Topology of Reasoning: Retrieved Cell Complex-Augmented Generation for Textual Graph Question Answering
Authors: Sen Zhao
Lincheng Zhou
Yue Chen
Ding Zou
Venue: ICLR 2026 Poster (2026)
Keywords: Retrieval Augmented Generation
Graph Question Answering
Graph Neural Network
Large Language Model
Textual Graphs
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: Retrieval-Augmented Generation (RAG) enhances the reasoning ability of Large Language Models (LLMs) by dynamically integrating external knowledge, thereby mitigating hallucinations and strengthening contextual grounding for structured data such as graphs. Nevertheless, most existing RAG variants for textual graphs concentrate on low-dimensional structures—treating nodes as entities (0-dimensional) and edges or paths as pairwise or sequential relations (1-dimensional), but overlook cycles, which are crucial for reasoning over relational loops. Such cycles often arise in questions requiring closed-loop inference about similar objects or relative positions. This limitation often results in incomplete contextual grounding and restricted reasoning capability. In this work, we propose Topology-enhanced Retrieval-Augmented Generation (TopoRAG), a novel framework for textual graph question answering that effectively captures higher dimensional topological and relational dependencies. Specifically, TopoRAG first lifts textual graphs into cellular complexes to model multi-dimensional topological structures. Leveraging these lifted representations, a topology-aware subcomplex retrieval mechanism is proposed to extract cellular complexes relevant to the input query, providing compact and informative topological context. Finally, a multi-dimensional topological reasoning mechanism operates over these complexes to propagate relational information and guide LLMs in performing structured, logic-aware inference. Empirical evaluations demonstrate that our method consistently surpasses existing baselines across diverse textual graph tasks.

Published as a conference paper at ICLR 2026
TOPOLOGY OF REASONING: RETRIEVED CELL GENERATION FOR TEXTUAL GRAPH QUESTION ANSWERING
Sen 7h Lincheng Zhou"?, Yue Chen', and Ding Zou Academy of Advanced Interdisciplinary Studies, Chongqing University of Posts and Telecommunications Chongqing, China
School of Computer Science and Technology. Chongqing University of Posts and Telecommunications Chongqing. China
3 Intelligent System Department, Zhongxing Telecom Equipment (ZTE), Changsha, Hunan, China
ABSTRACT
Retrieval-Augmented Generation (RAG) enhances the reasoning ability of Large Language Models (LLMs) by dynamically integrating external knowledge. thereby mitigating hallucinations and strengthening contextual grounding for structured data such as graphs. Nevertheless, most existing RAG variants for textual graphs concentrate on low-dimensional structures- treating nodes as en- tities (0-dimensional) and edges or paths as pairwise or sequential relations (I- dimensional), but overlook cycles, which are crucial for reasoning over relational loops. Such cycles often arise in questions requiring closed-loop inference about similar objects or relative positions. This limitation often results in incomplete contextual grounding and restricted reasoning capability. In this work, we pro- pose Topology-enhan -enhanccd Retrieval-Augmennted Generation (TopoRAG), a novel framework for textual graph question answering that effectively captures higher- dimensional topological and relational dependencies. Specifically, TopoRAG first lifts textual graphs into cellular complexes to model multi-dimensional topolog- ical structures. Leveraging these lifted representations, a topology-aware sub- complex retrieval mechanism is proposed to extract cellular complexes relevant the input query, providing compact and informative topological context. Finally, multi-dimensional topological reasoning mechanism operates over these plexes to propagate relational information and guide LLMs in performing struc- tured, logic-aware inference. Empirical evaluations demonstrate that our method consistently surpasses existing baselines across diverse textual graph tasks.
INTRODUCTION
Large Language Models (LLMs) exhibit strong language understanding and generation capabil- ities, but their reliance on pre-training corpora-limited in scope and immelinss-offen leads to hallucinations, producing inaccurate fabricated content that challenges knowledge-intensiee rea- soning Huang et al. (2023b). To mitigate these issues, Retrieval-Augmeent recently emerged as an effective approach Fan et al. (2024); [Sun et al. (2024); Baek al. (2023); Sen et al. (202)). dynamically retrieving relevant external knowledge and incorporating it into the generation process. By enhancing contextual grounding and factual accuracy, RAG improves rea- soning over structured data and reduces hallucination Gao et al. (2023). However, traditional RAG methods often overlook the structured dependencies among textual entities and struggle to capture global relational patterns, limiting their applicability for graph-structured reasoning tasks.
