HyperPatch: Sequential Knowledge Editing Under n-ary Structural Drift

# Sequential Knowledge Editing Under 𝑛-ary Structural Drift
Source: [https://arxiv.org/html/2606.03179](https://arxiv.org/html/2606.03179)
\(2026\)

###### Abstract\.

Large Language Models \(LLMs\) rely on Knowledge Editing \(KE\) to maintain temporal validity, yet real\-world knowledge is inherentlynn\-ary\. We demonstrate that in non\-stationary environments, sequential updates to complex relations induceStructural Drift, a phenomenon where the binary reification ofnn\-ary events into triples fractures relational atomicity\. This precipitatesStructure\-Conditioned Knowledge Transfer Failure\(SKTF\), a systematic mis\-grounding of the retriever frequently misdiagnosed as parametric hallucination\. To tackle this, we proposeHyperPatch, a parameter\-preserving framework that reformulates sequential KE as a stability problem over hypergraph manifolds\. HyperPatch preserves event integrity through three phases: \(i\)Structural Prior Initialization, establishing a topology\-aware embedding space via contrastive learning on a Hypergraph Neural Network \(HGNN\) to capture high\-order correlations; \(ii\)Sequential Topology Editing, utilizing a dual\-stage mechanism that employs SimHash\-based Topological Alignment for rapid conflict resolution and Topological LoRA Adaptation to track drift without backbone retraining; and \(iii\)Structure\-Conditioned Reasoning, which integrates globally consistent evidence from fused linguistic and structural manifolds\. On the MQuAKE\-CF and MQuAKE\-T benchmarks, HyperPatch achieves relative gains in Hop\-wise Accuracy \(H\-Acc\) of 96\.24% and 21\.06% over the strongest baseline, respectively\. Further ablations demonstrate superior reliability under continuousnn\-ary update streams, whereas the standard KG\-based variant suffers H\-Acc collapses of up to 88\.3% due to structural misalignment\. Our code is publicly available at[https://github\.com/Kevin20010912/HyperPatch\.git](https://github.com/Kevin20010912/HyperPatch.git)\.

Knowledge Editing; Hypergraph Editing; N\-ary Relations; Structural Drift; Retrieval\-Augmented Generation

††journalyear:2026††copyright:cc††conference:Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V\.2; August 9–13, 2026; Jeju Island, Republic of Korea\.††booktitle:Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V\.2 \(KDD 2026\), August 9–13, 2026, Jeju Island, Republic of Korea††isbn:979\-8\-4007\-2259\-2/2026/08††doi:10\.1145/3770855\.3817820††ccs:Computing methodologies Knowledge representation and reasoning††ccs:Information systems Language models††ccs:Information systems Question answering## 1\.Introduction

Large Language Models \(LLMs\) are increasingly used as the generator in multi\-hop Question Answering \(QA\) pipelines\(Zhonget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib15)\), where answers are produced by conditioning on external knowledge sources \(e\.g\., retrieved text or graph facts\)\. In such systems, end\-to\-end reliability depends not only on the parametric reasoning of LLMs, but also on whether the external knowledge being accessed remains current and consistently reachable through the system’s representation and retrieval interfaces\. When facts evolve, a practical maintenance primitive isKnowledge Editing\(KE\): performing localized updates that inject new facts while avoiding global retraining and minimizing collateral changes\(Menget al\.,[2022](https://arxiv.org/html/2606.03179#bib.bib6),[2023](https://arxiv.org/html/2606.03179#bib.bib7)\)\. Ideally, KE facilitates a “clean contract”: newly injected facts should be immediately actionable for downstream reasoning while maintaining global consistency\.

![Refer to caption](https://arxiv.org/html/2606.03179v1/x1.png)\(a\)
![Refer to caption](https://arxiv.org/html/2606.03179v1/x2.png)\(b\)
![Refer to caption](https://arxiv.org/html/2606.03179v1/x3.png)\(c\)

Figure 1\.SKTF undernn\-ary structural drift\. \(a\) Factorization to binary edges breaks event coupling and retrieves fragments\. \(b\) Binary walks create locally similar but globally invalid compositions\. \(c\) HyperPatch retrieves atomic hyperedges, preserving event consistency across updates\.Most prior work probes this contract in*static*regimes, implicitly assuming that the knowledge representation and the retriever’s embedding manifold remain aligned over time\(Menget al\.,[2022](https://arxiv.org/html/2606.03179#bib.bib6),[2023](https://arxiv.org/html/2606.03179#bib.bib7)\)\. Real deployments, however, experience sequential updates and schema evolution that introducestructural drift\(Gamaet al\.,[2014](https://arxiv.org/html/2606.03179#bib.bib8)\)\. We highlight a failure mode under such drift:Structure\-Conditioned Knowledge Transfer Failure \(SKTF\)\. SKTF arises when the topology mediating knowledge access \(e\.g\., how complex relations are factorized and connected\) diverges from the retriever’s learned embedding distribution\. As a result, the system may retrieve stale or structurally incompatible evidence despite the underlying knowledge being correctly updated, mis\-grounding the generator and producing confident errors that are often misattributed to hallucination or parametric conflicts\(Chenet al\.,[2022](https://arxiv.org/html/2606.03179#bib.bib9)\)\. We argue that, undernn\-ary structural shifts, these errors primarily reflect*retrieval\-manifold misalignment*rather than an inherent deficiency in the reasoning capacity\.

Specifically, SKTF stems from a mismatch between how facts arise as*events*and how they are represented for retrieval\. Real\-world knowledge is oftennn\-ary: an event jointly binds multiple entities, roles, attributes, and contextual qualifiers\(Wenet al\.,[2016](https://arxiv.org/html/2606.03179#bib.bib10)\)\. In contrast, standard Knowledge Graph \(KG\) pipelines typically*project*or*reify*such events into sets of binary triples\(Rossoet al\.,[2020](https://arxiv.org/html/2606.03179#bib.bib11)\)to support link\-based storage and embedding\-based retrieval\. While this approximation is often acceptable when the schema and data distribution are stable, it becomes brittle under sequential updates and evolving entity/query distributions\. Figure[1](https://arxiv.org/html/2606.03179#S1.F1)illustrates two drift mechanisms:\(a\) Event Factorization Drift, where decomposing annn\-ary event into loosely\-coupled edges weakens semantic coupling\. Under distribution shift \(e\.g\., a 2023 update to a player’s profile\), the retriever’s neighborhood is reshaped\. Fragments such as theRonaldoentity and thePremier Leaguerelation may remain proximal in embedding space despite belonging to different underlying events\. This yields evidence that is locally relevant yet*event\-incomplete*\(Thakuret al\.,[2021](https://arxiv.org/html/2606.03179#bib.bib12)\), as the retriever can no longer enforce the originalnn\-ary constraints\.\(b\) Spurious Multi\-hop Composition, where binary projections admit accidental multi\-hop paths that appear plausible hop\-by\-hop but fail to form a valid global chain when composed\(Minet al\.,[2019](https://arxiv.org/html/2606.03179#bib.bib13)\)\. In both cases, retrieval returns evidence that is locally plausible but globally inconsistent, so the generator is mis\-grounded not because the required knowledge is absent, but because the system assembles an invalid event structure from drifted binary proxies\.

Despite the urgency of SKTF, existing literature overlooks the structural dimension of editing\.Parametric Editing\(Menget al\.,[2022](https://arxiv.org/html/2606.03179#bib.bib6),[2023](https://arxiv.org/html/2606.03179#bib.bib7)\)effectively modifies single\-hop facts but struggles with distributed evidence\(Zhonget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib15)\)and suffers from catastrophic forgetting under sequential streams\(Kirkpatricket al\.,[2017](https://arxiv.org/html/2606.03179#bib.bib16)\)\. Conversely,Retrieval\-Augmented Editing\(Mitchellet al\.,[2022b](https://arxiv.org/html/2606.03179#bib.bib17); Hanet al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib18)\)relies on frozen, dense retrievers that are agnostic to evolving graph topology\. These methods assume embedding spaces remain aligned with knowledge structures, which is an assumption that fails asnn\-ary relations drift\. Currently, no framework explicitly models thestability of event compatibilityduring sequential editing\. This motivates a shift towardHypergraphs\. Unlike standard KGs, a hypergraph treats eachnn\-ary event as a single hyperedge, preserving the atomic unit that couples participants and constraints\(Fenget al\.,[2019](https://arxiv.org/html/2606.03179#bib.bib19); Haghighiet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib41)\)\. Hypergraph\-based Retrieval\-Augmented Generation \(RAG\)\(Luoet al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib35)\)can thus retrieve evidence as “event\-consistent units” rather than arbitrary triple chains, mitigating spurious composition\(Edgeet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib21)\)\. Crucially for editing, hypergraphs allow drift to be measured at the level of event compatibility\. As shown in Fig\.[1](https://arxiv.org/html/2606.03179#S1.F1)\(c\), while standard KGs fragment context into drifting triples, hyperedge representations maintain structural integrity\. This ensures that updates to a single participant do not decouple associated context, providing a robust substrate for scalable, sequential knowledge editing\.

In this paper, we reformulate sequential knowledge editing as a topological stability problem undernn\-ary structural drift\. We posit that the primary object to be preserved is theevent compatibility manifold, which is the latent structure governing hownn\-ary relations are retrieved and composed\. To this end, we introduceHyperPatch, a parameter\-preserving framework that stabilizes hyperedge representations through three core innovations: \(i\)Structural Prior Initialization:To mitigate SKTF, we synchronize the retriever’s embedding manifold with the evolving hypergraph topology via an HGNN and topological LoRA adaptation\. By grounding updates innn\-ary structural constraints, this replay\-free mechanism circumvents the catastrophic forgetting inherent in sequential editing\(Hartvigsenet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib22)\), maintaining a robust structural anchor as the knowledge base evolves\. \(ii\)Sequential Topology Editing:To tacklenn\-ary updates at scale, we implement a retrieval layer based on hyperedge\-centric hashing\. This facilitatesO​\(1\)O\(1\)structural mapping for rapid hyperedge replacement or expansion, effectively decoupling update latency from the cumulative edit volume\. \(iii\)Structure\-Conditioned Reasoning:For drift\-resilient inference, HyperPatch dynamically integrates retrieval manifolds with updatednn\-ary topologies\. This facilitates precise entity grounding and consistent traversal of reasoning paths, maintaining multi\-hop QA performance even under stochastic structural fluctuations\.

Our contributions are as follows:

- •We identify SKTF as a dominant error source in dynamic multi\-hop QA and provide a theoretical bound linking retrieval drift to reasoning risk innn\-ary settings\.
- •We proposeHyperPatch, the first framework to integrate hypergraph structural priors into sequential KE\. By preserving event integrity, HyperPatch robustly mitigates thenn\-ary factorization drift that fractures standard triple\-based editors\.
- •Evaluations on multi\-hop benchmarks demonstrate that HyperPatch achieves superior reliability \(96\.24% and 21\.06% H\-Acc\) and maintains robustness to distributional shifts, mitigating the catastrophic 42\.9%–88\.3% H\-Acc degradation inherent in KG\-based variant\. Simultaneously, HyperPatch delivers a25\.9×25\.9\\timesretrieval speedup over competitive knowledge editing frameworks\.

![Refer to caption](https://arxiv.org/html/2606.03179v1/x4.png)Figure 2\.The overall framework of HyperPatch\.
## 2\.Preliminaries

We formally define the representation ofnn\-ary knowledge \([Section2\.1](https://arxiv.org/html/2606.03179#S2.SS1)\), the sequential editing setting \([Section2\.2](https://arxiv.org/html/2606.03179#S2.SS2)\), and the structural drift that challenges contemporary systems \([Section2\.3](https://arxiv.org/html/2606.03179#S2.SS3)\)\.

