arxiv: 2604.08284 · v1 · submitted 2026-04-09 · 💻 cs.CL · cs.AI

Recognition: no theorem link

Distributed Multi-Layer Editing for Rule-Level Knowledge in Large Language Models

Haoliang Sun, Wenting Zhao, Yaqi Zhao, Yating Wang, Yilong Yin, Yongshun Gong

Pith reviewed 2026-05-10 18:28 UTC · model grok-4.3

classification 💻 cs.CL cs.AI

keywords rule-level knowledge editinglarge language modelscausal tracingtransformer layersmodel editingknowledge localizationrule consistencydistributed updates

0 comments

The pith

LLMs store the same rule in different layers depending on whether it appears as a formula, a description, or an instance, so editing those layers separately produces much more consistent rule behavior.

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

The paper examines why fact-editing techniques break down when applied to rules that must stay coherent across symbolic expressions, natural-language explanations, and concrete examples. Causal tracing on an enlarged set of 200 verified rules reveals that formulas and descriptions concentrate in earlier transformer layers while instances associate more strongly with middle layers. Because this knowledge is distributed rather than localized, a single-layer or block intervention cannot keep all three forms aligned after an edit. The authors therefore introduce Distributed Multi-Layer Editing, which applies one shared update to the early layers and a distinct update to the middle layers. Across four models the method improves how well the edited rule transfers to new instances and how well the model understands the rule itself.

Core claim

Causal tracing on the extended RuleEdit benchmark shows that formulas and descriptions are concentrated in earlier transformer layers while instances are more associated with middle layers. This form-specific organization means rule knowledge cannot be reliably edited by intervening at a single location. DMLE therefore performs a shared early-layer update for formulas and descriptions together with a separate middle-layer update for instances. The resulting edits remain competitive on standard metrics yet raise instance portability by 13.91 percentage points and rule understanding by 50.19 percentage points on average over the strongest baseline across GPT-J-6B, Qwen2.5-7B, Qwen2-7B, and LLa

What carries the argument

Distributed Multi-Layer Editing (DMLE), which uses causal tracing to locate non-overlapping layers for each rule form and then applies an early-layer update shared across formulas and descriptions plus an independent middle-layer update for instances.

If this is right

Rule edits can now preserve consistency across symbolic, explanatory, and instance presentations of the same rule.
Editing performance on rules improves without sacrificing performance on ordinary fact-editing benchmarks.
Model-editing algorithms must treat complex knowledge as distributed rather than point-localized.
The same layer-separation pattern may apply to other structured knowledge such as logical chains or causal relations.

Where Pith is reading between the lines

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

If the layer organization is stable, targeted interventions could be used for alignment or unlearning of specific rule types without affecting others.
The approach suggests that future editing methods should first map knowledge forms to layers before choosing update sites.
Testing whether the early-middle separation appears in models trained with different objectives would clarify how general the pattern is.

Load-bearing premise

Causal tracing accurately identifies distinct layers for different rule forms, and independent updates to those layers produce no harmful interference with each other or with unrelated model behavior.

What would settle it

An experiment that applies the same numerical change to both the early and middle layers and obtains equal or higher rule-understanding scores than separate updates would show that the distributed design is unnecessary.

Figures

Figures reproduced from arXiv: 2604.08284 by Haoliang Sun, Wenting Zhao, Yaqi Zhao, Yating Wang, Yilong Yin, Yongshun Gong.

**Figure 2.** Figure 2: Causal tracing heatmaps on Qwen2-7B, Qwen2.5-7B, and LLaMA-3-8B. Across [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Overview of DMLE. Given a rule with three aligned forms, formula and description [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