Generation (RAG) has
To address these challenges, Graph Retrieval-Augmenned Generation (GraphRAG) Edge et al. 2024): Hu et al. (2024); Mavromatis & Karypis (2025) extends conventional RAG by retrieving
"Contributing equally.
1 Cooresponnence Sen Zhao ezchanse@@cuuu.cdd..oo

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not only documents but also graph elements, which provide richer relational context for reasoning over textual graphs. G-Retriever He et al. (2024) introduces the first general GraphRAG framework for textual graphs, formulating retrieval as Prize-Collecting Steiner Tree problem to extract com- pact and relevant subgraphs. GNN-RAC AG Mavromatis & Karypis/ (2025) and SubgraphR AG Li [i et al.) (2025) further develop specialized retrieval modules to extract subgraphs from knowledge graphs. However, existing approaches, primarily operate on low-dimensional elements and largely ignore higher-dimennional topological structures such as cycles, which are crucial for reasoning over re- lational loops and complex dependencies in textual graphs. This limitation becomes more evident when considering the structural nature of reasoning itself. Recent empirical studies (Minegishi et al.) (2225) analyzing reasoning processes in large language models observe that stronger reasoning behaviors often involve recurrent dependency patterns that resemble cyelic structures reasoning graphs. Such observations suggest that effective reasoning may inherently rely on non-linear rela- tional organization, motivating the need to explicitly model cyclic dependencies in textual graphs.
In many real-world textual graphs, essential information arises not only from nodes (0-cells) that encode entity attributes, edges and paths (I-cells) representing pairwise or multi-hop relations, but also from cycles (2-cells) capturing higher-dimensional dependen- cies. As illustrated in Fig. [ reasoning over O-cells enables answering simple attribute- based questions (Fig. [a), while incorporating 1-cells supports inference over one-hop to multi- hop relational queries (Fig. [ b). However, certain queries require cyclic dependencies
Quary Aro
Und pupphe?
What the justin bleter broffar??
What
lurrelre to the lall of the mutl the same fooo?
of
Scane Graph
Knn Graph
Scens Graph
parera
wetal
Retrievall &
B-Giil (Node)
1-Col (Edgs and patho)
2-Gell (Circle)
Ressoning
came coll
Answer
Yes, the is purple.
jaxon
plece furniture table.
(4) Quetion
involving
invohinn
Figure 1: Illustration of question answering with varying dimen- sional topological characteristies.
among multiple entities, where the answer emerges only from reasoning over 2-cells. For example, the question in Fig. (c) involves a closed relational loop that links spatial relations with material consistency, which cannot be resolved by nodes and edges alone. Capturing structural information across multiple topological dimensions provides indispensable context for structured logical inference, as higher-dimenssonal dependencies complement lower-dimensional relations to enable reasoning beyond simple pairwise interactions. Consequently, retrieval and reasoning mechanisms that explicitly incorporate multi-dimensional topological features are essential for understanding and answering questions over complex textual graphs.
Generation (TopoRAG), a novel framework for textual graph question answering that explicitly models higher-dimension topological and relational dependencies. Specifically. TopoRAG first lifts input textual graphs into cellular complexes capture multi-ddimeniooal topological structures, including cycles that encode closed-loop dependencies critical for relational reasoning. Leveraging these lifted representations, a topology-aware subcomplex retrieval mechanism is introduced to extract cellular complexes that are most relevant to the input query, providing compact yet informative topological context for down- stream reasoning. Furthermore, a the retrieved complexes to propagate relational information across different topological dimensions, enabling structured, logic-aware inference that naturally integrates with LLM reasoning. Extensive experiments demonstrate that TopoRAG consistently outperforms state-of-the-arr baselines.
