Fusion Training for Mathematical Generalization in Large Language Models

Congfeng Cao; Jelke Bloem; Pengyu Zhang

REVIEW 4 major objections 3 minor 38 references

Fusion Training for Mathematical Generalization in Large Language Models

T0 review · 4 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Training one model to answer both concisely and with long chain-of-thought carries a measurable cost: the more short-answer data it sees, the worse its long-form math reasoning becomes.

desk verdict A useful, timely empirical map of TMF training dynamics, but the headline trade-off is undermined by a 5,120-token truncation cap that cuts most thinking traces and test outputs before the answer. read the letter →

arxiv 2608.09893 v1 pith:5AEDE3UT submitted 2026-08-10 cs.CL cs.AI

Congfeng Cao , Pengyu Zhang , Jelke Bloem This is my paper · ORCID

classification cs.CLcs.AI

keywords thinkingmodefusiondataratiotrainingschedulechain-of-thoughtmathematicalreasoningsupervisedfine-tuninginterferencelargelanguagemodels

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Thinking Mode Fusion (TMF) is a post-training recipe for giving one language model both a concise-answering mode and a long chain-of-thought reasoning mode, switched by chat template. The authors ask whether how much of each mode's data is used, and the order in which the modes are trained, changes what such a model can do. By sweeping seven thinking-to-non-thinking data ratios and three training schedules on math word problems, they find the interaction is asymmetric: adding non-thinking supervision degrades thinking-mode accuracy, while the reverse direction costs less. The paper also reports a negative correlation between the two modes' accuracies and shows that the best training schedule depends on the data ratio, with interleaved training the strongest average choice.

What carries the argument

The object under study is Thinking Mode Fusion (TMF): a single model whose chat template either leaves the <think></think> block empty and gives a short solution (non-thinking mode) or fills it with a long chain of thought (thinking mode). The experimental machinery is a full factorial sweep over seven values of the ratio $\rho$ (thinking to non-thinking) from 4:1 to 1:4 and three schedules — T-NT (all thinking examples first), NT-T (all non-thinking first), and Mix (interleaved to the target ratio) — with exact-match accuracy and response length as the measured outputs.

What would settle it

Train on one fixed set of math problems answered in both formats (empty think block with a short solution, and full chain of thought), holding difficulty and distribution constant while sweeping the data ratio. If thinking-mode accuracy no longer falls as non-thinking data rises, the trade-off is a dataset effect rather than an inherent property of mode fusion; conversely, if the negative slope persists on identical problems, the paper's central claim is confirmed.

Watch

Extended reading notes

Core claim

On a benchmark built from short-solution grade-school problems and long chain-of-thought Olympiad-style problems, the paper's central claim is that the two TMF modes compete inside one model. Holding thinking data fixed at 1,500 examples and varying non-thinking data from 375 to 6,000, thinking-mode accuracy falls as the non-thinking share grows; across all configurations, non-thinking and thinking accuracy are negatively correlated ($r = -0.58$, $R^2 = 0.34$), with a slope of $-0.91$, meaning a 0.01 gain in concise-answer accuracy is associated with about a 0.0091 loss in long-form reasoning accuracy. The schedule matters too: the interleaved Mix schedule gives the best average accuracy on both modes, but no single schedule is optimal at every data ratio.

Load-bearing premise

The load-bearing premise is that short GSM8K answers and long OpenMathReasoning chains cleanly instantiate the two modes, so the results are attributed to mode rather than to differences in problem difficulty, dataset distribution, or answer style.