### 2\.1\.nn\-ary Relational Knowledge Graphs

Real\-world events typically manifest asnn\-ary relational constraints where semantic validity depends on the joint participation of multiple entities and attributes\.

###### Definition 2\.0\(nn\-ary Fact\):

Annn\-ary factffis an atomic tuplef=\(r,\{v1,…,vn\}\)f=\(r,\\\{v\_\{1\},\\dots,v\_\{n\}\\\}\), wherer∈ℛr\\in\\mathcal\{R\}is the relation type and\{vi\}⊆𝒱\\\{v\_\{i\}\\\}\\subseteq\\mathcal\{V\}are the participating entities\. Unlike binary triples\(s,r,o\)\(s,r,o\),ffis atopological unitwhose semantics are lost under binary factorization\.

To preserve these higher\-order dependencies, we introduce aKnowledge Hypergraphstructure\.

###### Definition 2\.0\(Knowledge Hypergraph\):

A knowledge hypergraph isℋ=\(𝒱,ℰ\)\\mathcal\{H\}=\(\\mathcal\{V\},\\mathcal\{E\}\), where𝒱\\mathcal\{V\}is the set of entity vertices andℰ⊆2𝒱∖\{∅\}\\mathcal\{E\}\\subseteq 2^\{\\mathcal\{V\}\}\\setminus\\\{\\emptyset\\\}is the set of hyperedges\. Each hyperedgee∈ℰe\\in\\mathcal\{E\}represents annn\-ary factff, preserving event atomicity by connecting all\{vi\}\\\{v\_\{i\}\\\}participants\.

Each entityv∈𝒱v\\in\\mathcal\{V\}and hyperedgee∈ℰe\\in\\mathcal\{E\}is associated with a textual descriptionxv,xex\_\{v\},x\_\{e\}, projected into a structure\-aware latent space via an encoder to yield embeddings𝐱v,𝐱e∈ℝdtext\\mathbf\{x\}\_\{v\},\\mathbf\{x\}\_\{e\}\\in\\mathbb\{R\}^\{d\_\{\\text\{text\}\}\}\. The collective representations form the textual embedding matrix𝐗∈ℝN×dtext\\mathbf\{X\}\\in\\mathbb\{R\}^\{N\\times d\_\{\\text\{text\}\}\}, whereN=\|𝒱\|\+\|ℰ\|N=\|\\mathcal\{V\}\|\+\|\\mathcal\{E\}\|\.

### 2\.2\.Sequential Knowledge Editing

Sequential Knowledge Editing \(SKE\) involves a continuous stream of update requestsΔ=\{δ1,…,δT\}\\Delta=\\\{\\delta\_\{1\},\\dots,\\delta\_\{T\}\\\}\. Eachδt=\(fold→fnew\)\\delta\_\{t\}=\(f\_\{\\text\{old\}\}\\to f\_\{\\text\{new\}\}\)is a directive to transition the hypergraph fromℋt−1\\mathcal\{H\}\_\{t\-1\}toℋt\\mathcal\{H\}\_\{t\}\. A successful SKE framework must satisfy:

###### Definition 2\.0\(Edit Request\):

An edit requestδt\\delta\_\{t\}is a directive to insert, delete, or modify annn\-ary fact, denoted asδt=\(fold→fnew\)\\delta\_\{t\}=\(f\_\{\\text\{old\}\}\\to f\_\{\\text\{new\}\}\), wherefnewf\_\{\\text\{new\}\}represents the target knowledge state that must be incorporated into the hypergraph topology\.

The objective of Sequential Knowledge Editing \(SKE\) is to transition the system from state𝒮t−1\\mathcal\{S\}\_\{t\-1\}to𝒮t\\mathcal\{S\}\_\{t\}satisfying three conditions:

- •Reliability \(Edit Success\):The system correctly answers queriesQeditQ\_\{\\text\{edit\}\}targetingfnewf\_\{\\text\{new\}\}, ensuring the new knowledge is effectively integrated\(Yaoet al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib26)\)\.
- •Locality \(Specificity\):The system maintains performance on queriesQlocQ\_\{\\text\{loc\}\}targeting unrelated knowledge, thus mitigating the catastrophic forgetting characteristic of sequential learning\(Kirkpatricket al\.,[2017](https://arxiv.org/html/2606.03179#bib.bib16)\)\.
- •Structural Stability:The retrieval mechanism adapts to the evolving topology ofℋt\\mathcal\{H\}\_\{t\}to prevent retrieval drift, a challenge frequently overlooked in static retrieval\-augmented editing\.

### 2\.3\.Problem Formulation

The primary challenge in SKE isStructural Drift\. As edits accumulate, the topological distribution ofℋt\\mathcal\{H\}\_\{t\}diverges from the retriever’s original training prior𝒟0\\mathcal\{D\}\_\{0\}\. This precipitatesStructure\-Conditioned Knowledge Transfer Failure \(SKTF\), where retrieval becomes locally plausible but structurally invalid forfnewf\_\{\\text\{new\}\}\.

###### Problem\(SKE undernn\-ary Structural Drift\):

Given an initial hypergraphℋ0\\mathcal\{H\}\_\{0\}, a pre\-trained retrieval\-augmented reasoning modelℳ\\mathcal\{M\}, and a continuous stream ofnn\-ary edit requestsΔ=\{δ1,δ2,…,δT\}\\Delta=\\\{\\delta\_\{1\},\\delta\_\{2\},\\dots,\\delta\_\{T\}\\\}, our objective is to learn:

1. \(1\)AStructural Graph UpdateΨ​\(ℋt−1,δt\)→ℋt\\Psi\(\\mathcal\{H\}\_\{t\-1\},\\delta\_\{t\}\)\\to\\mathcal\{H\}\_\{t\}that modifies the hypergraph topology to explicitly incorporate the constraints offnewf\_\{\\text\{new\}\}\.
2. \(2\)AParameter\-Preserving Model AdaptationΦ​\(ℳ,δt\)→ℳt\\Phi\(\\mathcal\{M\},\\delta\_\{t\}\)\\to\\mathcal\{M\}\_\{t\}that aligns the retrieval embedding space with the updated topology without retraining backbone parameters\.

The goal is to maximize multi\-hop reasoning accuracy on the evolving query distributionPt​\(q\)P\_\{t\}\(q\)by ensuring that for anyqq, the retrieved hyperedgesTopK⁡\(q,ℋt\)\\operatorname\{TopK\}\(q,\\mathcal\{H\}\_\{t\}\)form a globally consistent event chain satisfyingfnewf\_\{\\text\{new\}\}\.

## 3\.Methodology

We proposeHyperPatch, a framework designed to resolveStructure\-Conditioned Knowledge Transfer Failure\(SKTF\) by enforcing topological consistency during sequential editing\. Unlike parametric editors that overwrite weights, HyperPatch maintains a persistent hypergraph structure, ensuring thatnn\-ary relations remain semantically atomic across continuous updates\.

### 3\.1\.Framework Overview

As illustrated in Figure[2](https://arxiv.org/html/2606.03179#S1.F2), the HyperPatch consists of three phases to align the retrieval mechanism with the shifting knowledge topology: \(a\)Structural Prior Initialization:We construct hypergraphℋ0\\mathcal\{H\}\_\{0\}and pre\-train an HGNN via contrastive learning, establishing a topology\-aware embedding space capturing high\-order entity correlations\. \(b\)Sequential Topology Editing:To handle a continuous edit streamΔ\\Delta, we introduce a dual\-stage update mechanism\. First, Topological Alignment \(Ψ\\Psi\) determines whether editδt\\delta\_\{t\}requires structural replacement or additive expansion\. Second, Topological LoRA Adaptation \(Φ\\Phi\) realigns embeddings with modified topology without backbone retraining, tracking structural drift\. \(c\)Structure\-Conditioned Reasoning:During inference, Dual\-Manifold Retrieval queries both linguistic and structural manifolds to synthesize globally consistent evidence for multi\-hop reasoning\.

### 3\.2\.Structural Prior Initialization

To provide robust structural priors for sequential editing, we pre\-train an HGNN on the initial hypergraphℋ0=\(𝒱0,ℰ0\)\\mathcal\{H\}\_\{0\}=\(\\mathcal\{V\}\_\{0\},\\mathcal\{E\}\_\{0\}\)\(Fenget al\.,[2019](https://arxiv.org/html/2606.03179#bib.bib19)\)\. This phase establishes a topology\-aware manifold where the latent representations of entities andnn\-ary facts are aligned\.

Event Alignment\.Let𝐱v∈ℝdtext\\mathbf\{x\}\_\{v\}\\in\\mathbb\{R\}^\{d\_\{\\text\{text\}\}\}and𝐱e∈ℝdtext\\mathbf\{x\}\_\{e\}\\in\\mathbb\{R\}^\{d\_\{\\text\{text\}\}\}denote textual embeddings for entityv∈𝒱0v\\in\\mathcal\{V\}\_\{0\}and hyperedgee∈ℰ0e\\in\\mathcal\{E\}\_\{0\}from a frozen encoder\. We introduce a learnable projectorP:ℝdtext→ℝdHGNNP:\\mathbb\{R\}^\{d\_\{\\text\{text\}\}\}\\to\\mathbb\{R\}^\{d\_\{\\text\{HGNN\}\}\}mapping text embeddings to the HGNN’s latent space:

\(1\)𝐡i\(0\)=P​\(𝐱i\),∀i∈𝒱0∪ℰ0\.\\mathbf\{h\}\_\{i\}^\{\(0\)\}=P\(\\mathbf\{x\}\_\{i\}\),\\quad\\forall i\\in\\mathcal\{V\}\_\{0\}\\cup\\mathcal\{E\}\_\{0\}\.
Contrastive Pre\-training\.The HGNN, denoted as𝒢θ\\mathcal\{G\}\_\{\\theta\}, propagates messages overℋ0\\mathcal\{H\}\_\{0\}to capture high\-order dependencies\. The pre\-training objective enforces “structural incidence,” ensuring that entities and the hyperedges they participate in reside closely in the latent space\. We optimize𝒢θ\\mathcal\{G\}\_\{\\theta\}via a binary cross\-entropy contrastive loss\. Let𝐳v\\mathbf\{z\}\_\{v\}and𝐳e\\mathbf\{z\}\_\{e\}be the output embeddings\. We define the set of positive incident pairs asℐ\+=\{\(v,e\)∣v∈e\}\\mathcal\{I\}^\{\+\}=\\\{\(v,e\)\\mid v\\in e\\\}and negative pairsℐ−\\mathcal\{I\}^\{\-\}via random sampling:

\(2\)ℒs=−1\|ℐ\+\|​∑\(v,e\)∈ℐ\+\[log⁡σ​\(𝐳v⊤​𝐳e\)\+𝔼e′∼ℐ−​\[log⁡\(1−σ​\(𝐳v⊤​𝐳e′\)\)\]\],\\mathcal\{L\}\_\{\\text\{s\}\}=\\frac\{\-1\}\{\|\\mathcal\{I\}^\{\+\}\|\}\\sum\_\{\(v,e\)\\in\\mathcal\{I\}^\{\+\}\}\\left\[\\log\\sigma\(\\mathbf\{z\}\_\{v\}^\{\\top\}\\mathbf\{z\}\_\{e\}\)\+\\mathbb\{E\}\_\{e^\{\\prime\}\\sim\\mathcal\{I\}^\{\-\}\}\\left\[\\log\(1\-\\sigma\(\\mathbf\{z\}\_\{v\}^\{\\top\}\\mathbf\{z\}\_\{e^\{\\prime\}\}\)\)\\right\]\\right\],whereσ​\(⋅\)\\sigma\(\\cdot\)is the sigmoid function\(Liet al\.,[2025b](https://arxiv.org/html/2606.03179#bib.bib38); Liao and Mok,[2024](https://arxiv.org/html/2606.03179#bib.bib42); Chenet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib44)\)\.

