arxiv: 2605.11906 · v1 · submitted 2026-05-12 · 💻 cs.CL

Recognition: 1 theorem link

· Lean Theorem

YFPO: A Preliminary Study of Yoked Feature Preference Optimization with Neuron-Guided Rewards for Mathematical Reasoning

Yifan Le

Pith reviewed 2026-05-13 05:22 UTC · model grok-4.3

classification 💻 cs.CL

keywords preference optimizationmathematical reasoningneuron-guided rewardsAttnLRPinternal representationsGSM8Klanguage model fine-tuningpost-training

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The pith

YFPO augments preference optimization by using activation margins of math-related neurons as auxiliary rewards.

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

The paper introduces YFPO, a framework that first identifies math-related neurons via AttnLRP and then adds their activation difference between preferred and dispreferred responses as an extra reward during preference optimization. This combines sample-level external signals with internal neuron-level information to guide training for mathematical reasoning. Preliminary tests on a small language model and the GSM8K benchmark show that the neuron signals can interact with standard optimization and sometimes raise reasoning accuracy. The approach is positioned as an early step toward finer-grained, more interpretable reasoning post-training that draws on the model's own representations.

Core claim

YFPO yokes external preference learning to internal neuron-level signals by constructing an auxiliary reward from the activation margin of AttnLRP-identified math neurons between preferred and dispreferred responses, allowing neuron-guided rewards to interact with standard preference optimization and occasionally improve mathematical reasoning performance.

What carries the argument

The YFPO framework, which uses AttnLRP to locate math-related neurons and builds an auxiliary reward from their activation margin between preferred and dispreferred responses.

If this is right

External preference data can be supplemented with internal activation signals for more effective optimization.
Reasoning-oriented post-training can become more interpretable by linking improvements to specific neuron groups.
Neuron-guided methods may enable finer control over which capabilities are reinforced during fine-tuning.
Similar internal signal integration could be explored for other reasoning domains beyond mathematics.

Where Pith is reading between the lines

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

Applying this to larger models might reveal whether the occasional improvements scale or become more consistent.
The approach could reduce dependence on curated preference datasets by tapping into the model's own representations.
Validating the math-related neurons across different model architectures would strengthen the method's reliability.
Extending the neuron identification to other AttnLRP applications could generalize the yoking technique.

Load-bearing premise

Neurons identified by AttnLRP as math-related truly encode capability-related information whose activation margin supplies a useful, non-noisy auxiliary reward signal.

What would settle it

If adding the neuron-guided auxiliary reward produces no consistent accuracy gain or causes degradation versus plain preference optimization on GSM8K or comparable math benchmarks.

Figures

Figures reproduced from arXiv: 2605.11906 by Yifan Le.

**Figure 2.** Figure 2: Training dynamics and GSM8K performance of YFPO on the 2K data subset. Left: external DPO [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

read the original abstract

Preference optimization has become an important post-training paradigm for improving the reasoning abilities of large language models. Existing methods typically rely on externally constructed preference data, using preferred and dispreferred responses as sample-level supervision. However, such external signals rarely make explicit use of capability-related information contained in the model's internal representations. For mathematical reasoning, certain neuron groups may exhibit activation patterns associated with mathematical knowledge, symbolic manipulation, or logical reasoning. Similar to reflexive behavioral signals, these internal activations may provide a coarse indication of whether the model is engaging math-related capabilities.We introduce YFPO, short for Yoked Feature Preference Optimization, a preliminary neuron-guided preference optimization framework for mathematical reasoning. YFPO first uses AttnLRP to identify math-related neurons, and then constructs an auxiliary reward from their activation margin between preferred and dispreferred responses. This design augments external preference learning with internal neuron-level signals. We conduct preliminary experiments on a small-scale language model using GSM8K as the main benchmark. Results suggest that neuron-level signals can interact with preference optimization and occasionally improve reasoning performance, offering a promising direction for more fine-grained and interpretable reasoning-oriented post-training.

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.

