arxiv: 2604.05383 · v1 · submitted 2026-04-07 · 💻 cs.AI

Recognition: 2 theorem links

· Lean Theorem

Towards Effective In-context Cross-domain Knowledge Transfer via Domain-invariant-neurons-based Retrieval

Jianzhi Yan , Zhiming Li , Le Liu , Zike Yuan , Shiwei Chen , Youcheng Pan , Buzhou Tang , Yang Xiang

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Danny Dongning Sun

Authors on Pith no claims yet

Pith reviewed 2026-05-10 19:27 UTC · model grok-4.3

classification 💻 cs.AI

keywords cross-domain transferin-context learninglogical reasoninglarge language modelsdomain-invariant neuronsretrieval methodLLM boosting

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The pith

Domain-invariant neuron vectors enable retrieval of cross-domain examples that boost LLM reasoning performance.

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

Large language models need demonstrations to reach strong logical reasoning but struggle when expert examples are unavailable in specialized domains. The paper shows that demonstrations from other domains can still help because many underlying logical structures are shared across fields. To locate suitable examples, the authors introduce DIN-Retrieval, which extracts a vector from domain-invariant neurons in hidden representations and uses it to match demonstrations by structural compatibility during in-context learning. Experiments on transfers between mathematical and logical reasoning tasks find that this approach yields higher accuracy than methods restricted to same-domain examples. The result matters because it reduces the need for domain experts to create tailored demonstrations for every new area.

Core claim

The paper claims that a domain-invariant neuron vector can be summarized from hidden representations to remain consistent across domains, allowing retrieval of cross-domain demonstrating examples that share reusable implicit logical structures and thereby improving in-context learning results for LLMs on reasoning problems.

What carries the argument

Domain-invariant-neurons-based retrieval (DIN-Retrieval), which builds a universal hidden representation to select structurally compatible cross-domain demonstrations for in-context learning.

If this is right

Reasoning accuracy rises when LLMs incorporate demonstrations from unrelated domains instead of only same-domain ones.
Expertise-scarce domains such as specialized mathematics or legal analysis become open to performance gains without custom expert examples.
The approach works across multiple transfer settings between mathematical and logical reasoning tasks.
Performance exceeds prior state-of-the-art methods that rely on in-domain demonstrations by an average of 1.8 points.

Where Pith is reading between the lines

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

LLMs appear to encode logical structures in neuron activations in a way that can be separated from domain-specific content.
Precomputing DIN vectors for large example collections could make cross-domain retrieval fast enough for real-time use.
The same neuron-based matching idea could be tested on tasks beyond reasoning, such as code generation where structural analogies cross domains.

Load-bearing premise

Substantial differences between domains still leave reusable implicit logical structures that can be captured effectively by the DIN vector for retrieval.

What would settle it

Applying DIN-Retrieval to new cross-domain reasoning task pairs and measuring no accuracy gain over random selection or standard in-domain retrieval would show the method does not deliver the claimed benefit.

Figures

Figures reproduced from arXiv: 2604.05383 by Buzhou Tang, Danny Dongning Sun, Jianzhi Yan, Le Liu, Shiwei Chen, Yang Xiang, Youcheng Pan, Zhiming Li, Zike Yuan.

**Figure 1.** Figure 1: Three types of failures in zero-shot LLMs. (A) Missing intermediate links, (B) incomplete branch integration, and (C) ignored blocking conditions 2022). While recent work has examined out-ofdistribution (OOD) robustness in ICL (Tang et al., 2023; Sun et al., 2024; Siska et al., 2024; Yuan et al., 2024; Honda and Oka, 2025; He et al., 2024; Cheng et al., 2025; He et al., 2025), these studies typically pres… view at source ↗

**Figure 2.** Figure 2: Overview of the proposed DIN-based ICL framework. The model identifies domain-invariant neurons (DINs) from source and target activations (A), constructs a stable DIN vector for representation (B), retrieves demonstrations via DIN vector similarity (C), and performs cross-domain chain-of-thought reasoning (D). drawn from a dataset D = {(xi , yi)} N i=1. This formulation allows the model to condition on the… view at source ↗