Parameter Preservation\.During initialization, gradients flow through bothPPand𝒢θ\\mathcal\{G\}\_\{\\theta\}\. Upon convergence,𝒢θ\\mathcal\{G\}\_\{\\theta\}is frozen to serve as a structural backbone\. This allows the subsequent adaptation phase \(Φ\\Phi\) to leverage topological low\-rank adaptation \(LoRA\) modules, preventing the collapse of the global topological prior while specializing in local updates\.

### 3\.3\.Sequential Topology Editing

To accommodate continuous updates, HyperPatch introduces a dual\-stage structural adaptation process that identifies topological discrepancies via hashing and aligns semantic components via linguishtic span extraction\.

#### 3\.3\.1\.Efficient Hyperedge Linking

To enable the structural updateΨ​\(ℋt−1,δt\)\\Psi\(\\mathcal\{H\}\_\{t\-1\},\\delta\_\{t\}\), HyperPatch must rapidly identify the hyperedgee∈ℰt−1e\\in\\mathcal\{E\}\_\{t\-1\}corresponding to the obsolete factfoldf\_\{\\text\{old\}\}\. We employ a SimHash\-based\(Mankuet al\.,[2007](https://arxiv.org/html/2606.03179#bib.bib28)\)locality\-sensitive hashing \(LSH\) approach to achieveO​\(1\)O\(1\)approximate nearest\-neighbor search\.

Specifically, we decompose a hyperedge’s textual representation intoMM4\-gram tokens𝒯=\{T1,…,TM\}\\mathcal\{T\}=\\\{T\_\{1\},\\dots,T\_\{M\}\\\}\. Each tokenTmT\_\{m\}is mapped to aKK\-bit binary vector𝐁m∈\{0,1\}K\\mathbf\{B\}\_\{m\}\\in\\\{0,1\\\}^\{K\}via a deterministic MD5 hash functionFMD5F\_\{\\text\{MD5\}\}\. As a result, the set of hashed binary vectors is given byℬ=\{𝐁1,…,𝐁M\}\\mathcal\{B\}=\\\{\\mathbf\{B\}\_\{1\},\\dots,\\mathbf\{B\}\_\{M\}\\\}, where each𝐁m\\mathbf\{B\}\_\{m\}corresponds to themm\-th 4\-gram token\. To aggregate these set of hashed binary vectors into a single structural fingerprint, each𝐁m\\mathbf\{B\}\_\{m\}is transformed into signed vectors𝐒m∈\{−1,\+1\}K\\mathbf\{S\}\_\{m\}\\in\\\{\-1,\+1\\\}^\{K\}, whereSm\(k\)=2​Bm\(k\)−1S\_\{m\}^\{\(k\)\}=2B\_\{m\}^\{\(k\)\}\-1\. The structural fingerprint𝐛∈\{0,1\}K\\mathbf\{b\}\\in\\\{0,1\\\}^\{K\}is generated by aggregating these vectors:

\(3\)𝐛\(k\)=𝕀​\(∑m=1MSm\(k\)\>0\)\.\\mathbf\{b\}^\{\(k\)\}=\\mathbb\{I\}\\left\(\\sum\\nolimits\_\{m=1\}^\{M\}S\_\{m\}^\{\(k\)\}\>0\\right\)\.To ensure retrieval scalability, fingerprints are indexed using aFAISSBinaryFlatindex\(Douzeet al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib29)\):Index←FAISSBinaryFlat​\(K\)\\texttt\{Index\}\\leftarrow\\texttt\{FAISSBinaryFlat\}\(K\)\. This mechanism allows HyperPatch to locatefoldf\_\{\\text\{old\}\}withinℋt−1\\mathcal\{H\}\_\{t\-1\}with minimal latency, effectively pruning the search space for large\-scale structural alignment\.

#### 3\.3\.2\.Entity Span Extraction for Knowledge Alignment

While hashing facilitates rapid retrieval, precise alignment requires a granular decomposition ofnn\-ary facts\. We define a span extraction function𝒮​\(e\)\\mathcal\{S\}\(e\)that maps a hyperedgeeeto an ordered sequence of semantic anchors\{s1,…,sk\}\\\{s\_\{1\},\\dots,s\_\{k\}\\\}\. To ensure compound entities are treated as atomic nodes, tokens are aggregated into a spansis\_\{i\}if they belong to a predefined set of Part\-of\-Speech \(POS\) tags𝒫=\{NOUN, PROPN, NUM, ADJ, PRON\}\\mathcal\{P\}=\\\{\\texttt\{NOUN, PROPN, NUM, ADJ, PRON\}\\\}, dependency roles𝒟=\{det, amod, pcomp, prep, advmod\}\\mathcal\{D\}=\\\{\\texttt\{det, amod, pcomp, prep, advmod\}\\\}, or relational connectors𝒜=\{“of”, “’s”, “and”, “\-”\}\\mathcal\{A\}=\\\{\\text\{\`\`of'', \`\`'s'', \`\`and'', \`\`\-''\}\\\}\.

The resulting sequence𝒮​\(e\)\\mathcal\{S\}\(e\)provides a formal basis for quantifying the structural discrepancy betweenfoldf\_\{\\text\{old\}\}andfnewf\_\{\\text\{new\}\}\. By analyzing these sequences, HyperPatch characterizes the precise nature of the topological shift—distinguishing among attribute modifications, entity replacements, and relational expansions\. This characterization subsequently steers both the topological modificationΨ\\Psiand the parameter\-efficient embedding adaptationΦ\\Phi, ensuring the hypergraph accurately reflects the updated knowledge state\.

#### 3\.3\.3\.Topological Conflict Resolution

To automate structural updateΨ​\(ℋt−1,δt\)\\Psi\(\\mathcal\{H\}\_\{t\-1\},\\delta\_\{t\}\), HyperPatch classifies each edit request into one of three topological operations\(Zhanget al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib39)\):Replace,Add, orIgnore\. This classification uses structural divergence between extracted entity spans offnewf\_\{\\text\{new\}\}and candidate hyperedges from SimHash indexing\.

For each top\-kkcandidateeold∈ℰt−1e\_\{\\text\{old\}\}\\in\\mathcal\{E\}\_\{t\-1\}retrieved via Hamming distance, we compute asymmetric span discrepancies:

\(4\)Δold=𝒮​\(eold\)∖𝒮​\(enew\),Δnew=𝒮​\(enew\)∖𝒮​\(eold\)\.\\Delta\_\{\\text\{old\}\}=\\mathcal\{S\}\(e\_\{\\text\{old\}\}\)\\setminus\\mathcal\{S\}\(e\_\{\\text\{new\}\}\),\\quad\\Delta\_\{\\text\{new\}\}=\\mathcal\{S\}\(e\_\{\\text\{new\}\}\)\\setminus\\mathcal\{S\}\(e\_\{\\text\{old\}\}\)\.
Replace Operation\.A candidateeolde\_\{\\text\{old\}\}is designated as aReplacetarget if and only if\|Δold\|=\|Δnew\|=1\|\\Delta\_\{\\text\{old\}\}\|=\|\\Delta\_\{\\text\{new\}\}\|=1, and and both discordant spans are non\-subject components\. Subject entities define event identity, while non\-subject modifications represent state transitions\. We define heuristic subject\-detectionϕ​\(⋅\):𝒮→\{0,1\}\\phi\(\\cdot\):\\mathcal\{S\}\\rightarrow\\\{0,1\\\}based on declarative structure where subjects precede predicates:

\(5\)ϕ​\(si\)=\{1,i<⌈\|𝒮​\(e\)\|2⌉0,otherwise\.\\phi\(s\_\{i\}\)=\\begin\{cases\}1,&i<\\lceil\\frac\{\|\\mathcal\{S\}\(e\)\|\}\{2\}\\rceil\\\\ 0,&\\text\{otherwise\}\\end\{cases\}\.LetΔold=\{so\}\\Delta\_\{\\text\{old\}\}=\\\{s\_\{o\}\\\}andΔnew=\{sn\}\\Delta\_\{\\text\{new\}\}=\\\{s\_\{n\}\\\}\. AReplaceoperation is executed ifϕ​\(so\)=0∧ϕ​\(sn\)=0\\phi\(s\_\{o\}\)=0\\wedge\\phi\(s\_\{n\}\)=0\. Formally, the hyperedge set is updated asℰt=\(ℰt−1∖\{eold\}\)∪\{enew\}\\mathcal\{E\}\_\{t\}=\(\\mathcal\{E\}\_\{t\-1\}\\setminus\\\{e\_\{\\text\{old\}\}\\\}\)\\cup\\\{e\_\{\\text\{new\}\}\\\}, overwriting the obsolete fact while maintaining the structural vertex incidence of the subject\.

Add Operation\.Conversely, if the subject identity is modified or the structural discrepancy remains bounded \(e\.g\.,\|Δold\|=\|Δnew\|=2\|\\Delta\_\{\\text\{old\}\}\|=\|\\Delta\_\{\\text\{new\}\}\|=2\), HyperPatch interprets the request as a semantic expansion or a distinct event\. In this case, anAddoperation is executed:ℰt=ℰt−1∪\{enew\}\\mathcal\{E\}\_\{t\}=\\mathcal\{E\}\_\{t\-1\}\\cup\\\{e\_\{\\text\{new\}\}\\\}\. This bifurcated logic ensures thatℋt\\mathcal\{H\}\_\{t\}faithfully incorporates the target statefnewf\_\{\\text\{new\}\}while preserving the structural integrity of the global knowledge base\.

Ignore Condition\.The Ignore operation serves as a safety guardrail for ambiguous or unsupported edit requests\. It is triggered when an edit request satisfies neither the Replace criteria, e\.g\., a valid single\-span non\-subject substitution, nor the bounded Add criteria, e\.g\., a structurally related expansion with limited span discrepancy\. In particular, requests with mismatched event identity or large unbalanced discrepancies, such asmax⁡\(\|Δold\|,\|Δnew\|\)\>2\\max\(\|\\Delta\_\{\\text\{old\}\}\|,\|\\Delta\_\{\\text\{new\}\}\|\)\>2, are treated as unreliable structural signals\. In these ambiguous scenarios, HyperPatch favors omission over potentially corruptive structural changes, thereby preserving the semantic consistency of the evolving hypergraph\.

#### 3\.3\.4\.Incremental Topological Adaptation

Following the structural update, we perform model adaptationΦ​\(ℳ,δt\)\\Phi\(\\mathcal\{M\},\\delta\_\{t\}\)by incrementally updating the hypergraph embeddings𝐙t\\mathbf\{Z\}\_\{t\}using a parameter\-efficient LoRA\-based HGNN\(Yanget al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib32); Chenet al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib40)\)\. This ensures that the retrieval manifold remains synchronized with the evolved topologyℋt\\mathcal\{H\}\_\{t\}, thereby mitigating retrieval drift\.

