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arxiv: 2507.00432 · v2 · pith:4B5WMF72new · submitted 2025-07-01 · 💻 cs.AI · cs.CL

Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning

Maggie Huan , Yuetai Li , Tuney Zheng , Xiaoyu Xu , Seungone Kim , Minxin Du , Radha Poovendran , Graham Neubig
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Xiang Yue
This is my paper

Pith reviewed 2026-05-19 00:55 UTC · model grok-4.3

classification 💻 cs.AI cs.CL
keywords LLM reasoningtransferabilitysupervised fine-tuningreinforcement learninggeneral capabilitiesrepresentation driftmath reasoningpost-training
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The pith

Reinforcement learning on math data preserves general LLM capabilities while supervised fine-tuning erodes them.

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

The paper tests whether strong math reasoning in large language models reflects genuine broader problem-solving gains or narrow specialization. Broad evaluations of existing models show limited transfer to science, coding, planning and instruction tasks. Controlled experiments on one base model using only math data then isolate the tuning method as the key variable: reinforcement learning maintains performance across domains while supervised fine-tuning produces forgetting. Internal analyses trace the difference to large shifts in latent representations and output distributions under supervised fine-tuning, shifts that reinforcement learning largely avoids.

Core claim

When the same base model is trained on identical math-only data, reinforcement learning versions retain strong performance on scientific QA, agent planning, coding and instruction-following, whereas supervised fine-tuning versions lose these general capabilities. Latent-space and token-distribution measurements show that supervised fine-tuning produces substantial drift away from the model's original general-domain structure while reinforcement learning largely preserves that structure.

What carries the argument

Direct comparison of reinforcement learning versus supervised fine-tuning on fixed math reasoning data, with latent representation similarity and output token distribution shift as the metrics that quantify preservation or loss of general capabilities.

If this is right

  • Reasoning models trained with reinforcement learning on math data should retain higher performance on non-math tasks than those trained with supervised fine-tuning.
  • Post-training pipelines that rely heavily on supervised fine-tuning of distilled reasoning data are likely to produce models with reduced general capabilities.
  • Standard math benchmark gains alone are unreliable indicators of overall model improvement because transfer to other domains is weak under supervised fine-tuning.
  • Latent representation stability during training is a practical diagnostic for whether a reasoning model will keep its general abilities.

Where Pith is reading between the lines

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

  • Hybrid training schedules that begin with supervised fine-tuning for rapid math gains and then switch to reinforcement learning could reduce drift while controlling compute cost.
  • The same stability difference between the two tuning methods may appear when the narrow domain is coding or science rather than math.
  • Developers evaluating new reasoning models should include representation-drift measurements alongside benchmark scores to predict generalization.

Load-bearing premise

The chosen mix of math, scientific QA, agent planning, coding and instruction tasks is broad enough to stand in for general capabilities and that observed differences trace to tuning method rather than data composition or scale details.

What would settle it

A new training run on the same base model and math data in which supervised fine-tuning is modified to explicitly limit representation drift and is then shown to retain general-task performance at levels comparable to reinforcement learning.

read the original abstract

Math reasoning has become the poster child of progress in large language models (LLMs), with new models rapidly surpassing human-level performance on benchmarks like MATH and AIME. But as math leaderboards improve week by week, it is worth asking: do these gains reflect broader problem-solving ability or just narrow overfitting? To answer this question, we evaluate over 20 open-weight reasoning-tuned models across a broad suite of tasks, including math, scientific QA, agent planning, coding, and standard instruction-following. We surprisingly find that most models that succeed in math fail to transfer their gains to other domains. To rigorously study this phenomenon, we conduct controlled experiments on Qwen3-14B models using math-only data but different tuning methods. We find that reinforcement learning (RL)-tuned models generalize well across domains, while supervised fine-tuning (SFT)-tuned models often forget general capabilities. Latent-space representation and token-space distribution shift analyses reveal that SFT induces substantial representation and output drift, while RL preserves general-domain structure. Our results suggest a need to rethink standard post-training recipes, particularly the reliance on SFT-distilled data for advancing reasoning models.

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

2 major / 2 minor

Summary. The paper claims that math reasoning gains in LLMs largely fail to transfer to other domains such as scientific QA, agent planning, coding, and instruction-following. Evaluations across more than 20 open-weight models show limited generalization, while controlled experiments on Qwen3-14B using math-only data demonstrate that RL-tuned models preserve general capabilities and latent-domain structure better than SFT-tuned models, which induce substantial representation and output drift.