**Figure 3.** Figure 3: Perplexity increase from pruning DINs vs. random neurons across the last six layers. Results are averaged over 300 trials. The solid line denotes mean PPL increase after pruning DINs, while the dashed line and shaded areas indicate the random pruning baseline (mean with 95th and 99th percentiles) ▼ indicates statistically significant improvement (p < 0.05). to −2), significantly exceeding the random pruni… view at source ↗

**Figure 5.** Figure 5: Case study illustrating a binary branching [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 6.** Figure 6: Case study illustrating a blocking-condition [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 8.** Figure 8: Mean DIN accuracy across different combinations of kratio and layer range. but over-selection may introduce noise [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 7.** Figure 7: Effect of key hyperparameters on DINbased ICL performance. Left: Increasing kratio generally leads to slightly higher DIN accuracy. Right: DIN subspaces extracted from deeper layers tend to outperform shallower ones. We investigate how key hyperparameters affect the effectiveness of DIN selection and its downstream impact on in-context reasoning. Specifically, we analyze the influence of the selection… view at source ↗

read the original abstract

Large language models (LLMs) have made notable progress in logical reasoning, yet still fall short of human-level performance. Current boosting strategies rely on expert-crafted in-domain demonstrations, limiting their applicability in expertise-scarce domains, such as specialized mathematical reasoning, formal logic, or legal analysis. In this work, we demonstrate the feasibility of leveraging cross-domain demonstrating examples to boost the LLMs' reasoning performance. Despite substantial domain differences, many reusable implicit logical structures are shared across domains. In order to effectively retrieve cross-domain examples for unseen domains under investigation, in this work, we further propose an effective retrieval method, called domain-invariant neurons-based retrieval (\textbf{DIN-Retrieval}). Concisely, DIN-Retrieval first summarizes a hidden representation that is universal across different domains. Then, during the inference stage, we use the DIN vector to retrieve structurally compatible cross-domain demonstrations for the in-context learning. Experimental results in multiple settings for the transfer of mathematical and logical reasoning demonstrate that our method achieves an average improvement of 1.8 over the state-of-the-art methods \footnote{Our implementation is available at https://github.com/Leon221220/DIN-Retrieval}.

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

The paper introduces DIN-Retrieval to pull cross-domain examples via low-variance neurons for LLM reasoning, claiming a 1.8-point average gain, but the results do not isolate whether the method actually captures shared logical structures.

read the letter

The main takeaway is that this work shows cross-domain demonstrations can improve LLM performance on math and logic tasks, with their DIN-Retrieval method delivering the reported lift over existing retrieval baselines. They identify neurons with low activation variance across domains, summarize them into a vector, and use that vector to fetch examples at inference time. That approach is the concrete new piece here, moving past plain similarity search for in-context learning. The paper does a solid job laying out the practical problem of expertise-scarce domains and running experiments across several transfer settings for mathematical and logical reasoning. The implementation link is a plus for anyone who wants to check the details. The central assumption is that domain-invariant neurons encode reusable logical patterns rather than just generic features. The experiments compare against standard in-domain and retrieval methods, but they do not include the direct control that would test this: swapping the DIN vector for a non-invariant summary like a final-layer token or random neuron subset while holding the rest of the retrieval fixed. Without that, the 1.8-point number could come from better overall example selection instead of the claimed structure transfer. The rest of the setup looks like typical LLM evaluation—no obvious data issues or circular claims in the reported results. Citations track the usual ICL and retrieval papers without gaps that stand out. This paper is aimed at people building retrieval-augmented prompting systems for reasoning, especially where in-domain examples are scarce. A reader who needs a new retrieval trick for cross-domain transfer will get usable ideas from the method section and the reported numbers. It is worth sending to peer review because the idea is straightforward to implement and the gains are positive, even though the mechanism claim needs tighter evidence. Ask the authors for the missing ablation and clearer breakdowns by task type.

Referee Report

2 major / 2 minor

Summary. The paper proposes DIN-Retrieval, a method that first identifies domain-invariant neurons (DIN) with low activation variance across source domains to form a universal hidden representation, then uses the aggregated DIN vector at inference to retrieve cross-domain in-context demonstrations for LLMs. It claims this enables effective transfer of implicit logical structures across substantially different domains (e.g., mathematical and logical reasoning), yielding an average 1.8 improvement over state-of-the-art in-domain and retrieval baselines, with code released at https://github.com/Leon221220/DIN-Retrieval.