Specifically, we utilize the pre\-trained HGNN encoder as a frozen structural backbone to preserve global regularities while allowing gradients to propagate through a learnable projector𝜽proj\\boldsymbol\{\\theta\}\_\{\\text\{proj\}\}and injected low\-rank adapters𝜽LoRA\\boldsymbol\{\\theta\}\_\{\\text\{LoRA\}\}\. LetfHGNN​\(ℋt,𝐗t;𝜽\)f\_\{\\text\{HGNN\}\}\(\\mathcal\{H\}\_\{t\},\\mathbf\{X\}\_\{t\};\\boldsymbol\{\\theta\}\)denote the encoder with parameters𝜽=𝜽base∪𝜽proj∪𝜽LoRA\\boldsymbol\{\\theta\}=\\boldsymbol\{\\theta\}\_\{\\text\{base\}\}\\cup\\boldsymbol\{\\theta\}\_\{\\text\{proj\}\}\\cup\\boldsymbol\{\\theta\}\_\{\\text\{LoRA\}\}\. The adaptation is framed as a constrained optimization task:

\(6\)min𝜽proj,𝜽LoRA⁡ℒstruct​\(fHGNN​\(ℋt,𝐗t;𝜽base,𝜽proj,𝜽LoRA\)\),\\min\_\{\\boldsymbol\{\\theta\}\_\{\\text\{proj\}\},\\boldsymbol\{\\theta\}\_\{\\text\{LoRA\}\}\}\\mathcal\{L\}\_\{\\text\{struct\}\}\\left\(f\_\{\\text\{HGNN\}\}\(\\mathcal\{H\}\_\{t\},\\mathbf\{X\}\_\{t\};\\boldsymbol\{\\theta\}\_\{\\text\{base\}\},\\boldsymbol\{\\theta\}\_\{\\text\{proj\}\},\\boldsymbol\{\\theta\}\_\{\\text\{LoRA\}\}\)\\right\),where𝜽base\\boldsymbol\{\\theta\}\_\{\\text\{base\}\}remains frozen\. The updated embeddings𝐙t\\mathbf\{Z\}\_\{t\}are then cached to facilitate real\-time, structure\-aware retrieval without the prohibitive cost of full backbone retraining\.

### 3\.4\.Structure\-Conditioned Reasoning

The final phase of HyperPatch utilizes the updated hypergraphℋt\\mathcal\{H\}\_\{t\}and the adapted modelℳt\\mathcal\{M\}\_\{t\}to perform multi\-hop reasoning\. We explicitly addressStructural Driftby ensuring the reasoning process is grounded in both linguistic semantics and the evolved topology\.

Table 1\.Knowledge editing performance on MQuAKE\-CF\-3K and MQuAKE\-T\. Parameter\-preserving methods are applicable to both proprietary and open\-source models, whereas parameter\-tuning baselines are restricted to open\-source settings \(metrics in %\)\. Gain \(%\) denotes the relative gain over the strongest baseline\. The best results are bolded, and the second best are underlined\.#### 3\.4\.1\.Iterative Question Decomposition

To navigate thenn\-ary relational structure ofℋt\\mathcal\{H\}\_\{t\}, we decompose a complex queryq\(0\)q^\{\(0\)\}into an ordered sequence of atomic sub\-questions𝒬=\{q\(1\),…,q\(I\)\}\\mathcal\{Q\}=\\\{q^\{\(1\)\},\\dots,q^\{\(I\)\}\\\}using an LLM\-based planner\(Ammannet al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib37)\)\. To maintain global consistency, we implement a state\-aware injection mechanism where each subsequent sub\-question is conditioned on the preceding intermediate answera\(i−1\)a^\{\(i\-1\)\}:

\(7\)q\(i\)←Inject​\(q\(i\),\[ENT\],a\(i−1\)\)\.q^\{\(i\)\}\\leftarrow\\text\{Inject\}\(q^\{\(i\)\},\\text\{\{\[ENT\]\}\},a^\{\(i\-1\)\}\)\.Eachq\(i\)q^\{\(i\)\}is answered byℳt\\mathcal\{M\}\_\{t\}, yielding a reasoning chainA=\{a\(1\),…,a\(I\)\}\\text\{A\}=\\\{a^\{\(1\)\},\\dots,a^\{\(I\)\}\\\}\. This iterative refinement transforms multi\-hop reasoning into a sequence of dependent RAG steps, each conditioned on the topological neighborhood of the previous hop’s result\.

#### 3\.4\.2\.Dual\-Manifold Retrieval

Standard retrievers often suffer fromStructure\-Conditioned Knowledge Transfer Failure\(SKTF\) because they rely exclusively on pre\-trained linguistic similarity, which fails to reflect sequential topological updates\. HyperPatch mitigates this by querying two distinct latent manifolds: theSemantic Manifold\(𝒵text\\mathcal\{Z\}\_\{\\text\{text\}\}\) and theTopological Manifold\(𝒵HGNN\\mathcal\{Z\}\_\{\\text\{HGNN\}\}\)\(Liet al\.,[2025a](https://arxiv.org/html/2606.03179#bib.bib36)\)\.

Manifold Alignment\.For a sub\-queryq\(i\)q^\{\(i\)\}, we generate a linguistic embedding𝐱text∈ℝdtext\\mathbf\{x\}\_\{\\text\{text\}\}\\in\\mathbb\{R\}^\{d\_\{\\text\{text\}\}\}using the backbone encoder\. To synchronize this with the updated topology, we project𝐱text\\mathbf\{x\}\_\{\\text\{text\}\}into the structure\-aware latent space via the frozen projectorPP\(Eq\. \([1](https://arxiv.org/html/2606.03179#S3.E1)\)\):

\(8\)𝐱HGNN=P​\(𝐱text\)∈ℝdHGNN\.\\mathbf\{x\}\_\{\\text\{HGNN\}\}=P\(\\mathbf\{x\}\_\{\\text\{text\}\}\)\\in\\mathbb\{R\}^\{d\_\{\\text\{HGNN\}\}\}\.
Joint Evidence Retrieval\.HyperPatch performs parallel Maximum Inner Product Search \(MIPS\) across both manifolds\. For a sub\-queryq\(i\)q^\{\(i\)\}at hopii, the candidate sets are retrieved as:

\(9\)𝒞text\\displaystyle\\mathcal\{C\}\_\{\\text\{text\}\}=TopKj∈\{𝒱t∪ℰt\}⁡\(𝐱text⊤​𝐳text,j‖𝐱text‖​‖𝐳text,j‖\),\\displaystyle=\\operatorname\{TopK\}\_\{j\\in\\\{\\mathcal\{V\}\_\{t\}\\cup\\mathcal\{E\}\_\{t\}\\\}\}\\left\(\\frac\{\\mathbf\{x\}\_\{\\text\{text\}\}^\{\\top\}\\mathbf\{z\}\_\{\\text\{text\},j\}\}\{\\\|\\mathbf\{x\}\_\{\\text\{text\}\}\\\|\\\|\\mathbf\{z\}\_\{\\text\{text\},j\}\\\|\}\\right\),𝒞HGNN\\displaystyle\\mathcal\{C\}\_\{\\text\{HGNN\}\}=TopKj∈\{𝒱t∪ℰt\}⁡\(𝐱HGNN⊤​𝐳HGNN,j‖𝐱HGNN‖​‖𝐳HGNN,j‖\),\\displaystyle=\\operatorname\{TopK\}\_\{j\\in\\\{\\mathcal\{V\}\_\{t\}\\cup\\mathcal\{E\}\_\{t\}\\\}\}\\left\(\\frac\{\\mathbf\{x\}\_\{\\text\{HGNN\}\}^\{\\top\}\\mathbf\{z\}\_\{\\text\{HGNN\},j\}\}\{\\\|\\mathbf\{x\}\_\{\\text\{HGNN\}\}\\\|\\\|\\mathbf\{z\}\_\{\\text\{HGNN\},j\}\\\|\}\\right\),where𝒱t∪ℰt\\mathcal\{V\}\_\{t\}\\cup\\mathcal\{E\}\_\{t\}denotes the updated universe of entities and hyperedges\. This dual\-manifold aggregation identifies evidence that is both linguistically salient and topologically congruent\. The final retrieved context is the union:𝒞\(i\)=𝒞text∪𝒞HGNN\\mathcal\{C\}^\{\(i\)\}=\\mathcal\{C\}\_\{\\text\{text\}\}\\cup\\mathcal\{C\}\_\{\\text\{HGNN\}\}\. This ensures a balanced context that preserves semantic intent while respecting structural constraints imposed by the edit streamΔ\\Delta\.

Reasoning Synthesis\.Following retrieval, HyperPatch merge hyperedges and de\-duplicate overlapping spans to ensure factual density\. This grounded context is then provided to the generatorGGto predict the intermediate answera\(i\)a^\{\(i\)\}\. This mechanism specifically counters SKTF: even if linguistic embeddings remain biased toward the initial prior𝒟0\\mathcal\{D\}\_\{0\}, the structure\-aware embeddings, which are adapted viaΦ\\Phi, provide the necessary corrective signal to track the evolved topology ofℋt\\mathcal\{H\}\_\{t\}\.

### 3\.5\.Theoretical Complexity Bound

Sequential KE demands update latency independent of\|ℰ\|\|\\mathcal\{E\}\|\. We establish HyperPatch’s theoretical efficiency guarantee\.

###### Theorem 3\.1\(Editing Efficiency\):

LetKKdenote the SimHash fingerprint length,\|T\|\|T\|thenn\-gram tokens per edit,ddthe embedding dimension, andrrthe LoRA rank withr≪dr\\ll d\. The amortized complexity per edit isO​\(K⋅\|T\|\+d⋅r\)O\(K\\cdot\|T\|\+d\\cdot r\), independent of\|ℰ\|\|\\mathcal\{E\}\|\.

###### Proof Sketch\.

The editing phase comprises two coupled operations\.\(i\) SimHash Linking: Computing theKK\-bit fingerprint from\|T\|\|T\|nn\-grams via MD5 hashing and majority voting requiresO​\(K⋅\|T\|\)O\(K\\cdot\|T\|\)\. LSH\-based retrieval fromFAISSBinaryFlatisO​\(1\)O\(1\)amortized w\.r\.t\.\|ℰ\|\|\\mathcal\{E\}\|, yielding constant\-time conflict resolution\.\(ii\) LoRA Adaptation: Updating𝐖\+𝐀𝐁⊤\\mathbf\{W\}\+\\mathbf\{AB\}^\{\\top\}where𝐀∈ℝd×r\\mathbf\{A\}\\in\\mathbb\{R\}^\{d\\times r\},𝐁∈ℝr×d\\mathbf\{B\}\\in\\mathbb\{R\}^\{r\\times d\}reduces complexity fromO​\(d2\)O\(d^\{2\}\)toO​\(d⋅r\)O\(d\\cdot r\)sincer≪dr\\ll d\. The synergy is critical as SimHash localizes updates toO​\(1\)O\(1\)hyperedges, while LoRA ensures each update costsO​\(d⋅r\)O\(d\\cdot r\)notO​\(d2\)O\(d^\{2\}\), yieldingO​\(K⋅\|T\|\+d⋅r\)O\(K\\cdot\|T\|\+d\\cdot r\)independent of\|ℰ\|\|\\mathcal\{E\}\|\. This achieves speedups ofdr\\frac\{d\}\{r\}over parametric methods and\|ℰ\|log⁡\|ℰ\|\\frac\{\|\\mathcal\{E\}\|\}\{\\log\|\\mathcal\{E\}\|\}over exhaustive retrieval, ensuring scalability to millions of hyperedges and enabling real\-time editing\. ∎

###### Theorem 3\.2\(Amortized Reasoning Scalability\):

LetKKbe the SimHash fingerprint length,\|T\|\|T\|the tokens per edit,ddthe embedding dimension,rrthe LoRA rank \(r≪dr\\ll d\), andIIthe number of reasoning hops\. The cost per multi\-hop query isO​\(I⋅\(d2\+log⁡\|ℋ\|⋅d\)\)O\(I\\cdot\(d^\{2\}\+\\log\|\\mathcal\{H\}\|\\cdot d\)\)\.