Significance. If the central empirical findings hold after addressing controls, the work is significant for post-training research: it provides evidence favoring RL over SFT for reasoning improvements without sacrificing breadth, supported by both large-scale model evaluations and mechanistic analyses of latent spaces and token distributions. The scale of the model survey and the focus on transferability rather than benchmark chasing are strengths.

major comments (2)
  1. [§4] §4 (Controlled Experiments): The claim that RL and SFT conditions are matched on math-only data requires explicit confirmation that auxiliary components (e.g., reward model, verifier, or sampling strategy) in the RL setup were trained exclusively on the same math-only corpus without additional general-domain exposure or differing optimization steps; without these details the attribution of generalization and drift differences to the tuning method versus training dynamics remains open to the confound noted in the stress-test.
  2. [§3] §3 (Task Suite and Metrics): The broad suite is presented as capturing general capabilities, yet the manuscript provides limited justification or controls for why performance differences can be attributed to tuning method rather than uneven task difficulty, data overlap with math corpora, or model-scale specifics; adding per-task statistical tests or ablation on task selection would make the cross-domain transfer claim more robust.
minor comments (2)
  1. [Figures 3-5] Figure captions and legends for the latent-space and distribution-shift plots should explicitly state the number of samples and the exact distance metrics used to improve reproducibility.
  2. [Abstract and §1] The abstract and introduction use 'forget general capabilities' without a precise operational definition; a short clarification tying it to the specific metrics reported would aid readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation of our controlled experiments and strengthen the robustness of our transferability claims. We address each major comment below.

read point-by-point responses

  1. Referee: [§4] §4 (Controlled Experiments): The claim that RL and SFT conditions are matched on math-only data requires explicit confirmation that auxiliary components (e.g., reward model, verifier, or sampling strategy) in the RL setup were trained exclusively on the same math-only corpus without additional general-domain exposure or differing optimization steps; without these details the attribution of generalization and drift differences to the tuning method versus training dynamics remains open to the confound noted in the stress-test.

    Authors: We agree that explicit confirmation is required to rule out confounds. In the revised manuscript we will add a dedicated paragraph (and supporting appendix) that details the construction of the reward model, verifier, and sampling strategy. This section will confirm that all auxiliary components were derived exclusively from the math-only corpus, with no general-domain data and with optimization steps matched to the SFT baseline except for the RL objective itself. These additions will directly support attribution to the tuning method. revision: yes

  2. Referee: [§3] §3 (Task Suite and Metrics): The broad suite is presented as capturing general capabilities, yet the manuscript provides limited justification or controls for why performance differences can be attributed to tuning method rather than uneven task difficulty, data overlap with math corpora, or model-scale specifics; adding per-task statistical tests or ablation on task selection would make the cross-domain transfer claim more robust.

    Authors: We appreciate the suggestion for additional controls. While the task suite draws from standard, widely adopted benchmarks chosen to span distinct capability domains, we will strengthen the manuscript by (1) reporting per-task statistical tests (bootstrap confidence intervals and paired significance tests) on the RL vs. SFT differences and (2) adding a short ablation that repeats the main comparisons on a reduced task subset. We will also include a brief overlap analysis (n-gram and embedding similarity) between the math training data and each evaluation domain. These revisions will make the attribution to tuning method more rigorous without altering the core findings. revision: yes

Circularity Check

0 steps flagged

No circularity in empirical evaluation chain

full rationale

The paper reports direct empirical measurements of model performance on external benchmarks (math, scientific QA, coding, instruction-following) plus controlled RL-versus-SFT experiments on Qwen3-14B with math-only data, followed by post-hoc analyses of latent representations and token distributions. No equations, fitted parameters, or predictions are presented as derivations; all claims rest on observed differences against held-out tasks rather than reducing to self-referential inputs or self-citation chains. The central contrast between RL preservation and SFT drift is therefore self-contained observational content, not tautological by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions about benchmark validity and that observed differences stem from tuning method rather than unmeasured factors.

axioms (1)
  • domain assumption Standard benchmarks like MATH, AIME, scientific QA, coding, and planning tasks measure distinct and transferable capabilities.
    Invoked when interpreting lack of transfer as evidence against broad generalization.

pith-pipeline@v0.9.0 · 5762 in / 1101 out tokens · 28589 ms · 2026-05-19T00:55:33.197978+00:00 · methodology

discussion (0)

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Forward citations

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