Desk Editor's Note private letter to a colleague

YFPO yokes AttnLRP neuron margins into preference optimization as an auxiliary reward for math reasoning, but the abstract gives no numbers or controls so the occasional gains cannot be assessed.

read the letter

The paper introduces YFPO, which first runs AttnLRP to locate math-related neurons and then adds the activation margin between preferred and dispreferred responses as an extra term in the preference optimization objective. That specific combination of attribution method and reward construction is new, even if it sits on top of existing tools like AttnLRP and standard DPO-style losses. The motivation is also clear: standard preference data gives only sample-level signals, while internal neuron activations might supply a finer-grained, capability-related cue for mathematical reasoning. The work is honest about being preliminary and limits itself to a small model on GSM8K, which keeps expectations in check. What it does well is to make the internal-representation idea concrete rather than leaving it at the level of a suggestion. The framing around “yoked” features is simple and the goal of more interpretable post-training is reasonable for the narrow setting of math reasoning. The soft spots are not minor. The abstract only claims that the method “occasionally improve[s]” performance, with no quantitative deltas, no baseline comparisons, no statistical tests, and no ablation on the neuron-selection step. The stress-test concern lands: there is no mention of intervention tests such as activation patching or neuron ablation to show that the identified neurons are causally tied to reasoning rather than to surface features of the preference pairs. Without those checks, any auxiliary signal could produce the same occasional bump. The paper therefore does not yet supply evidence that the neuron-guided reward is doing the work claimed. This is the kind of early sketch that might interest a small group already working on interpretability inside alignment pipelines, but it offers little to a reader who needs reproducible gains or causal grounding. It does not deserve a serious referee right now; the evidential base is too thin and the central claim cannot be evaluated from what is shown. I would not bring it to a reading group or cite it until the full experiments and controls appear.

Referee Report

2 major / 0 minor

Summary. The manuscript introduces YFPO (Yoked Feature Preference Optimization), a preliminary neuron-guided preference optimization framework for mathematical reasoning. It first applies AttnLRP to identify math-related neurons, then constructs an auxiliary reward from the activation margin between preferred and dispreferred responses, augmenting standard preference optimization. Preliminary experiments on a small-scale language model with the GSM8K benchmark are reported to show that neuron-level signals can occasionally improve reasoning performance.

Significance. If the central claim holds under rigorous validation, the work would demonstrate a viable path for incorporating internal, capability-related representations into post-training objectives, potentially yielding more interpretable and targeted improvements in reasoning tasks compared to purely external preference signals.

major comments (2)

[Abstract] Abstract: the central claim that neuron-guided rewards 'occasionally improve' reasoning performance is unsupported by any quantitative results, baselines, statistical significance tests, or ablation details, which are load-bearing for assessing whether the auxiliary signal contributes beyond standard preference optimization.
[Method] Method description (neuron identification and reward construction): the assumption that AttnLRP-identified neurons encode causally relevant math capability information is not validated by intervention experiments such as activation patching or neuron ablation; without these, the activation margin may reflect spurious correlations rather than useful signals for GSM8K performance.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our preliminary study. We address each major comment below and indicate planned revisions to the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that neuron-guided rewards 'occasionally improve' reasoning performance is unsupported by any quantitative results, baselines, statistical significance tests, or ablation details, which are load-bearing for assessing whether the auxiliary signal contributes beyond standard preference optimization.

Authors: We agree the abstract phrasing is imprecise and the preliminary nature of the work limits the strength of the claim. The experiments on a small-scale model with GSM8K show performance gains in select configurations relative to standard preference optimization, but without full statistical testing or exhaustive ablations. In revision we will update the abstract and results section to report concrete accuracy deltas, include the standard DPO baseline explicitly, and qualify the 'occasionally' language with the observed conditions. Comprehensive significance testing will be noted as outside the scope of this preliminary study. revision: partial
Referee: [Method] Method description (neuron identification and reward construction): the assumption that AttnLRP-identified neurons encode causally relevant math capability information is not validated by intervention experiments such as activation patching or neuron ablation; without these, the activation margin may reflect spurious correlations rather than useful signals for GSM8K performance.