In this work, we propose Topology-enhanced
topological reasoning mechanism operates over
2 RELATED WORKS
Large Language Models (LLMs) have shown impressive capabilities in language understanding and text generation, yet they remain constrained by the boundaries of their pre-training corpus, lacking domain-specific expertise, real-time updates, and proprietary knowledge. These limitations
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frequently manifest hallucinations, where models produce inaccurate or fabricated content Huang et al. (023b)) To address this issue, Retrieval-Augee Augmented Generation (RAG) Fan et al. (2024) : Sun
al.
2024); Back al. (2023): Sen et al. 2023) has emerged as promising paradigm.
RAG enhances LLMs by dynamically retricving relevant external knowledge and incorporating into the generation process, thereby improving factual aceuracy, contextual grounding, and inter- pretability [aao et al. (2023). Nevertheless, existing RAG methods are not without shortcomings in real-world applications. They often overlook structured dependencies among textual entities, rely on lengthy concatenated snippets that may obscure critical information (the "lost in the middle" problem [Liu al.] (2024)), and struggle capture global structural patterns essential for tasks such as query-focused summarization.
To address these challenges, Graph Retrieval-Augmentc Generation (GraphRAG) Edge al. (2024); Hu et al.] (2024); Mavromatis & Karypis (2025) extends conventional RAG by retrieving not only documents but also graph elements such as nodes, triples, and subgraphs. Building on this idea, G-Retriever He et al. (2024) introduces the first general RAG framework for textual graphs, formulating retrieval as a Prize-Collecting Steiner Tree problem to extract compact and relevant sub- graphs. GNN-RAG Mavromatis & Karypis (2025) improves knowledge graph QA by integrating GNN-based representations for task-specific subgraph selection, and SubgraphRAG et al. (2025) incorporates lightweight triple scoring and distance encoding to achieve efficient subgraph retrieval. Nevertheless, existing methods overlook high-dimensional cyclic dependencies, motivating our ap- proach to incorporate multi-dimensional cell structures for enhanced retrieval and reasoning.
We also discuss related works on graphs & LLMs, and topological deep learning in Appendix
3 PRELIMINARIES
Definition 1. (Cell Complex Hansen & Ghrist (2019)) A regular cell complex is topolog-
ical space X decomposed into a collection of disjoint subspaces (To Jae referred to as cells, satisfying the following conditions:
1. For each point p E X, 3 open neighborhood intersects only finitely many cells.
2. For any pair of cells F. Fy,, the intersection 2, O Fy is nonempty if and only if xy C Fo. where Iy denotes the topological closure of Ta.
3. Each cell Ia is homeomorphic to an open ball in R" for some non-negative integer n.
4. (Regularity) The closure Io of every cell is homeomorphic to a closed ball in R with the interior mapped homeomorphically onto H, itself.
Definition 2. cellular lifting map is a function f g - X from the space of graphs G to the space of regular cell complexes X, satisfying that two graphs G1, G2 E G are isomorphic if and only their corresponding cell complexes (Gi and f((22) are isomorphic. Intuitively, a cell complex is built hierarchically by first considering O-cells (vertices), then attaching 1-cells (edges) via their endpoints, and further incorporating higher-dinnn dimensional cells by gluing disks along cycles.
Definition 3. (Retrieved Cell Complex-Augmented Question Answering). Given a textual graph G GV, E, {tn hnev, {t )eee), where each node E V and edge E is associated with textual attributes tn E D and te E DL',, we lift 9 into a regular cell complex X through a cellular lifting map f : G X. The resulting complex X {xa} contains multi-diimensionl structures, including O-cells (nodes), 1-cells (edges/paths), and higher-dimensions cells (e.g., 2-cells as cycles).
To enable retrieval, query is first encoded by language model into dense representation:
zq = LM(Q) E Rdd
Each cell Fo E is also represented by an embedding Za. obtained from its textual attributes together with a topological descriptor =á that summarizes its d-dimensional structure. We then apply a top-k similarity-based based retrieval strategy to select the most relevant cells:
X TopK e cos(2q,=0) =d)
(2)
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where cos(:..) denotes cosine similarity. This step yields candidate set of cells X Tog (Io spanning multiple topologiaal dimensions.