###### Proof Sketch\.

For each reasoning hopi∈\{1​…​I\}i\\in\\\{1\\dots I\\\}, manifold alignment via projectorPPincursO​\(d2\)O\(d^\{2\}\)cost\. Evidence retrieval utilizes dual\-manifold MIPS; with HNSW indexing, retrieval complexity isO​\(log⁡\|ℋ\|⋅d\)O\(\\log\|\\mathcal\{H\}\|\\cdot d\)\. Thus, the total reasoning cost is dominated by the reasoning depthIIand latent dimensionalitydd, scaling logarithmically with the knowledge base size\. This enables HyperPatch to handle millions ofnn\-aryrelations with real\-time performance\. ∎

Both phases are sub\-linear or independent of the total facts\|ℋ\|\|\\mathcal\{H\}\|\.

## 4\.Experiments

### 4\.1\.Experimental Setup

Datasets\.We evaluate HyperPatch on theMQuAKEbenchmark\(Zhonget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib15)\), using two widely\-used non\-overlapping subsets:MQuAKE\-CF\-3k\-v2andMQuAKE\-T\. MQuAKE\-CF\-3k\-v2 is a 3,000\-instance counterfactual benchmark designed to resolve reasoning ambiguities in earlier versions, while MQuAKE\-T contains 1,868 real\-world temporal editing instances\. Unlike temporal knowledge graph benchmarks that provide explicit timestamps or validity intervals, MQuAKE\-T represents temporal evolution as discrete factual state transitions, where an outdated fact is replaced by its updated counterpart\. Therefore, these temporal changes can be naturally modeled as structural Replace/Add operations over atomicnn\-ary events, without requiring a separate temporal reasoning branch\. As shown in Table[2](https://arxiv.org/html/2606.03179#S4.T2), MQuAKE\-CF\-3K\-v2 is evenly distributed across 2\-hop, 3\-hop, and 4\-hop questions\. Most 2\-hop questions involve one or two edits, whereas 4\-hop questions generally require more edits, reflecting the increased complexity of deeper reasoning chains\. In contrast, MQuAKE\-T is dominated by 2\-hop and 3\-hop questions, with only two 4\-hop cases\. Together, these two subsets provide a rigorous testbed for evaluating sequentialnn\-ary editing under both counterfactual and temporal knowledge updates across different reasoning depths\.

Table 2\.Distribution of multi\-hop questions by number of edits and hop count in MQuAKE\-CF\-3K\-v and MQuAKE\-T\.Evaluation Metrics\.Following\(Guet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib31)\), we employ Multi\-hop Accuracy\(M\-Acc\)and Hop\-wise Answering Accuracy\(H\-Acc\)\. M\-Acc evaluates final answer correctness, whereas H\-Acc requires every intermediate reasoning step to be correct, serving as our primary metric by mitigating coincidental successes from flawed reasoning\.

Baselines\.We compare HyperPatch with two categories of representative knowledge editing approaches\. \(i\) Theparameter\-preservingbaselines include MeLLo\(Zhonget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib15)\), PokeMQA\(Guet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib31)\), and KeDKG\(Luet al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib30)\), which edit knowledge without modifying model parameters\. \(ii\) In contrast, theparameter\-based methodsinvolve fine\-tuning or memory injection, such as FT\(Zhuet al\.,[2020](https://arxiv.org/html/2606.03179#bib.bib33)\), ROME\(Menget al\.,[2022](https://arxiv.org/html/2606.03179#bib.bib6)\), and MEMIT\(Menget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib7)\)\.

Implementation Details\.We utilize GAT\(Veličkovićet al\.,[2018](https://arxiv.org/html/2606.03179#bib.bib34)\)as the HGNN backbone, projecting 1536\-dimensional text embeddings into a 256\-dimensional latent manifold\. Structural retrieval leverages 128\-bit SimHash signatures for Hamming\-distance approximate nearest neighbor \(ANN\) search\. Top\-kkparameters for hyperedge linking are set to 2/70/1200 \(CF\-3k\-v2: 1/100/All edits\) and 1/23 \(T: 1/All edits\)\. Linguistic parsing is handled via spaCy’sen\_core\_web\_lg\. We employGPT\-4o\-minifor hypergraph construction and question decomposition, withGPT\-4o\-miniandQwen3\-8Bas reasoning backbones\. Experiments are executed on a single NVIDIA H100\-NVL\-94G GPU\.

### 4\.2\.Main Results

Table[1](https://arxiv.org/html/2606.03179#S3.T1)summarizes the performance of HyperPatch compared to state\-of\-the\-art baselines\. We observe several key findings:

Superior Reasoning Stability and Scalability\.HyperPatch consistently exceeds all baselines in Multi\-hop Accuracy \(M\-Acc\) and the more stringent Hop\-wise Accuracy \(H\-Acc\)\. OnMQuAKE\-CF\-3K\-v2\(Qwen3\-8B\), HyperPatch yields relative H\-Acc gains of79\.96%,88\.17%, and89\.20%across 1\-, 100\-, and all\-edit settings, respectively\. For GPT\-4o\-mini, relative improvement reaches96\.24%in the all\-edit scenario\. While baseline performance collapses as edit volume increases, HyperPatch maintains structural stability, demonstrating robustness under dense update streams\.

Mitigation of Event Factorization Drift\.The performance gap exposes two failure modes in current editors: \(i\)Localization Error, where inaccurate update anchoring induces internal contradictions; and \(ii\)Retrieval Misalignment, where triple\-based methods \(e\.g\., KeDKG\) suffer fromEvent Factorization Drift, i\.e\., the binary reification ofnn\-ary facts yielding incomplete subgraphs\. This forces the generator to rely on stale parametric priors rather than updated evidence\. Conversely, HyperPatch preserves relational atomicity via its hypergraph manifold, identifying globally consistent event structures despite significant drift\.

Bridging the Model Disparity\.While proprietary models typically excel in instruction\-following, HyperPatch empowers open\-source models \(e\.g\., Qwen3\-8B\) to achieve reasoning parity with closed\-source counterparts\. Notably, Qwen3\-8B equipped with HyperPatch occasionally outperforms GPT\-4o\-mini\-based baselines\. This suggests that structural alignment effectively decouples reasoning efficacy from model scale, enabling smaller open\-source models to compete in knowledge\-intensive multi\-hop tasks\.

Non\-Parametric Robustness vs\. Parametric Interference\.To assess weight modification risks, we compared HyperPatch against parametric editors \(FT, ROME, MEMIT\)\. Even with oracle sub\-queries to minimize reasoning noise, these methods failed to maintain consistency\. Direct parameter overwriting frequently inducescatastrophic interference, disrupting pre\-trained reasoning paths, which is a degradation that intensifies with cumulative updates\. HyperPatch’s non\-parametric approach sidesteps the plasticity\-stability trade\-off by offloading knowledge storage to a stable hypergraph substrate, thereby preserving reasoning integrity without compromising internal model logic\.

Table 3\.Ablation study quantifying the relative contribution of individual components\. Colored indicators denote the relative percentage change compared to the full HyperPatch model\. Best results arebolded; second\-best areunderlined\(metrics in %\)\.![Refer to caption](https://arxiv.org/html/2606.03179v1/x5.png)Figure 3\.Candidate Retrieval: Efficiency vs\. Effectiveness\.![Refer to caption](https://arxiv.org/html/2606.03179v1/x6.png)Figure 4\.Top\-kkof Maximum Inner Product Search \(MIPS\)\.
### 4\.3\.Efficiency and Scalability Study

#### 4\.3\.1\.Efficiency Study

We evaluate retrieval efficiency by comparing SimHash and FAISS against a brute\-force cosine similarity baseline\. As illustrated in Figure[3](https://arxiv.org/html/2606.03179#S4.F3), while all methods yield comparable accuracy across edit settings, the efficiency gap widens significantly as the number of edits scales\. In the most demanding “all\-edited” scenario, SimHash and FAISS reduce total query latency from 105\.97s to 4\.08s, a25\.9×25\.9\\timesspeedup, without sacrificing M\-Acc or H\-Acc\. These results validate that our retrieval framework provides the high scalability necessary for real\-time, large\-scale knowledge editing applications\. See Appendix[A\.1](https://arxiv.org/html/2606.03179#A1.SS1)for extended study on editing efficacy\.

#### 4\.3\.2\.Impact of Retrieval Depth \(kk\)

Figure[4](https://arxiv.org/html/2606.03179#S4.F4)examines how varying the retrieval depthk∈\{1,30,60\}k\\in\\\{1,30,60\\\}in Maximum Inner Product Search \(MIPS\) affects H\-Acc\. Counter\-intuitively, largerkkvalues do not improve performance;k=1k=1achieves the highest accuracy across most scenarios\. This suggests that a minimal set of highly relevant candidates is sufficient for multi\-hop reasoning\. Conversely, increasingkkinflates the token count and introduces extraneous or conflicting noise into the LLM’s context, which degrades reasoning precision and increases inference overhead\. Maintaining a concise context window \(k=1k=1\) ensures a higher signal\-to\-noise ratio, which is critical for scalable QA systems operating under context length constraints\.

#### 4\.3\.3\.Neural Scaling Law

To quantify how model capacity and edit volume influence performance, we analyze M\-Acc and H\-Acc scaling\. As shown in Figure[5](https://arxiv.org/html/2606.03179#S4.F5), M\-Acc follows the power\-law, with a highR2R^\{2\}confirming predictable scaling, providing a robust framework for estimating system behavior at scale\. The negative exponents characterize performance decay as complexity increases\. Notably, sensitivity to dimensionality \(β=−0\.48\\beta=\-0\.48\) exceeds that of edit volume \(α=−0\.08\\alpha=\-0\.08\), suggesting excessive dimensionality triggers overfitting\. In contrast, H\-Acc a disparate scaling regime\. While the positive coefficients suggest marginal gains from increased capacity and data, the lowerR2R^\{2\}reveals a more stochastic behavior\. H\-Acc is governed by local graph properties and the stability of specific reasoning paths, making it highly sensitive to the Event Factorization Drift identified in our structural analysis\.

![Refer to caption](https://arxiv.org/html/2606.03179v1/x7.png)Figure 5\.
M\-Acc Neural Scaling Law H\-Acc Neural Scaling Law
z=93\.57⋅x−0\.08\+1\.62⋅y−0\.48z=93\.57\\cdot x^\{\-0\.08\}\+1\.62\\cdot y^\{\-0\.48\}z=74\.44⋅x0\.03\+3\.14⋅y0\.23z=74\.44\\cdot x^\{0\.03\}\+3\.14\\cdot y^\{0\.23\}
R2=0\.9692R^\{2\}=0\.9692R2=0\.5673R^\{2\}=0\.5673

### 4\.4\.Ablation Study

We conduct ablation studies to quantify the contribution of each component to HyperPatch’s performance, as summarized in[Table3](https://arxiv.org/html/2606.03179#S4.T3)\.