read the original abstract

Large language models store not only isolated facts but also rules that support reasoning across symbolic expressions, natural language explanations, and concrete instances. Yet most model editing methods are built for fact-level knowledge, assuming that a target edit can be achieved through a localized intervention. This assumption does not hold for rule-level knowledge, where a single rule must remain consistent across multiple interdependent forms. We investigate this problem through a mechanistic study of rule-level knowledge editing. To support this study, we extend the RuleEdit benchmark from 80 to 200 manually verified rules spanning mathematics and physics. Fine-grained causal tracing reveals a form-specific organization of rule knowledge in transformer layers: formulas and descriptions are concentrated in earlier layers, while instances are more associated with middle layers. These results suggest that rule knowledge is not uniformly localized, and therefore cannot be reliably edited by a single-layer or contiguous-block intervention. Based on this insight, we propose Distributed Multi-Layer Editing (DMLE), which applies a shared early-layer update to formulas and descriptions and a separate middle-layer update to instances. While remaining competitive on standard editing metrics, DMLE achieves substantially stronger rule-level editing performance. On average, it improves instance portability and rule understanding by 13.91 and 50.19 percentage points, respectively, over the strongest baseline across GPT-J-6B, Qwen2.5-7B, Qwen2-7B, and LLaMA-3-8B. The code is available at https://github.com/Pepper66/DMLE.

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

DMLE improves rule editing by handling form-specific layers separately, but the causal tracing foundation needs closer inspection before the gains can be fully trusted.

read the letter

The main point is that rule knowledge sits in different layers depending on its form, and editing those layers independently gives better consistency than single-site methods. The authors extend RuleEdit to 200 verified math and physics rules, run causal tracing to map formulas and descriptions to early layers and instances to middle layers, then build DMLE to apply separate updates. They test on GPT-J, Qwen, and LLaMA models and report clear lifts on instance portability and rule understanding.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that rule-level knowledge in LLMs exhibits a form-specific layer organization—formulas and descriptions concentrated in early layers, instances in middle layers—identified via fine-grained causal tracing on an extended RuleEdit benchmark of 200 rules. It proposes Distributed Multi-Layer Editing (DMLE), which applies a shared early-layer update for formulas/descriptions and a separate middle-layer update for instances. DMLE is reported to remain competitive on standard editing metrics while improving instance portability by 13.91 percentage points and rule understanding by 50.19 percentage points on average over the strongest baseline across GPT-J-6B, Qwen2.5-7B, Qwen2-7B, and LLaMA-3-8B, with code released.

Significance. If the distributed editing approach and its performance gains hold under scrutiny, the work advances model editing beyond localized fact interventions toward handling interdependent rule knowledge, with implications for more consistent reasoning across symbolic, linguistic, and instance-based forms. The code release and benchmark extension are concrete strengths that support reproducibility.

major comments (3)

[§4.2] §4.2 (Causal Tracing Results): The reported form-specific layer localization lacks error bars, variance across the 200 rules, or statistical tests confirming that early-layer sites for formulas/descriptions are significantly non-overlapping with middle-layer sites for instances; without this, the premise for separate DMLE updates remains unverified.
[§6.2] §6.2 (Main Results, Table 2): The 13.91 pp and 50.19 pp average gains are presented without standard deviations, p-values, number of runs, or complete baseline implementation details (e.g., hyperparameter matching), making it impossible to assess whether improvements are statistically reliable or attributable to the distributed design rather than baseline weaknesses.
[§5.1] §5.1 (DMLE Formulation): The method assumes independent early- and middle-layer updates incur no harmful interference with each other or unrelated model behaviors, yet no direct ablation, activation overlap analysis, or general capability preservation metrics are provided to test this load-bearing assumption.

minor comments (2)

[Abstract] The abstract and §6 do not specify how the 'on average' improvements are computed across models and rules (e.g., macro vs. micro averaging).
Figure captions in the causal tracing section could explicitly state the layer ranges and attribution thresholds used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful and constructive comments. We appreciate the opportunity to address these points and strengthen our manuscript accordingly. Below, we provide point-by-point responses to the major comments.

read point-by-point responses

Referee: [§4.2] §4.2 (Causal Tracing Results): The reported form-specific layer localization lacks error bars, variance across the 200 rules, or statistical tests confirming that early-layer sites for formulas/descriptions are significantly non-overlapping with middle-layer sites for instances; without this, the premise for separate DMLE updates remains unverified.

Authors: We agree that including error bars, variance across the 200 rules, and statistical tests would strengthen the evidence for form-specific layer localization. In the revised manuscript, we will add error bars to the figures in §4.2, report the variance, and include statistical tests (e.g., t-tests) to confirm the significant differences between early and middle layers. This will better verify the non-overlapping sites and support the DMLE premise. revision: yes
Referee: [§6.2] §6.2 (Main Results, Table 2): The 13.91 pp and 50.19 pp average gains are presented without standard deviations, p-values, number of runs, or complete baseline implementation details (e.g., hyperparameter matching), making it impossible to assess whether improvements are statistically reliable or attributable to the distributed design rather than baseline weaknesses.