Editorial extensions

If this is right

Adding cheap short-answer data to a reasoning model will trade away some long-form reasoning accuracy; the trade-off can be modulated but not eliminated by choosing a different schedule.
Interleaved (Mix) training is the safest default when the deployment mix of simple and hard queries is unknown, because it ranks best on average across ratios.
The optimal training order is ratio-dependent, so a deployment that knows its query mix can pick a schedule to favor one mode.
Response length tracks the trade-off: ratios and schedules that favor thinking accuracy also produce longer outputs, consistent with length reflecting reasoning effort.
Evaluations of fused models should report both modes; reporting only one can conceal the cost paid by the other.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the non-thinking and thinking datasets differ in both answer length and problem difficulty, the measured "mode" trade-off may partly be a difficulty or domain effect; a same-problem, two-format control would separate these.
With $R^2 = 0.34$, most of the variance in the accuracies is not explained by the aggregate negative correlation, so schedule choice and per-ratio effects are doing real work; modeling the joint dependence on ratio and schedule could tighten the picture.
A natural next experiment is to keep the same problem set and vary only response format; if thinking accuracy stops falling when the underlying problems are identical, the claimed inherent tension would need to be reframed as data-distribution interference.
The slope of $-0.91$ gives practitioners a rough exchange rate: a one-point gain in concise accuracy costs nearly one point of reasoning accuracy, so the economically sensible ratio depends on the actual proportion of simple versus hard queries in production.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The first thing you should know: this is the first systematic look at how data ratio and training schedule interact in Qwen3-style Thinking Mode Fusion post-training, and the released Fusion Bench is a real resource. The second thing: I would not trust the central “inherent tension” claim yet, because the thinking mode is trained and evaluated under a 5,120-token cap while the thinking traces average around 12k tokens.

What is genuinely new and good: prior work introduced TMF and analyzed inference-side mode separation, but nobody had varied the data ratio and schedule in a controlled factorial way. Fixing T=1500, sweeping ratios from 1:4 to 4:1, comparing T-NT, NT-T, and Mix across three runs, and releasing code and data is a sensible way to ask the question. The qualitative finding that Mix is robust across ratios and that the optimal schedule depends on the ratio is plausible and worth pursuing.

Now the soft spots, in proportion. The stress-test concern about truncation is real and load-bearing. Appendix A.6 sets max_seq_length=5120 while Table 1 reports thinking training examples with mean length 11,877 tokens. Standard SFT truncation cuts the long CoT before the boxed answer, so for most thinking examples the model is never trained to produce the final answer. Evaluation is worse: A.7 caps generation at max_new_tokens=5120, but thinking test references average 11,992 tokens, so most generated responses are cut before an answer can be extracted. Table 3 reports thinking Len values above 5,120 (e.g., 7,027.6), which contradicts the stated cap and suggests an undocumented or inconsistent length limit. With the thinking mode incompletely trained and evaluated, the observed ratio-dependent degradation and the r=-0.58 correlation cannot cleanly be attributed to TMF dynamics.

There are also confounds the reader flagged. The two modes are instantiated with different datasets (OpenMathReasoning vs GSM8K) that differ in difficulty and answer style, so mode is confounded with dataset. All conditions train for one epoch, so total gradient steps vary by a factor of 4 across the ratio sweep, conflating mixture proportion with training volume. The negative correlation is a descriptive fit to outcome data, not evidence of an inherent tension, and no confidence intervals are reported.

Who is this for? Practitioners deciding how to mix thinking and non-thinking data in post-training. It deserves a serious referee, not a desk reject, because the question is timely and the design is mostly clean. But it needs major revision: fix truncation (either train/eval with longer limits or filter/truncate consistently and report exclusion rates), add a same-problem dual-mode control, hold total gradient steps fixed, and report variability. I would not cite the headline result in its current form, but I would send it to review with a request for those controls.

Referee Report

4 major / 3 minor

Summary. The paper studies Thinking Mode Fusion (TMF) in Qwen3-4B via LoRA-based supervised fine-tuning, varying the ratio of thinking-mode data (OpenMathReasoning long chain-of-thought traces) to non-thinking-mode data (GSM8K short solutions) across seven ratios (T:NT from 1:4 to 4:1) and three training schedules (T-NT, NT-T, Mix). It reports that increasing non-thinking supervision degrades thinking-mode accuracy, that the optimal schedule depends on the data ratio, and that the two modes exhibit a negative correlation (r = -0.58, R^2 = 0.34), which it interprets as an inherent tension. The authors release a benchmark, Fusion Bench, with code and data.