Authors: We accept this point. AttnLRP is used to surface candidate neurons on the basis of attribution scores, but no causal interventions were performed. We will revise the method and limitations sections to state explicitly that the identified neurons rest on correlational evidence and that the activation-margin reward could capture spurious patterns. The discussion will frame causal validation via patching or ablation as necessary future work. revision: yes

Circularity Check

0 steps flagged

No circularity: auxiliary reward is constructed directly from measured activations

full rationale

The paper defines YFPO by first running AttnLRP to locate math-related neurons and then computing an activation-margin auxiliary reward between preferred and dispreferred responses; this margin is used as an additive term in the preference objective. No equation or step reduces the final performance claim to a fitted parameter, a self-referential definition, or a self-citation chain. The derivation remains a straightforward construction from external identification and observed differences, with no load-bearing uniqueness theorem or ansatz imported from prior author work.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that AttnLRP can isolate neurons whose activation patterns reliably indicate engagement of mathematical capabilities and that the margin between preferred and dispreferred responses yields a useful training signal.

axioms (1)

domain assumption Certain neuron groups exhibit activation patterns associated with mathematical knowledge, symbolic manipulation, or logical reasoning that can be identified by AttnLRP.
Invoked in the description of how the auxiliary reward is constructed from internal representations.

pith-pipeline@v0.9.0 · 5501 in / 1153 out tokens · 48733 ms · 2026-05-13T05:22:14.972480+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
YFPO first uses AttnLRP to identify math-related neurons, and then constructs an auxiliary reward from their activation margin between preferred and dispreferred responses.

Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages · 6 internal anchors

[2]

Advances in Neural Information Processing Systems , year=

Learning to Summarize with Human Feedback , author=. Advances in Neural Information Processing Systems , year=

work page
[3]

Advances in Neural Information Processing Systems , year=

Training Language Models to Follow Instructions with Human Feedback , author=. Advances in Neural Information Processing Systems , year=

work page
[4]

Advances in Neural Information Processing Systems , year=

Direct Preference Optimization: Your Language Model is Secretly a Reward Model , author=. Advances in Neural Information Processing Systems , year=

work page
[6]

International Conference on Machine Learning , year=

KTO: Model Alignment as Prospect Theoretic Optimization , author=. International Conference on Machine Learning , year=

work page
[8]

Advances in Neural Information Processing Systems , year=

SimPO: Simple Preference Optimization with a Reference-Free Reward , author=. Advances in Neural Information Processing Systems , year=

work page
[13]

International Conference on Machine Learning , year=

Axiomatic Attribution for Deep Networks , author=. International Conference on Machine Learning , year=

work page
[14]

Computational Linguistics , volume=

Probing Classifiers: Promises, Shortcomings, and Advances , author=. Computational Linguistics , volume=

work page
[15]

Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics , year=

Knowledge Neurons in Pretrained Transformers , author=. Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics , year=

work page
[16]

Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics , year=

Language-Specific Neurons: The Key to Multilingual Capabilities in Large Language Models , author=. Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics , year=

work page
[17]

International Conference on Machine Learning , year=

AttnLRP: Attention-Aware Layer-Wise Relevance Propagation for Transformers , author=. International Conference on Machine Learning , year=

work page
[18]

Qwen2 Technical Report

Qwen2 Technical Report , author=. arXiv preprint arXiv:2407.10671 , year=

work page internal anchor Pith review Pith/arXiv arXiv
[19]

Step-dpo: Step-wise preference optimization for long-chain reasoning of llms, 2024

Step-DPO: Step-wise Preference Optimization for Long-chain Reasoning of LLMs , author=. arXiv preprint arXiv:2406.18629 , year=

work page arXiv
[20]

2026 , eprint=

CRANE: Causal Relevance Analysis of Language-Specific Neurons in Multilingual Large Language Models , author=. 2026 , eprint=

work page 2026
[21]

Reduan Achtibat, Maximilian Dreyer, Ilona Eisenbraun, Sebastian Bosse, Thomas Wiegand, Wojciech Samek, and Sebastian Lapuschkin. 2024. Attnlrp: Attention-aware layer-wise relevance propagation for transformers. In International Conference on Machine Learning

work page 2024
[22]