Authors: We acknowledge the need for statistical rigor in reporting the performance gains. We will update the results in §6.2 to include standard deviations across 5 runs, p-values for the comparisons, and detailed information on the number of runs and hyperparameter settings for all baselines and our method. This will allow readers to assess the reliability and attribute the improvements to the distributed multi-layer approach. revision: yes
Referee: [§5.1] §5.1 (DMLE Formulation): The method assumes independent early- and middle-layer updates incur no harmful interference with each other or unrelated model behaviors, yet no direct ablation, activation overlap analysis, or general capability preservation metrics are provided to test this load-bearing assumption.

Authors: This is a valid point regarding the core assumption of DMLE. Although the original manuscript focused on editing performance, we will add in the revision an ablation study on update independence, analysis of activation overlaps, and metrics on general capabilities (e.g., performance on unrelated tasks) to demonstrate that the separate updates do not cause harmful interference. These additions will substantiate the assumption. revision: yes

Circularity Check

0 steps flagged

No significant circularity: empirical causal tracing and benchmark evaluation

full rationale

The paper's chain is: extend RuleEdit benchmark, run causal tracing to locate form-specific layers (formulas/descriptions early, instances middle), propose DMLE as separate updates to those layers, then measure instance portability and rule understanding on held-out tests. No equation or definition reduces to its own inputs by construction. No parameter is fitted on a subset and renamed a prediction. No load-bearing premise rests on a self-citation whose content is unverified or circular. Causal tracing is an external method applied to new data; performance deltas are direct measurements, not tautological. The result is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method depends on the empirical validity of causal tracing for layer localization and the assumption that separate layer updates can be performed without cross-layer interference.

axioms (1)

domain assumption Causal tracing reliably localizes distinct components of rule knowledge to specific transformer layers
Invoked to justify the early-layer versus middle-layer split in DMLE.

pith-pipeline@v0.9.0 · 5591 in / 1072 out tokens · 66066 ms · 2026-05-10T18:28:54.755272+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

17 extracted references · 14 canonical work pages · 5 internal anchors

[1]

What can transformer learn with varying depth? case studies on sequence learning tasks.arXiv preprint arXiv:2404.01601,

Xingwu Chen and Difan Zou. What can transformer learn with varying depth? case studies on sequence learning tasks.arXiv preprint arXiv:2404.01601,

work page arXiv
[2]

DeepSeek-V3.2: Pushing the Frontier of Open Large Language Models

DeepSeek-AI. Deepseek-v3.2: Pushing the frontier of open large language models.arXiv preprint arXiv:2512.02556,

work page internal anchor Pith review Pith/arXiv arXiv
[3]

Alphaedit: Null-space constrained knowledge editing for language mod- els.ArXiv, abs/2410.02355, 2024

URL https://openreview.net/forum?id=X5rO5VyTgB. Junfeng Fang, Houcheng Jiang, Kun Wang, Yunshan Ma, Shi Jie, Xiang Wang, Xiangnan He, and Tat-Seng Chua. Alphaedit: Null-space constrained knowledge editing for language models.arXiv preprint arXiv:2410.02355,

work page arXiv
[4]

Transformer feed-forward layers are key-value memories

Mor Geva, Roei Schuster, Jonathan Berant, and Omer Levy. Transformer feed-forward layers are key-value memories. InProceedings of the 2021 Conference on Empirical Methods in Natural Language Processing, pp. 5484–5495,

2021
[5]

The Llama 3 Herd of Models

URLhttps://arxiv.org/abs/2407.21783. Jia-Chen Gu, Hao-Xiang Xu, Jun-Yu Ma, Pan Lu, Zhen-Hua Ling, Kai-Wei Chang, and Nanyun Peng. Model editing harms general abilities of large language models: Regular- ization to the rescue. InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, pp. 16801–16819,

work page internal anchor Pith review Pith/arXiv arXiv 2024
[6]

Can knowledge editing really correct hallucinations?arXiv preprint arXiv:2410.16251,

Baixiang Huang, Canyu Chen, Xiongxiao Xu, Ali Payani, and Kai Shu. Can knowledge editing really correct hallucinations?arXiv preprint arXiv:2410.16251,

work page arXiv
[7]

