem-type breakdown for GF(13), paralleling the results in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Results for RL training of mixed reasoning models in the extended setting, where the RL dataset [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Pass@k results and per-problem-type breakdown for the extended GF(11) setting, where the [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Example of a 2-part composition problem over [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗

discussion (0)

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Reference graph

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