Mohammad Gheshlaghi Azar, Mark Rowland, Bilal Piot, Daniel Guo, Daniele Calandriello, Michal Valko, and R \'e mi Munos. 2023. A general theoretical paradigm to understand learning from human preferences. arXiv preprint arXiv:2310.12036

work page arXiv 2023
[23]

Yonatan Belinkov. 2022. Probing classifiers: Promises, shortcomings, and advances. Computational Linguistics, 48(1):207--219

work page 2022
[24]

Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, and 1 others. 2021. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168

work page internal anchor Pith review Pith/arXiv arXiv 2021
[25]

Damai Dai, Li Dong, Yaru Hao, Zhifang Sui, Baobao Chang, and Furu Wei. 2022. Knowledge neurons in pretrained transformers. In Proceedings of the 60th Annual Meeting of the Association for Computational Linguistics

work page 2022
[26]

Kawin Ethayarajh, Winnie Xu, Niklas Muennighoff, Dan Jurafsky, and Douwe Kiela. 2024. Kto: Model alignment as prospect theoretic optimization. International Conference on Machine Learning

work page 2024
[27]

Jiwoo Hong, Noah Lee, and James Thorne. 2024. Orpo: Monolithic preference optimization without reference model. arXiv preprint arXiv:2403.07691

work page arXiv 2024
[28]

Yifan Le and Yunliang Li. 2026. https://arxiv.org/abs/2601.04664 Crane: Causal relevance analysis of language-specific neurons in multilingual large language models . Preprint, arXiv:2601.04664

work page arXiv 2026
[29]

Hunter Lightman, Vineet Kosaraju, Yura Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. 2023. Let's verify step by step. arXiv preprint arXiv:2305.20050

work page internal anchor Pith review Pith/arXiv arXiv 2023
[30]

Yu Meng, Mengzhou Xia, and Danqi Chen. 2024. Simpo: Simple preference optimization with a reference-free reward. In Advances in Neural Information Processing Systems

work page 2024
[31]

Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, and 1 others

Long Ouyang, Jeffrey Wu, Xu Jiang, Diogo Almeida, Carroll L. Wainwright, Pamela Mishkin, Chong Zhang, Sandhini Agarwal, Katarina Slama, Alex Ray, and 1 others. 2022. Training language models to follow instructions with human feedback. Advances in Neural Information Processing Systems

work page 2022
[32]

Manning, and Chelsea Finn

Rafael Rafailov, Archit Sharma, Eric Mitchell, Stefano Ermon, Christopher D. Manning, and Chelsea Finn. 2023. Direct preference optimization: Your language model is secretly a reward model. Advances in Neural Information Processing Systems

work page 2023
[33]

John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347

work page internal anchor Pith review Pith/arXiv arXiv 2017
[34]

Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, Y. K. Li, Y. Wu, and Daya Guo. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300

work page internal anchor Pith review Pith/arXiv arXiv 2024
[35]

Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul F

Nisan Stiennon, Long Ouyang, Jeffrey Wu, Daniel M. Ziegler, Ryan Lowe, Chelsea Voss, Alec Radford, Dario Amodei, and Paul F. Christiano. 2020. Learning to summarize with human feedback. Advances in Neural Information Processing Systems

work page 2020
[36]

Mukund Sundararajan, Ankur Taly, and Qiqi Yan. 2017. Axiomatic attribution for deep networks. International Conference on Machine Learning

work page 2017
[37]

Tianyi Tang, Wenyang Luo, Haoyang Huang, Dongdong Zhang, Xiaolei Wang, Xin Zhao, Furu Wei, and Ji-Rong Wen. 2024. Language-specific neurons: The key to multilingual capabilities in large language models. In Proceedings of the 62nd Annual Meeting of the Association for Computational Linguistics

work page 2024
[38]

Qiying Yu and 1 others. 2025. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476

work page internal anchor Pith review Pith/arXiv arXiv 2025