Topological Manifold\.Compared to a semantic\-only baseline, omitting the topological manifold significantly degrades multi\-hop QA performance\. While semantic similarity identifies lexically relevant nodes, it fails to bridge lexically distant but structurally pivotal entities\. The topological manifold captures higher\-order relational neighborhoods, ensuring globally coherent reasoning chains, especially when lexical signals are sparse or ambiguous\.

Subject\-Detection in Conflict Resolution\.Disabling span\-based conflict resolution increases erroneousReplaceoperations, underscoring the necessity of subject\-level cues for target disambiguation\. Absent these cues, the system conflates semantically proximate but topologically distinct facts, triggering unintended overwrites\. This module ensures that updates are grounded in the correct structural context, preserving the fidelity of the sequential knowledge stream\.

SimHash Indexing\.To evaluate the efficacy of our hyperedge linking, we replace the SimHash and FAISS\-based candidate selection with random sampling\. This results in a collapse of linking accuracy and a surge in incorrect edits\. These findings confirm that our LSH\-based retrieval is more than a latency optimization; it acts as a high\-precision filter that prunes the search space to semantically and topologically congruent candidates\.

Topological LoRA Adaptation\.Removing the LoRA modules yields consistent accuracy degradation across all configurations, indicating that incremental HGNN adaptation is vital for maintaining representation quality as the knowledge base evolves\. While the structural prior remains robust, LoRA facilitates parameter\-efficient realignment with newly injected content\. By dynamically recalibrating entity\-event proximities, LoRA effectively counters structural drift, mitigating the neighborhood reshaping effect, without inducing catastrophic forgetting in the backbone\.

Relational Atomicity: Hypergraph vs\. Triple Structure\.A core thesis of our work is thatnn\-ary hypergraphs preventEvent Factorization Drift\. Replacing the hypergraph structure with conventional binary triples leads to a sharp performance collapse across all evaluation settings \(Table[3](https://arxiv.org/html/2606.03179#S4.T3)\)\. The degradation confirms that binary reification fragments complex events, fracturing the semantic coupling required for multi\-hop traversal\. Hypergraphs preserve the atomic integrity of relational constraints, which is essential for consistent reasoning under structural drift\.

Efficacy of Question Decomposition\.We examine the impact of decomposition quality\. Initially utilizing a LLaMA\-2\-7B model from the KeDKG\(Luet al\.,[2025](https://arxiv.org/html/2606.03179#bib.bib30)\)framework, we observed limited generalization on complex updates\. Replacing this with a GPT\-4o\-mini\-based decomposer yielded significant gains \([Table3](https://arxiv.org/html/2606.03179#S4.T3), rows inblue\)\. This underscores that high\-fidelity decomposition is a prerequisite for effective sequential editing, as it provides the necessary plan for the subsequent dual\-manifold retrieval and reasoning synthesis steps\.

Table 4\.Knowledge editing framework comparison\.

## 5\.Related Work

Sequential Knowledge Editing \(SKE\)\.SKE aims to modify factual priors in LLMs under non\-stationary edit streams\.Parametricmethods, such as ROME\(Menget al\.,[2022](https://arxiv.org/html/2606.03179#bib.bib6)\)and MEMIT\(Menget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib7)\), perform localized weight interventions; however, sequential updates often trigger weight\-space instability, leading to catastrophic forgetting\(Hartvigsenet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib22)\)and multi\-hop reasoning failures\(Zhonget al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib15)\)\. Meta\-learning approaches like MEND\(Mitchellet al\.,[2022a](https://arxiv.org/html/2606.03179#bib.bib14)\)improve update scalability but remain sensitive to variance in continuous streams\. Conversely,memory\-basededitors like SERAC\(Mitchellet al\.,[2022b](https://arxiv.org/html/2606.03179#bib.bib17)\)and GRACE\(Hartvigsenet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib22)\)bypass weight modification via external caches but typically treat edits asi\.i\.d\.key\-value pairs, ignoring the latent structural dependencies between facts\. Recent work has questioned whether the editing benchmarks and metrics properly reflect reliable editing behavior, especially in terms of locality and robustness under realistic evaluation settings\(Liuet al\.,[2026](https://arxiv.org/html/2606.03179#bib.bib45),[2025](https://arxiv.org/html/2606.03179#bib.bib46)\)\. As categorized in Table[4](https://arxiv.org/html/2606.03179#S4.T4), HyperPatch diverges from these reactive paradigms through aProactive Temporal Policy: we introduce upfront structural adaptation to preserve thetopological atomicityrequired for consistent multi\-hop reasoning across sequential edit streams\.

Retrieval\-Augmented Generation \(RAG\)\.RAG decouples knowledge acquisition from parametric reasoning using external corpora\(Lewiset al\.,[2020](https://arxiv.org/html/2606.03179#bib.bib24)\)or graphs\(Edgeet al\.,[2024](https://arxiv.org/html/2606.03179#bib.bib21)\)\. Retrieval reliability is inherently vulnerable to non\-stationary distribution shifts\(Thakuret al\.,[2021](https://arxiv.org/html/2606.03179#bib.bib12); Gamaet al\.,[2014](https://arxiv.org/html/2606.03179#bib.bib8)\)where query distributions diverge from training priors\(Mallenet al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib3)\)\. While retrieval editors\(Hanet al\.,[2023](https://arxiv.org/html/2606.03179#bib.bib18)\)typically assume static embedding manifolds, we identifyfactorization drift, the erosion ofnn\-ary event integrity within binary latent spaces, as a fundamental failure mode\. HyperPatch introducesDual\-Manifold Retrievalto synchronize the semantic manifold with a structure\-aware HGNN latent space, ensuring evidence remains topologically congruent across sequential updates\.

Symbolic Structure vs\. Latent Synchronization\.Property graphs and temporal knowledge graphs can preserve evolving facts through edge attributes, qualifiers, or temporal metadata at the symbolic level\. However, such symbolic updates do not necessarily update the dense retriever’s latent manifold, which may remain biased toward stale pre\-edit priors\. As a result, a knowledge base can be symbolically correct while still being functionally misaligned with neural retrieval, especially in multi\-hop QA where constraints are often implicit, linguistically diverse, or distributed across multiple reasoning steps\. In contrast, HyperPatch treats sequential editing as a neuro\-symbolic synchronization problem: structural updates modify thenn\-ary hypergraph state, while topological adaptation realigns the structure\-aware embedding manifold with the evolved topology\. This distinction moves beyond symbolic filtering or attribute matching, ensuring that updated events are both explicitly stored and retrievable through latent similarity\.

Hypergraph Representation Learning\.Real\-world knowledge comprises complexnn\-ary relations that resist lossless decomposition into binary triples\(Wenet al\.,[2016](https://arxiv.org/html/2606.03179#bib.bib10)\)\. Traditional KG embeddings\(Bordeset al\.,[2013](https://arxiv.org/html/2606.03179#bib.bib23)\)typically rely on binary reification, which decouples semantic associations and inducesreification bottlenecks, i\.e\., the loss of joint coupling between participants\. Hypergraph Neural Networks \(HGNNs\)\(Fenget al\.,[2019](https://arxiv.org/html/2606.03179#bib.bib19); Yadatiet al\.,[2019](https://arxiv.org/html/2606.03179#bib.bib20); Zheng and Worring,[2025](https://arxiv.org/html/2606.03179#bib.bib43)\)offer a principled alternative by encodingnn\-ary relations as atomic topological units, effectively capturing higher\-order correlations\. While HGNNs have been utilized for static tasks like cross\-document QA\(Tuet al\.,[2020](https://arxiv.org/html/2606.03179#bib.bib25)\), their utility in sequential knowledge editing remains unaddressed\. HyperPatch leverages thetopological atomicityof hypergraphs to provide a robust substrate for dynamic updates\. By treating events as unified hyperedges rather than fragmented triple\-chains, we preclude the spurious composition failures characteristic of reified binary systems \(see Table[4](https://arxiv.org/html/2606.03179#S4.T4)\)\.

## 6\.Conclusion

We present HyperPatch, a framework that mitigatesstructural driftin sequential knowledge editing\. By replacing fragmented binary triples with atomic hyperedges and leveragingO​\(1\)O\(1\)SimHash\-based alignment, HyperPatch ensures LLM reasoning remains grounded in evolving topologies\. Experimental results demonstrate that HyperPatch achieves state\-of\-the\-art H\-Acc \(96\.24% and 21\.06%\) on complex benchmarks, mitigating the severe accuracy collapses \(42\.9%–88\.3%\) inherent in KG\-based variants\. Combined with a25\.9×25\.9\\timesretrieval speedup, these findings underscore that topological integrity is as critical as parametric fidelity for the development of reliable, long\-lived knowledge\-augmented LLMs\.

###### Acknowledgements\.

This work is partially supported by the National Science and Technology Council \(NSTC\), Taiwan \(Grants: NSTC\-114\-2640\-E\-A49\-011, 114\-2222\-E\-A49\-004, and 114\-2639\-E\-A49\-001\-ASP\)\.