Significance. If the empirical claims were valid, this would be a useful practical study of an under-explored post-training design choice, with clear implications for how to schedule and mix thinking and non-thinking supervision in hybrid reasoning models. The paper has notable strengths: it releases code and data, uses a full factorial design across ratios and schedules, averages over three runs, and formulates concrete research questions. However, the central quantitative claims rest on experimental comparisons that are confounded in ways the manuscript does not address. The length-truncation issue in particular calls into question whether the thinking mode was trained and evaluated in a way that measures long-form reasoning at all. The paper is therefore not yet ready for publication; the claims need re-analysis or re-experimentation before they can support the stated conclusions.

major comments (4)

[Appendix A.6/A.7; Tables 1-3] This is the most load-bearing issue and needs to be fixed before the central claim can be assessed.
[Section 3; Tables 1-2]
[Appendix A.1/A.6; Eq. (6)]
[Section 5.5; Figure 5; Table 3]

minor comments (3)

[Section 5.4; Table 3]
[Table 3 caption and Appendix A.7]
[Section 5.2]

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's claims are empirical measurements from controlled experimental runs, not derivations from self-referential definitions.

full rationale

The paper's central claims are empirical: increasing non-thinking supervision degrades thinking-mode accuracy, schedules modulate the trade-off, and the two modes show a negative correlation. These are presented as measurements from full-factorial SFT runs (Section 4.4, Table 3, Figure 5), not as predictions derived from the definitions of the modes. The data ratio is defined by Eq. (1), rho = N_T / N_NT, and the schedules are explicit orderings (Eqs. (2)-(4)); none of these definitions presuppose the observed accuracy outcomes. The regression line in Section 5.5 is fitted to the measured accuracies and used descriptively, which is standard empirical analysis rather than a fitted input renamed as a prediction. The mode operationalization (GSM8K with empty think blocks vs. OpenMathReasoning long traces) is an experimental design choice that could threaten validity, but it does not make the conclusion true by construction; the paper measures an interaction rather than deriving one from the mode definitions. No load-bearing self-citation chain appears: the only invoked external framework is Qwen3's TMF design, cited as prior work, and no uniqueness theorem or ansatz is imported from the authors' own prior papers to force the conclusion. Potential concerns about length truncation (Appendix A.6 and A.7) bear on the validity of the measured accuracy numbers, but they are correctness risks, not circularity: the numbers are not constructed to equal the inputs. The paper is therefore self-contained as an empirical study, and no circular step can be exhibited with a quote and a specific reduction.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the data ratio sweep, which is anchored to a hand-chosen thinking data size and a curated thinking dataset. There are no newly postulated physical or mathematical entities; the main assumptions are domain-level operationalizations of the two modes and the representativeness of one-epoch LoRA training. The regression slope and correlation are fitted outputs, not free inputs.

free parameters (3)

Thinking-mode training set size N_T = 1500
Chosen by hand to anchor the ratio sweep; all data-ratio conditions fix thinking data at 1,500, so the trade-off curve depends on this choice.
Pass-rate threshold for filtering OpenMathReasoning thinking data = 0.96
Selects the thinking-mode training subset; affects the difficulty and length distribution of the long reasoning traces.
Test-set subsample size = 375 examples per mode
Set to 0.25 times the thinking data cap (standard_index); small test sets make accuracy differences across schedules hard to distinguish from noise.