The task is defined as follows: given natural language query and the lifted cell complex X, the model must retrieve the most relevant subcomplexes X and reason over their multi dimensinnl structures to generate answer A. Formally, the QA function is
f (9, Q, + A,
(3)
where A is a natural language sequence generated by the LLM under the conditional likelihood
pa(A Q;x)) II po (ees
(4)
Here, [Pe; ] denotes the concatenation of soft prompt embeddings Pe. query tokens, and re- trieved subcomplex representations, while acs represents the prefix of A up to step i
Training proceeds by maximizing the likelihood of the ground-truth answer A
max log Po P.
Pe:: Q: X*]);
(5)
where only the soft prompt parameters Pe are updated, while the LLM parameters 0 remain fixed.
THE TOPORAG FRAMEWORK
In this section, we present the architecture of TopoRAG (illustrated in Figure a topology- enhanced retrieval-augmented generation framework designed for textual graph question answering. TopoRAG composed of four key components. First, the Cellular Representation Lifting module transforms input textual graphs into regular cell complexes, providing expressive multi multi-dimensional topological representations that go beyond nodes and edges. Second, the Topology-awarr Subcom- plex Retrieval module identifies the most relevant subcomplexes with respect the query by jointly considering semantic similarity and topological structure. Third, the Multi cilliiddimesionall Toooooog ical Reasoning module propagates relational information across different topological dimensions, enabling structured and logic-aware inference. Finally, the Cell Complex-Augmented Generation module integrates retrieved subcomplex representations into the LLM guide answer generation, ensuring faithful and topology-consistent consistent responses.
4.1 CELLULAR REPRESENTATION LIFTING
Given a textual graph G = EV, tne tEEE, we aim to lift it into a higher-dimensional topological space that faithfully encodes both relational and structural dependencies. This is achieved by constructing a regular cell complex X through a cellular lifting map f : g + +X
We first regard G I-dimensional cell complex, where each vertex v E V corresponds to O-cell 20 E (0)), and each edge (u, v) E E corresponds to a 1-cell x!! ((.,) E (1) attached to its endpoint O-cells x and a. This forms the cellular 1-skeleton:
x - x U (xtw,,) (u, EJ.
To elaborate, consider b, E D as the text attributes of vertex v and ((w.)) E D4 as those of edge (u, v). Utilizing pre-trained LMM such as SentenceBert (Reimers & Gurevych 2019). we apply the LM to these attributes, yielding the representations:
Z LM(L.) E IRd, =(u,e) LM(((u.)) e Rd.
where d denotes the dimension of the output vector. This yields cellular embeddings for both nodes and edges, which serve as the lifted representation in the subsequent module.
To incorporate high-dimensional topological structures, extend (1) by identifying fundamental cycles. Specificallyy we fix a spanning tree T C G and apply the quotient map:
?: + G/T,
(8)
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Celluler Representation Litting
Topology-aaae Subcomplex Retrieval
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LM
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Cruph encoder
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Figure 2: The overview aapology-enhancee aetrieval-Augmente Framework.
which collapses T to a single point. Each non-tree edge = (u, E E' \ T then induces fundamental cycle by connecting e with the unique path in T between and For every such cycle, attach 2-cell xe (2) via the attaching map
Pa aD = S G())
(9)
that glues the boundary of disk D the cycle. Formally, the 2-cells is
(2) ta D |
(10)
The resulting cell complex X = ( U x U (2) augments the original graph with multi- dimensional topological structures.
Proposition 1. G/T& is homotopy-equivalent to G, and y induces an isomorphism on the first ho- mology group H, GG;
Proof. Contractibility of the spanning tree. A spanning tree T is connected and acyclic, hence contractible. In topological terms, a contractible subspace can be continuously shrunk to a point within itself.
Collapsing a contractible subspace. Consider the quotient map y G - G/T that identifies all points of 7 single vertex up. Collapsing a contractible subspace is deformation retraction up to homotopy: there exists continuous map r G + G/T and homotopy G x [0 G such that (xx 0) x and Hxx, 1) r(z) for æ E G, with r roys idg/T. Therefore, and G/T are homotopy-equivalee
Induced isomorphism on first homology. groups. Hence the induced map 7 H (G; Z) H. (G/T;Z) is an isomorphism.
spaces have isomorphic homology
Intuition graph terms. The spanning tree T contains no cycles, so collapsing it does not remove merge any cycles in G. Each fundamental cycle in G (formed by non-tree edge and the unique tree path connecting its endpoints) is preserved in G/T as a loop based at the collapsed tree vertex. Therefore, the first homology group H1 H1(G) - which measures independent cycles remains unchanged.