## References

- P\. J\. L\. Ammann, J\. Golde, and A\. Akbik \(2025\)Question decomposition for retrieval\-augmented generation\.InProceedings of the Annual Meeting of the Association for Computational Linguistics \(ACL\),Cited by:[§3\.4\.1](https://arxiv.org/html/2606.03179#S3.SS4.SSS1.p1.5)\.
- A\. Bordes, N\. Usunier, A\. Garcia\-Duran, J\. Weston, and O\. Yakhnenko \(2013\)Translating embeddings for modeling multi\-relational data\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Vol\.26,pp\. 2787–2795\.Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p4.2)\.
- J\. Chen, Q\. Shao, D\. Chen, and W\. Yu \(2025\)Decoupling spatio\-temporal prediction: when lightweight large models meet adaptive hypergraphs\.InProceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining \(KDD\),Cited by:[§3\.3\.4](https://arxiv.org/html/2606.03179#S3.SS3.SSS4.p1.3)\.
- W\. Chen, D\. Guo, N\. Duan, and M\. Zhou \(2022\)Rich knowledge, poor reasoning? a qualitative analysis of Knowledge Graph Embedding models\.InProceedings of the Conference of the North American Chapter of the Association for Computational Linguistics \(NAACL\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p2.1)\.
- Y\. Chen, X\. Wang, and C\. Chen \(2024\)Hyperedge importance estimation via identity\-aware hypergraph attention network\.InProceedings of the ACM International Conference on Information and Knowledge Management \(CIKM\),Cited by:[§3\.2](https://arxiv.org/html/2606.03179#S3.SS2.p3.8)\.
- M\. Douze, A\. Guzhva, C\. Deng, J\. Johnson, G\. Szilvasy, P\. Mazaré, M\. Lomeli, L\. Hosseini, and H\. Jégou \(2025\)The faiss library\.InIEEE Transactions on Big Data \(IEEE\),Vol\.12,pp\. 346–361\.Cited by:[§3\.3\.1](https://arxiv.org/html/2606.03179#S3.SS3.SSS1.p2.16)\.
- D\. Edge, H\. Trinh, N\. Cheng, J\. Bradley, A\. Chao, A\. Mody, S\. Truitt, and J\. Larson \(2024\)From local to global: a graph RAG approach to query\-focused summarization\.InarXiv preprint arXiv:2404\.16130,Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[§5](https://arxiv.org/html/2606.03179#S5.p2.1)\.
- Y\. Feng, H\. You, Z\. Zhang, R\. Ji, and Y\. Gao \(2019\)Hypergraph neural networks\.InProceedings of the AAAI Conference on Artificial Intelligence \(AAAI\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[§3\.2](https://arxiv.org/html/2606.03179#S3.SS2.p1.2),[§5](https://arxiv.org/html/2606.03179#S5.p4.2)\.
- J\. Gama, I\. Žliobaitė, A\. Bifet, M\. Pechenizkiy, and A\. Bouchachia \(2014\)A survey on concept drift adaptation\.InACM Computing Surveys \(CSUR\),Vol\.46,pp\. 1–37\.Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p2.1),[§5](https://arxiv.org/html/2606.03179#S5.p2.1)\.
- H\. Gu, K\. Zhou, X\. Han, N\. Liu, R\. Wang, and X\. Wang \(2024\)Pokemqa: programmable knowledge editing for multi\-hop question answering\.InProceedings of the Annual Meeting of the Association for Computational Linguistics \(ACL\),Cited by:[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.13.13.1),[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.8.8.1),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p2.1),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p3.1),[Table 4](https://arxiv.org/html/2606.03179#S4.T4.1.1.2.1.3)\.
- V\. Haghighi, B\. Soltani, N\. Shabani, J\. Wu, Y\. Zhang, L\. Yao, Q\. Z\. Sheng, and J\. Yang \(2024\)TROPICAL: transformer\-based hypergraph learning for camouflaged fraudster detection\.InIEEE International Conference on Data Mining \(ICDM\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2)\.
- S\. Han, D\. Schuurmans,et al\.\(2023\)Memory\-augmented large language models are computationally universal\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[§5](https://arxiv.org/html/2606.03179#S5.p2.1)\.
- T\. Hartvigsen, S\. Swami, X\. Yin, X\. R\. Peng, and K\. Chang \(2024\)Aging with GRACE: lifelong model editing with discrete key\-value adapters\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p5.6),[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- J\. Kirkpatrick, R\. Pascanu, N\. Rabinowitz, J\. Veness, G\. Desjardins, A\. A\. Rusu, K\. Milan, J\. Quan, T\. Ramalho, A\. Grabska\-Barwinska,et al\.\(2017\)Overcoming catastrophic forgetting in neural networks\.InProceedings of the National Academy of Sciences \(PNAS\),Vol\.114,pp\. 3521–3526\.Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[2nd item](https://arxiv.org/html/2606.03179#S2.I1.i2.p1.1)\.
- P\. Lewis, E\. Perez, A\. Piktus, F\. Petroni, V\. Karpukhin, N\. Goyal, H\. Küttler, M\. Lewis, W\. Yih, T\. Rocktäschel,et al\.\(2020\)Retrieval\-augmented generation for knowledge\-intensive NLP tasks\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p2.1)\.
- D\. Li, K\. Bi, J\. Guo, and X\. Cheng \(2025a\)Tailoring table retrieval from a field\-aware hybrid matching perspective\.InProceedings of the Conference on Empirical Methods in Natural Language Processing \(EMNLP\),Cited by:[§3\.4\.2](https://arxiv.org/html/2606.03179#S3.SS4.SSS2.p1.2)\.
- Z\. Li, J\. Wang, J\. Liang, J\. Cui, X\. Zhao, and J\. Liang \(2025b\)Uncertainty\-guided graph contrastive learning from a unified perspective\.InProceedings of the International Joint Conference on Artificial Intelligence \(IJCAI\),Cited by:[§3\.2](https://arxiv.org/html/2606.03179#S3.SS2.p3.8)\.
- S\. Liao and P\. Mok \(2024\)Hypergraph\-enhanced contrastively regularized transformer for multi\-behavior e\-commerce product recommendation\.InIEEE International Conference on Data Mining \(ICDM\),Cited by:[§3\.2](https://arxiv.org/html/2606.03179#S3.SS2.p3.8)\.
- W\. Liu, H\. Xu, B\. Liu, Z\. Deng, H\. Wang, J\. Wang, R\. Li, Y\. W\. Teh, and W\. S\. Lee \(2025\)Is model editing built on sand? revealing its illusory success and fragile foundation\.InarXiv preprint arXiv:2510\.00625,Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- W\. Liu, H\. Xu, H\. Liu, Z\. Deng, R\. Li, H\. Huang, Y\. W\. Teh, and W\. S\. Lee \(2026\)Are we evaluating the edit locality of llm model editing properly?\.InarXiv preprint arXiv:2601\.17343,Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- Y\. Lu, Y\. Zhou, J\. Li, Y\. Wang, X\. Liu, D\. He, F\. Liu, and M\. Zhang \(2025\)Knowledge editing with dynamic knowledge graphs for multi\-hop question answering\.InProceedings of the AAAI Conference on Artificial Intelligence \(AAAI\),Cited by:[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.14.14.1),[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.9.9.1),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p3.1),[§4\.4](https://arxiv.org/html/2606.03179#S4.SS4.p7.1),[Table 4](https://arxiv.org/html/2606.03179#S4.T4.1.1.2.1.4)\.
- H\. Luo, H\. E, G\. Chen, Y\. Zheng, X\. Wu, Y\. Guo, Q\. Lin, Y\. Feng, Z\. Kuang, M\. Song, Y\. Zhu, and A\. T\. Luu \(2025\)HyperGraphRAG: retrieval\-augmented generation via hypergraph\-structured knowledge representation\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2)\.
- A\. Mallen, A\. Asai, V\. Zhong, R\. Das, D\. Khashabi, and H\. Hajishirzi \(2023\)When not to trust your LLM: known\-unknowns and the paradox of prioritization\.InProceedings of the Annual Meeting of the Association for Computational Linguistics \(ACL\),Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p2.1)\.
- G\. S\. Manku, A\. Jain, and A\. Das Sarma \(2007\)Detecting near\-duplicates for web crawling\.InProceedings of the 16th international conference on World Wide Web \(WWW\),Cited by:[§3\.3\.1](https://arxiv.org/html/2606.03179#S3.SS3.SSS1.p1.4)\.
- K\. Meng, D\. Bau, A\. Andonian, and Y\. Belinkov \(2022\)Locating and editing factual associations in GPT\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p1.1),[§1](https://arxiv.org/html/2606.03179#S1.p2.1),[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.5.5.1),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p3.1),[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- K\. Meng, A\. Sharma, A\. Andonian, Y\. Belinkov, and D\. Bau \(2023\)Mass\-editing memory in a transformer\.InProceedings of the International Conference on Learning Representations \(ICLR\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p1.1),[§1](https://arxiv.org/html/2606.03179#S1.p2.1),[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.6.6.1),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p3.1),[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- S\. Min, E\. Wallace, S\. Singh, M\. Gardner, H\. Hajishirzi, and L\. Zettlemoyer \(2019\)Compositional questions do not necessitate multi\-hop reasoning\.InProceedings of the Annual Meeting of the Association for Computational Linguistics \(ACL\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p3.3)\.
- E\. Mitchell, C\. Lin, A\. Bosselut, C\. Finn, and C\. D\. Manning \(2022a\)Fast model editing at scale\.InProceedings of the International Conference on Learning Representations \(ICLR\),Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- E\. Mitchell, C\. Lin, A\. Bosselut, C\. D\. Manning, and C\. Finn \(2022b\)Memory\-based model editing at scale\.InProceedings of the International Conference on Machine Learning \(ICML\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- P\. Rosso, D\. Yang, and P\. Cudré\-Mauroux \(2020\)Beyond triplets: hyper\-relational knowledge graph embedding for link prediction\.InProceedings of the international conference on World Wide Web \(WWW\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p3.3)\.
- N\. Thakur, N\. Reimers, A\. Rücklé, A\. Srivastava, and I\. Gurevych \(2021\)BEIR: a heterogeneous benchmark for zero\-shot evaluation of information retrieval models\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p3.3),[§5](https://arxiv.org/html/2606.03179#S5.p2.1)\.
- M\. Tu, G\. Zhou, J\. Su, and J\. Nie \(2020\)Document\-level relation extraction with adaptive thresholding and localized context pooling\.InProceedings of the AAAI Conference on Artificial Intelligence \(AAAI\),Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p4.2)\.
- P\. Veličković, G\. Cucurull, A\. Casanova, A\. Romero, P\. Liò, and Y\. Bengio \(2018\)Graph Attention Networks\.InProceedings of the International Conference on Learning Representations \(ICLR\),Cited by:[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p4.1)\.
- J\. Wen, J\. Li, Y\. Mao, S\. Chen, and R\. Zhang \(2016\)Learning structured embeddings of knowledge bases\.InProceedings of the AAAI Conference on Artificial Intelligence \(AAAI\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p3.3),[§5](https://arxiv.org/html/2606.03179#S5.p4.2)\.
- N\. Yadati, M\. Nimishakavi, P\. Yadav, V\. Nitin, A\. Louis, and P\. Talukdar \(2019\)HyperGCN: a new method for training graph convolutional networks on hypergraphs\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p4.2)\.
- Z\. Yang, J\. Han, C\. Wang, and H\. Liu \(2025\)Graphlora: structure\-aware contrastive low\-rank adaptation for cross\-graph transfer learning\.InProceedings of the ACM SIGKDD Conference on Knowledge Discovery and Data Mining \(KDD\),Cited by:[§3\.3\.4](https://arxiv.org/html/2606.03179#S3.SS3.SSS4.p1.3)\.
- Y\. Yao, P\. Wang, B\. Tian,et al\.\(2023\)Editing large language models: problems, methods, and opportunities\.InProceedings of the Conference on Empirical Methods in Natural Language Processing \(EMNLP\),Cited by:[1st item](https://arxiv.org/html/2606.03179#S2.I1.i1.p1.2)\.
- Z\. Zhang, Z\. Geng, Y\. Ma, T\. Wang, K\. Lv, and X\. Liu \(2025\)Conflict\-aware knowledge editing in the wild: semantic\-augmented graph representation for unstructured text\.InAdvances in Neural Information Processing Systems \(NeurIPS\),Cited by:[§3\.3\.3](https://arxiv.org/html/2606.03179#S3.SS3.SSS3.p1.2)\.
- Y\. Zheng and M\. Worring \(2025\)Modeling edge\-specific node features through co\-representation neural hypergraph diffusion\.InProceedings of the ACM International Conference on Information and Knowledge Management \(CIKM\),Cited by:[§5](https://arxiv.org/html/2606.03179#S5.p4.2)\.
- Z\. Zhong, C\. D\. Manning, C\. Potts, and D\. Chen \(2023\)MQuAKE: assessing knowledge editing in language models via multi\-hop questions\.InProceedings of the Conference on Empirical Methods in Natural Language Processing \(EMNLP\),Cited by:[§1](https://arxiv.org/html/2606.03179#S1.p1.1),[§1](https://arxiv.org/html/2606.03179#S1.p4.2),[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.12.12.2),[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.7.7.1),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p1.2),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p3.1),[Table 4](https://arxiv.org/html/2606.03179#S4.T4.1.1.2.1.2),[§5](https://arxiv.org/html/2606.03179#S5.p1.1)\.
- C\. Zhu, A\. S\. Rawat, M\. Zaheer, S\. Bhojanapalli, D\. Li, F\. Yu, and S\. Kumar \(2020\)Modifying memories in transformer models\.InarXiv preprint arXiv:2012\.00363,Cited by:[Table 1](https://arxiv.org/html/2606.03179#S3.T1.2.1.4.4.2),[§4\.1](https://arxiv.org/html/2606.03179#S4.SS1.p3.1)\.