Significance. If the central attribution holds, the work could meaningfully extend in-context learning to expertise-scarce domains by reducing reliance on expert-crafted same-domain examples. The open-source implementation is a clear strength for reproducibility and follow-up work.

major comments (2)

[Experimental results] Experimental results section: the reported average 1.8 improvement is not isolated to the domain-invariance hypothesis. No ablation is presented that replaces the DIN vector with a non-invariant summary (e.g., last-layer CLS token or random neuron subset) while keeping the retrieval mechanics identical; without this control, the gain could arise from general semantic quality rather than reusable logical structures.
[Method] Method section: the DIN selection criterion (low variance across source domains) is defined, but no analysis or visualization demonstrates that the selected neurons specifically encode shared logical patterns (proof steps, deduction structures) rather than other transferable features; direct evidence for this interpretation is required to support the central claim.

minor comments (2)

[Abstract] Abstract: the claim of 'an average improvement of 1.8' should specify the exact tasks, number of domains, baselines, and whether the improvement is statistically significant.
[Method] Notation: the precise aggregation operation used to form the DIN vector from selected neurons should be stated explicitly (e.g., mean, concatenation) rather than described only as 'summarizes a hidden representation'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. The comments highlight important ways to strengthen the attribution of our results to the domain-invariance hypothesis and to provide more direct support for our interpretation of the selected neurons. We address each major comment below.

read point-by-point responses

Referee: [Experimental results] Experimental results section: the reported average 1.8 improvement is not isolated to the domain-invariance hypothesis. No ablation is presented that replaces the DIN vector with a non-invariant summary (e.g., last-layer CLS token or random neuron subset) while keeping the retrieval mechanics identical; without this control, the gain could arise from general semantic quality rather than reusable logical structures.

Authors: We agree that the current experiments do not fully isolate the contribution of domain invariance. In the revised version we will add an ablation study that keeps the retrieval pipeline fixed but substitutes the DIN vector with non-invariant alternatives (last-layer CLS token and random neuron subsets of matching dimensionality). The results of this control will be reported alongside the main tables to clarify whether the observed gains are attributable to invariance rather than general semantic quality. revision: yes
Referee: [Method] Method section: the DIN selection criterion (low variance across source domains) is defined, but no analysis or visualization demonstrates that the selected neurons specifically encode shared logical patterns (proof steps, deduction structures) rather than other transferable features; direct evidence for this interpretation is required to support the central claim.

Authors: We acknowledge that the manuscript currently lacks direct evidence linking the low-variance neurons to reusable logical structures. We will add a new analysis subsection that includes (i) activation heatmaps of the selected neurons on matched logical steps across domains and (ii) qualitative examples showing how these neurons respond to analogous deduction patterns (e.g., modus ponens steps) in mathematical and logical reasoning tasks. This material will be placed in the method or experimental section to support the central interpretation. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical method is self-contained

full rationale

The paper proposes DIN-Retrieval as a practical, empirical technique: neurons are selected for low activation variance across source domains, their representations are aggregated into a DIN vector, and this vector is used at inference time to retrieve cross-domain examples for in-context learning. All central claims (feasibility of cross-domain transfer and 1.8-point average gains) rest on experimental comparisons against external baselines and SOTA methods rather than on any derivation that reduces to its own inputs by construction. No self-definitional loops, fitted parameters renamed as predictions, load-bearing self-citations, or ansatzes smuggled via prior work appear in the described chain. The hypothesis that DIN vectors encode reusable logical structures is presented as an assumption to be tested, not as a premise that is definitionally true.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on one domain assumption and one invented entity; no free parameters are mentioned.

axioms (1)

domain assumption Reusable implicit logical structures are shared across different domains despite substantial differences.
Explicitly stated in the abstract as the basis for cross-domain transfer feasibility.

invented entities (1)

Domain-invariant neurons (DIN) no independent evidence
purpose: Summarize a hidden representation that is universal across domains for retrieval of compatible demonstrations.
New concept introduced by the paper with no mention of prior independent validation.

pith-pipeline@v0.9.0 · 5528 in / 1153 out tokens · 69312 ms · 2026-05-10T19:27:21.788768+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

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unclear
Relation between the paper passage and the cited Recognition theorem.