assumptions (4)

domain assumption GSM8K with empty think blocks and short solutions operationalizes the non-thinking mode.
The non-thinking mode is defined by this dataset; no validation that it isolates the mode from problem difficulty (Section 3).
domain assumption OpenMathReasoning with long chain-of-thought solutions operationalizes the thinking mode.
The thinking mode is defined by this dataset; it differs from GSM8K in difficulty and length, so mode is confounded with dataset (Section 3).
domain assumption One epoch of LoRA fine-tuning on Qwen3-4B with fixed hyperparameters captures TMF training dynamics.
No experiments with other model sizes, full fine-tuning, or multiple epochs; the observed effects may not generalize (Appendix A.6).
domain assumption Exact-match accuracy on boxed final answers is a valid metric for both modes.
Used for both GSM8K and OpenMathReasoning; penalizes formatting differences and does not measure reasoning quality directly (Appendix A.7).

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Cite this review

Pith. "Pith review of Fusion Training for Mathematical Generalization in Large Language Models." pith.science (2026). https://pith.science/paper/5AEDE3UT

@misc{pith2026260809893,
  author       = {Pith},
  title        = {Pith review of: Fusion Training for Mathematical Generalization in Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5AEDE3UT}},
  note         = {Machine review of arXiv:2608.09893}
}

read the original abstract

Thinking Mode Fusion (TMF) enables large language models to support both concise responses and long-form reasoning by unifying a non-thinking mode and a thinking mode within a single model. However, its training dynamics, including the \emph{data ratio} and \emph{training schedule} between the two modes, remain underexplored. In this work, we present a systematic study of TMF by analyzing the effects of the training schedule and data ratio between thinking and non-thinking modes. Focusing on mathematical problem solving, we construct a benchmark with multiple thinking-to-non-thinking data ratios and three training schedules. Our results reveal an asymmetric interaction between the two modes: increasing the ratio of non-thinking supervision reduces the accuracy of the thinking mode. We further show that different training schedules modulate this trade-off and that the optimal schedule depends on the data ratio. Finally, we quantify a negative correlation between non-thinking and thinking mode supervision, highlighting an inherent tension between these two modes. These findings provide practical guidance for designing effective TMF training settings. All code and data are released to support further research at: \href{https://github.com/caocongfeng/Fusion-Bench.git}{\textbf{Fusion Bench}}.

Figures

Figures reproduced from arXiv: 2608.09893 by the authors.

**Figure 2.** Overview of Thinking Mode Fusion training design. We construct two datasets: thinking mode and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** The effect of different training schedules under [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Performance comparison of accuracy and reasoning length under different data ratios and training schedule [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Scatter plot of different training schedules and [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: An overview of the experimental design for [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.

[1] [1]

Chain-of-Thought Prompting Elicits Reasoning in Large Language Models , url =

Wei, Jason and Wang, Xuezhi and Schuurmans, Dale and Bosma, Maarten and ichter, brian and Xia, Fei and Chi, Ed and Le, Quoc V and Zhou, Denny , booktitle =. Chain-of-Thought Prompting Elicits Reasoning in Large Language Models , url =

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Large Language Models are Zero-Shot Reasoners , url =

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The Eleventh International Conference on Learning Representations , year=

Self-Consistency Improves Chain of Thought Reasoning in Language Models , author=. The Eleventh International Conference on Learning Representations , year=

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2024 , eprint=

OpenAI o1 System Card , author=. 2024 , eprint=

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[5] [5]

2025 , primaryClass=

GPT-5.1: A smarter, more conversational ChatGPT , author=. 2025 , primaryClass=

work page 2025

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2025 , eprint=

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2021 , eprint=

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Calc- X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems

Kadl c \'i k, Marek and S tef \'a nik, Michal and Sotolar, Ondrej and Martinek, Vlastimil. Calc- X and Calcformers: Empowering Arithmetical Chain-of-Thought through Interaction with Symbolic Systems. Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing. 2023. doi:10.18653/v1/2023.emnlp-main.742

work page doi:10.18653/v1/2023.emnlp-main.742 2023