Proposition 2. Each non-tree edge e E E E induces a unique fundamental cycle in G. which becomes nontrivial loop in G/T. The collection of these loops forms a basis of the first homology group H, (G; Z), capturing all independent cycles and providing a concise topological summary of the graph.
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Proof. Let G EV be finite connected graph and T C G spanning tree.
Existence and uniqueness of fundamental cycles. For each non-tree edge e (u. v) E E there exists unique simple path PT (u, in T connecting and by acyclicity of T. Concatenating e with Pr (u, v) defines a unique simple cycle C. = e Pr(u, v) C. G. Under the quotient map y G G/T that collapses T to point, the tree-path (r(u,t) is mapped to that point, Ce becomes a nontrivial loop in G/T.
Spanning and independence in homology. The cyclomatic number of G Bi -
which equals the number of non-tree edges. Thus there are exactly 31 (G) fundamental cycles.
Any cycle in G be expressed linear combination of these fundamental cycles: traversing cycle, each time a non-tree edge e encountered, the corresponding C. can be used to eliminate segments along T.
These cycles are independent in Hi (G), because under 7, each fundamental cycle maps to distinct loop in G/T, and loops around different edges of wedge of circles are linearly independent in homology.
Hence the set {[C.] | EX T forms a basis of (G). Different choices of spanning tree yield different sets of fundamental cycles edge sets, but the corresponding homology classes always span H1 (G). Therefore, these loops capture all independent cyclic dependencies of G. providing concise topological summary suitable for lifting G into a higher- nigher-dimensional cell complex.
4.2 TOPOLOGY-AWARY SUBCOMPLEX RETRIEVAL
Given a query zg we first encode into d-dimensional embedding:
2 LM(gg)) E R
(11)
To retrieve the most relevant cells, we compute the cosine similarity between by and the embeddings of 0- and --eells:
x TopK ( cos(zgs =gx),
(12)
where d {0, } denotes the dimension, 2 is the embeddings of d-cell xd, These provide the top-k relevant 0- and 1-cells.
Prize assignment. Each selected O-cell o0 E (() and 1-cell e x(") is assigned a descending prize according its ranking:
k -r, if x' is ranked r-th among top-k cells, i= 0,
prize(x*)
(13)
0, otherwise,
For each 2-cell 2² (2), its prize is computed from the prizes of its boundary cells:
prize(a²)
Σ Σ prize(=*) cost(>²),
(14)
dE(0.1) =d
where agx²2 denote the sets of boundary d-cells of x² and cost(x²) = =1a,22 C2 penalizes larger faces with a tunable constant C2. Top-k 2-cells are selected based on this prize ranking, denoted as x²?)) ensuring that all selected 2-cells share boundary cells with the chosen 0- and 1-cells.
Subcomplex selection. The final subcomplex X maximizes the total prize while controlling size:
X argmax X'cx, x' connected (0.1.2) 27EXXO
Σ
Σ
prize(=") cost(X"),
(15)
where cost(X") is a size-dependent penalty.The boundary consistency constraint ensures that any selected 2-cell x² E (2) has all its boundary 0- and 1-cells included (*(0) and X*(I), preserving topological coherence.
The resulting topology-aware subcomplex selection problem can be seen as a generalization of Prize-Collecting Steiner Tree (PCST) problem (Bienstock al. 1993) higher-dimennsonal cell

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complexes with multi nulti-diimensional prizes and size-dependent penalties. We adopt near-linear time approximation algorithm Hegde et al. (2015) to efficiently identify near-optimal connected sub- complex X This ensures that the final subcomplex captures the most query- query-relevant structures across all cell dimensions, while maintaining computational efficiency and topological validity.