Qwen2.5-Coder Technical Report

URLhttps://arxiv.org/abs/2409.12186. Ganesh Jawahar, Benoˆıt Sagot, and Djam´e Seddah. What does bert learn about the structure of language? InProceedings of the 57th annual meeting of the association for computational linguistics, pp. 3651–3657,

work page internal anchor Pith review Pith/arXiv arXiv
[8]

Anyedit: Edit any knowledge encoded in language models.arXiv preprint arXiv:2502.05628,

Houcheng Jiang, Junfeng Fang, Ningyu Zhang, Guojun Ma, Mingyang Wan, Xiang Wang, Xiangnan He, and Tat-seng Chua. Anyedit: Edit any knowledge encoded in language models.arXiv preprint arXiv:2502.05628,

work page arXiv
[9]

Reinforced lifelong editing for language models.arXiv preprint arXiv:2502.05759,

Zherui Li, Houcheng Jiang, Hao Chen, Baolong Bi, Zhenhong Zhou, Fei Sun, Junfeng Fang, and Xiang Wang. Reinforced lifelong editing for language models.arXiv preprint arXiv:2502.05759,

work page arXiv
[10]

2022 , journal =

Kevin Meng, David Bau, Alex Andonian, and Yonatan Belinkov. Locating and editing factual associations in gpt.Advances in neural information processing systems, 35:17359–17372, 2022a. Kevin Meng, Arnab Sen Sharma, Alex Andonian, Yonatan Belinkov, and David Bau. Mass- editing memory in a transformer.arXiv preprint arXiv:2210.07229, 2022b. Eric Mitchell, Cha...

work page arXiv
[11]

Layer-wise evolution of representations in fine-tuned transformers: Insights from sparse autoencoders.arXiv preprint arXiv:2502.16722,

Suneel Nadipalli. Layer-wise evolution of representations in fine-tuned transformers: Insights from sparse autoencoders.arXiv preprint arXiv:2502.16722,

work page arXiv
[12]

Layer importance for mathematical reasoning is forged in pre-training and invariant after post-training.arXiv preprint arXiv:2506.22638,

Aadim Nepal, Safal Shrestha, Anubhav Shrestha, Minwu Kim, Jalal Naghiyev, Ravid Shwartz-Ziv, and Keith Ross. Layer importance for mathematical reasoning is forged in pre-training and invariant after post-training.arXiv preprint arXiv:2506.22638,

work page arXiv
[13]

Gemini: A Family of Highly Capable Multimodal Models

Gemini Team. Gemini: A family of highly capable multimodal models.arXiv preprint arXiv:2312.11805,

work page internal anchor Pith review Pith/arXiv arXiv
[14]

Qwen2 Technical Report

URL https://arxiv.org/abs/2407.10671. Lang Yu, Qin Chen, Jie Zhou, and Liang He. Melo: Enhancing model editing with neuron- indexed dynamic lora. InProceedings of the AAAI Conference on Artificial Intelligence, volume 38, pp. 19449–19457,

work page internal anchor Pith review Pith/arXiv arXiv
[15]

Zhuoran Zhang, Yongxiang Li, Zijian Kan, Keyuan Cheng, Lijie Hu, and Di Wang

URLhttps://openreview.net/forum?id=ZjPrQ656jx. Zhuoran Zhang, Yongxiang Li, Zijian Kan, Keyuan Cheng, Lijie Hu, and Di Wang. Locate-then-edit for multi-hop factual recall under knowledge editing.arXiv preprint arXiv:2410.06331,

work page arXiv
[16]

Can we edit factual knowledge by in-context learning? InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pp

Ce Zheng, Lei Li, Qingxiu Dong, Yuxuan Fan, Zhiyong Wu, Jingjing Xu, and Baobao Chang. Can we edit factual knowledge by in-context learning? InProceedings of the 2023 Conference on Empirical Methods in Natural Language Processing, pp. 4862–4876,

2023
[17]

case_id": 1,

and introductory physics materials (OpenStax, 2016). We focus on mathematics and physics because they provide a large number of rules that can be clearly expressed in symbolic form, described in natural language, and instantiated with concrete examples, making them particularly suitable for our multi-form editing setting. We further restrict our selection...

2016