## Appendix AExtended Experiments

### A\.1\.Editing Efficacy

Hyperedge Linking Efficacy\.We specifically analyze theReplaceediting operation, as it represents the most critical bottleneck for structural integrity\. In this setting, the system must accurately localize an existing hyperedge to be superseded; a failure in linking directly results in a missed edit or an erroneous graph modification\. In contrast,Addoperations are non\-destructive and less sensitive to linking precision, as they treat incoming knowledge as independent structural expansions\. Figure[6](https://arxiv.org/html/2606.03179#A1.F6)\(left\) illustrates the F1\-score performance of HyperPatch compared to brute\-force cosine similarity and random selection across various top\-kkretrieval thresholds\. While the cosine baseline represents an exhaustive upper bound for retrieval accuracy, it is computationally prohibitive in large\-scale sequential environments\. HyperPatch achievesF1F\_\{1\}scores nearly identical to cosine similarity while operating on a significantly pruned search space\. By utilizing SimHash signatures and binary indexing, HyperPatch balances high\-dimensional retrieval precision with orders\-of\-magnitude improvements in computational latency \(detailed in[Section4\.3](https://arxiv.org/html/2606.03179#S4.SS3)\), offering a scalable alternative to traditional dense similarity metrics\.

![Refer to caption](https://arxiv.org/html/2606.03179v1/x8.png)Figure 6\.Hyperedge linking efficacy and conflict resolution accuracy\. \(Left\)F1​@​kF\_\{1\}@kperformance for identifyingReplaceoperations across varying retrieval depths\. \(Right\) Confusion matrix validating the discriminative accuracy of HyperPatch’s topological conflict resolution logic\.Table 5\.Memory footprint comparison at 3,000 edits\. Memory values are reported in MB\. CF\-All denotes Hop\-wise Accuracy on the MQuAKE\-CF\-3K\-v2 all\-edit setting\.Topological Conflict Resolution Accuracy\.To evaluate the discriminative reliability of the decision logicΨ\\Psi, we assess its capacity to disambiguateReplaceandAddoperations\. Figure[6](https://arxiv.org/html/2606.03179#A1.F6)\(right\) presents the confusion matrix for theMQuAKE\-CF\-3k\-v2dataset, utilizing ground\-truth labels based on semantic intent\. The results reveal exceptional discriminative fidelity: HyperPatch correctly linked 2,151 of 2,153Replacecases, achieving a 99\.9% precision rate with zero missed matches\. This high precision is critical for hypergraph stability, ensuring that topological modifications are anchored to existing structures without inducing unintended overwrites\. The ability to maintain such accuracy despite the linguistic variance ofnn\-ary facts further validates the robustness of our span\-based alignment mechanism\.

![Refer to caption](https://arxiv.org/html/2606.03179v1/x9.png)

\(a\)

![Refer to caption](https://arxiv.org/html/2606.03179v1/x10.png)

\(b\)

![Refer to caption](https://arxiv.org/html/2606.03179v1/x11.png)

\(c\)

Figure 7\.Retrieval\-induced recall error\. \(a\) successful evidence grounding in the first reasoning hop; \(b\) a relational mismatch in the second hop, where entity\-centric overlap dominates the retrieval signal; \(c\) the target hyperedge present in the updated topology but missed by the retriever\.Three panels illustrating a retrieval\-induced recall error: successful first\-hop grounding, erroneous retrieval via entity overlap, and the missed ground\-truth relational hyperedge\.![Refer to caption](https://arxiv.org/html/2606.03179v1/x12.png)

\(a\)

![Refer to caption](https://arxiv.org/html/2606.03179v1/x13.png)

\(b\)

![Refer to caption](https://arxiv.org/html/2606.03179v1/x14.png)

\(c\)

Figure 8\.Reasoning\-induced contextual noise\. \(a\) valid initial reasoning step; \(b\) introduction of a redundant distractor that induces contextual interference; \(c\) the correct ground\-truth hyperedge, which was successfully retrieved but ignored by the reasoning module\.Three panels illustrating reasoning\-induced contextual noise: a valid initial reasoning step, redundant or conflicting information, and the correct ground\-truth hyperedge\.Old Knowledge:New Knowledge:Ciudad de Murcia is associated with the sport of association football\.Ciudad de Murcia is associated with the sport of basketball\.Multi\-hop Question:association football was created in the country of England\.What is the capital of the country where the sport associated withThe capital of England is London\.Ciudad de Murcia was originated?basketball was created in the country of Soviet Union\.The capital of Soviet Union is Russellville\.StageKnowledge Graph \(KEDKG\)Hypergraph \(HyperPatch\)Initial Graph State\(1\)\. Ciudad de Murcia→\\rightarrowsport→\\rightarrowassociation football→\\rightarrowcountry→\\rightarrowEngland→\\rightarrowcapital→\\rightarrowLondon \(2\)\. basketball→\\rightarrowcountry→\\rightarrowSoviet Union→\\rightarrowcapital→\\rightarrowRussellville\(1\)\. Ciudad de Murcia←\\leftarrow\[Ciudad de Murcia is associated with the sport of association football\.\]→\\rightarrowassociation football←\\leftarrow\[association football was created in the country of England\. \]→\\rightarrowEngland←\\leftarrow\[The capital of England is London\. \]→\\rightarrowLondon \(2\)\. basketball←\\leftarrow\[basketball was created in the country of Soviet Union\.\]→\\rightarrowSoviet Union←\\leftarrow\[The capital of Soviet Union is Russellville\.\]→\\rightarrowRussellvilleNew Knowledge Extraction\(Ciudad de Murcia, is associated, basketball\)Ciudad de Murcia is associated with the sport of basketball\. — Ciudad de Murcia — basketballPost\-Edit Graph StateCiudad de Murcia→\\rightarrow\(sport→\\rightarrowassociation football→\\rightarrowcountry→\\rightarrowEngland→\\rightarrowcapital→\\rightarrowLondon\) & \(is associated→\\rightarrowbasketball→\\rightarrowcountry→\\rightarrowSoviet Union→\\rightarrowcapital→\\rightarrowRussellville\)\(1\)\. association football←\\leftarrow\[association football was created in the country of England\. \]→\\rightarrowEngland←\\leftarrow\[The capital of England is London\. \]→\\rightarrowLondon \(2\)\. Ciudad de Murcia←\\leftarrow\[Ciudad de Murcia is associated with the sport of basketball\.\]→\\rightarrowbasketball←\\leftarrow\[basketball was created in the country of Soviet Union\.\]→\\rightarrowSoviet Union←\\leftarrow\[The capital of Soviet Union is Russellville\.\]→\\rightarrowRussellvilleMulti\-hop Reasoning Patha\(1\)a^\{\(1\)\}: association football,a\(2\)a^\{\(2\)\}: England,a\(3\)a^\{\(3\)\}: Londona\(1\)a^\{\(1\)\}: basketball,a\(2\)a^\{\(2\)\}: Soviet Union,a\(3\)a^\{\(3\)\}: Russellville

Table 6\.Qualitative comparison of knowledge editing between standard KG andnn\-ary Hypergraph \(3\-hop\)\.Blueindicates correct answers;redindicates incorrect answers from spurious composition\.
### A\.2\.Memory Footprint Analysis

Memory serves as a vital substrate for preserving relational atomicity undernn\-ary structural drift\. Although HyperPatch incurs higher storage overhead than triple\-based methods, the additional cost remains modest in absolute terms\. At 3,000 edits, HyperPatch requires 64\.21MB, compared with 5\.68MB for KeDKG\. This overhead yields a substantial gain in reasoning reliability, improving CF\-All H\-Acc from 36\.77% to 69\.57%\. As shown in Table[5](https://arxiv.org/html/2606.03179#A1.T5), the graph structure of HyperPatch occupies only 6\.40MB, which is comparable to KeDKG\. Most of the additional memory comes from the structure\-aware manifold embeddings, which require 57\.75MB\. This indicates that the memory increase is not caused by excessive graph storage, but by the latent representations needed to resolvenn\-ary drift in non\-stationary environments\. In contrast, triple\-based reification induces structural fragmentation, leading to severe accuracy degradation despite its smaller memory footprint\.

### A\.3\.Error Analysis

To provide a granular understanding of system limitations, we categorize failure modes into two primary types:retrieval\-induced recall errorsandreasoning\-induced contextual noise\. Crucially, we observe that these errors stem from the underlying hypergraph\-based RAG pipeline rather than the knowledge editing mechanism itself\. In the following cases, while the hypergraph topology was successfully updated to reflect the new facts, the downstream retrieval and reasoning modules, which remain agnostic to our editing proposal, introduced independent architectural bottlenecks\.

Recall ErrorFigure[7](https://arxiv.org/html/2606.03179#A1.F7)illustrates a recall failure originating from the retrieval manifold rather than a failed edit\. In the first reasoning hop \(Figure[7](https://arxiv.org/html/2606.03179#A1.F7)\(a\)\), the system correctly identifies Michael Scheuer’s employer as the British Broadcasting Corporation \(BBC\)\. However, in the subsequent hop \(Figure[7](https://arxiv.org/html/2606.03179#A1.F7)\(b\)\), the retriever erroneously fetches a hyperedge related to William Le Baron Jenney\. While the edit successfully placed the target fact \(Narendra Modi as director, Figure[7](https://arxiv.org/html/2606.03179#A1.F7)\(c\)\) into the graph, the retrieval module favored entity overlap \(BBC\) over the specific relational intent of the query\. This shows that recall errors belong to the base retriever’s limitations and do not indicate a failure in the structural update logic\.

Contextual NoiseFigure[8](https://arxiv.org/html/2606.03179#A1.F8)demonstrates a reasoning\-induced error\. As shown in Figure[8](https://arxiv.org/html/2606.03179#A1.F8)\(a\), the initial sub\-question is resolved correctly\. During the second hop, the system successfully retrieves the edited ground\-truth fact \(Geoffrey Chaucer’s association with “Shaman King”, Figure[8](https://arxiv.org/html/2606.03179#A1.F8)\(c\)\)\. However, the RAG context is contaminated by a redundant, noisy hyperedge from the previous step \(Figure[8](https://arxiv.org/html/2606.03179#A1.F8)\(b\)\)\. This distraction causes the generator to select the incorrect sub\-answer\. This failure is purely a reasoning bottleneck within the LLM\-based RAG process; the fact that the correct edited knowledge was retrieved confirms that the knowledge editing component performed as intended\.

### A\.4\.Qualitative Study

As shown in Table[6](https://arxiv.org/html/2606.03179#A1.T6), the initial knowledge states thatCiudad de Murcia is associated with the sport of association football, and thatassociation football was created in the country of England, whose capital is London\. A new fact later replaces the sport associated withCiudad de Murciatobasketball, prompting an edit\. In the knowledge graph setting, each triple is decomposed into binary relations such as\(Ciudad de Murcia→\\rightarrowsport→\\rightarrowassociation football\)and\(association football→\\rightarrowcountry→\\rightarrowEngland\)\. After the new fact is introduced, the edited graph appends the new relation\(Ciudad de Murcia→\\rightarrowsport→\\rightarrowbasketball\)while retaining the old one, causing both to coexist\. As a result, the downstream multi\-hop pathCiudad de Murcia→\\rightarrowassociation football→\\rightarrowEngland→\\rightarrowLondonremains reachable, yielding outdated answers\. In contrast, the hypergraph structure preserves each sentence as an atomic hyperedge, maintaining semantic integrity\. The original hyperedge indicating that Ciudad de Murcia is associated with association football is removed entirely and replaced by a new hyperedge stating that it is associated with basketball\. As a result, the updated multi\-hop path proceeds throughbasketball, then toSoviet Union, and finally reaches the correct answerRussellville\.