DIN-Retrieval first summarizes a hidden representation that is universal across different domains... neurons whose activation polarities remain consistent across source and target domains based on cross-domain z-score statistics
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We identify DINs by selecting neurons whose activation polarities remain consistent... I = {k | zS_k > τ ∧ zT_k > τ} ∪ ...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

CoDA: Towards Effective Cross-domain Knowledge Transfer via CoT-guided Domain Adaptation
cs.AI 2026-04 unverdicted novelty 6.0

CoDA aligns cross-domain latent reasoning representations in LLMs via CoT distillation and MMD to enable effective knowledge transfer without in-domain demonstrations.

Reference graph

Works this paper leans on

7 extracted references · 6 canonical work pages · cited by 1 Pith paper · 1 internal anchor

[1]

Training Verifiers to Solve Math Word Problems

Training verifiers to solve math word prob- lems.arXiv preprint arXiv:2110.14168. Damai Dai, Li Dong, Yaru Hao, Zhifang Sui, Baobao Chang, and Furu Wei. 2021. Knowledge neu- rons in pretrained transformers.arXiv preprint arXiv:2104.08696. Qingxiu Dong, Lei Li, Damai Dai, Ce Zheng, Jingyuan Ma, Rui Li, Heming Xia, Jingjing Xu, Zhiyong Wu, Baobao Chang, Xu ...

work page internal anchor Pith review Pith/arXiv arXiv 2021
[2]

Farahani, S

A survey on in-context learning. InProceed- ings of the 2024 Conference on Empirical Methods in Natural Language Processing, pages 1107–1128, Miami, Florida, USA. Association for Computational Linguistics. Abolfazl Farahani, Sahar V oghoei, Khaled Rasheed, and Hamid R. Arabnia. 2020. A brief review of domain adaptation.Preprint, arXiv:2010.03978. Yaroslav...

work page arXiv 2024
[3]

FOLIO: Natural Language Reasoning with First-Order Logic

Coverage-based example selection for in- context learning. InFindings of the Association for Computational Linguistics: EMNLP 2023, pages 13924–13950, Singapore. Association for Computa- tional Linguistics. Simeng Han, Hailey Schoelkopf, Yilun Zhao, Zhenting Qi, Martin Riddell, Luke Benson, Lucy Sun, Eka- terina Zubova, Yujie Qiao, Matthew Burtell, David ...

work page arXiv 2023
[4]

Protoreasoning: Prototypes as the foundation for generalizable reasoning in llms

Protoreasoning: Prototypes as the founda- tion for generalizable reasoning in llms.Preprint, arXiv:2506.15211. Xuanli He, Yuxiang Wu, Oana-Maria Camburu, Pasquale Minervini, and Pontus Stenetorp. 2024. Us- ing natural language explanations to improve robust- ness of in-context learning. InProceedings of the 62nd Annual Meeting of the Association for Compu...

work page arXiv 2024
[5]

Learning to re- trieve prompts for in-context learning.arXiv preprint arXiv:2112.08633,

Learning to retrieve prompts for in-context learning.arXiv preprint arXiv:2112.08633. Hassan Sajjad, Nadir Durrani, and Fahim Dalvi. 2022. Neuron-level interpretation of deep nlp models: A survey.Transactions of the Association for Computa- tional Linguistics, 10:1285–1303. Abulhair Saparov and He He. 2022. Language models are greedy reasoners: A systemat...

work page arXiv 2022
[6]

Learning to retrieve in-context examples for large language models,

Analysing neurons across languages and tasks in large language models. InProceedings of the 2024 Conference on Empirical Methods in Natural Language Processing. Liang Wang, Nan Yang, and Furu Wei. 2023. Learning to retrieve in-context examples for large language models.arXiv preprint arXiv:2307.07164. Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma...

work page arXiv 2024
[7]

The Legend of Zelda is not on the Top 10 list

The results confirm that deeper layer ranges and moderate kratio values yield the most reliable DIN subspaces across tasks. Notably, the highest DIN accuracy (0.659) is achieved with kratio = 0.03 and layer range L −4:−1, indicating that quality can sometimes outweigh quantity when selecting stable neurons. These results highlight the importance of carefu...