4.3 MULTI-DIMENSIONAL TOPOLOGICAL REASONING
After retrieving the query-relevant subcomplex X XX- xX we propagate semantic and relational information across different topologiaal dimensions to enable structured reasoning over the enriched cell complex. We employ a two-stage message passing mechanism that leverages the multi-dimensional structure of the complex. In the first stage, information is propagated along the I-skeleton, between O-cells and 1-cells, over L hops:
UPDATE' (n'.. (1)),, (())))) I X U UX
1= 1=1,...,1 L,
(16)
where (x) aggregates messages from faces, and (x) aggregates messages from cofaces:
m 1+1 (x) AG Mc h!),
4+ (z) AGG My (h hty,,
(17)
mc
with F(x) and C(z) denoting the sets of faces and cofaces of æ.
In the second stage, cells of all dimensions exchange information with higher-dimensiona neigh- bors to capture multi-dimensional topological context. For each cell x E X", the representation is updated as
h L++ = UPDATE (h. (.)()) me (a(++(x)))
(18)
where my I++1 (x) aggregates messages from adjacent cells via shared cofaces. Specifically, the mes- sages are defined
(x) (M) (h h hatt)
(19)
with (2) the set of cells adjacent via shared coface.
To generate a fixed-dimensionl representation of the entire subcomplex, we aggregate the embed- dings of all its cells:
hx- = POOL ( E ( U xx (x)x))))) TR
(20)
where POOL can be implemented as mean pooling over the cell embeddings, and d, denotes the dimension of the resulting subcomplex representation. This aggregated embedding hx- encodes both the semantic attributes of individual cells and the dilliiidimnsionall topological context of the subcomplex, serving input to the Cell Complex-Augmentee Generation module for query-guided answer generation.
4.4 CELL COMPLEX-AUGMENTER GENERATION
With the subcomplex embedding hx. obtained from the Multi-dimensional Topological Reasoning module, we integrate it into pretrained LLM to guide query-aware answer generation. First, we align the subcomplex embedding to the LLM's hidden space via multilayer perceptron (MLP):
h x MIP (hxx)) E IR:
(21)
where di is the hidden dimension of the LLM. The projected vector hx- acts as a soft prompt, providing structured, topologically-infommed guidance the L.M.
To leverage the LLM's text reasoning capabilities, we also transform the retrieved subcomplex into a textualized format, denoted as textualize (X*), by flattening the textual attributes all cells while preserving the structural hierarchy. Given natural language query Zg. we concatenate it with the textualized subcomplex and feed into the LLM's embedding layer:
h TextFmmeederr wtw.bbeddddee(ttxaaieeeeee (x xrg)) E TR Lxd.
(22)

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where [::-] denotes concatenation, L is the number of tokens, and the TextEmbedder is frozen pretrained LLM embedding layer.
The final answer Y is generated autoregressively, conditioned on both the soft subcomplex prompt hx- and the textual token embeddings h4:
Po.e (Y X xx) =
11 p (Uk yea. [ hx]):
(23)
where 0 denotes the frozen LLM parameters and & denotes the trainable parameters of the MLP and the subcomplex encoder. Gradients are backpropagated through hx-, enabling the subcomplex encoder to learn to generate embeddings that are optimally informative for downstream generation.
5
EXPERIMENTS
5.1 EXPERIMENT SETUP
Datasets, Following prior work He et al. (2024), we use three existing datasets to conduct experi- ments WebOSP Yih et al. 2016), exxplaGraphe Saha et al. (2021) and SceneGraphs Hudson & Manning 2019). These datasets are standardized into a uniform format suitable for graph ques- tion answering He et al. (2024), allowing consistent evaluation across diverse reasoning tasks. More details about these datasets are provided in Appendix
Comparison Methods. To evaluate the performance of TopoRAG, we consider three categories of baselines. We provide more details in Appendix D
Inference-only LLMs directly answer questions using the textual graph as input, including zero-shot prompting, zero-shot Chain-of ciii-offThhhee Thought (Zero-Cor (oso-Coo)) Kojima et al. (2022), Build-a- -arapa prompting (CoT-BAG) Wang et al. (202)) and KAPING Baek al. (2023), a snowledge-augmentn
zero-shot
approach; Frozen LLMs with prompt tuning keep model parameters fixed while optimizing the input prompt, including soft prompt tuning, GraphToken Perozzi et al. (2024), G-Retriever[He et al. (2024) with frozen LLM and SubgraphRAG et al. (2025); Tuned LLMs update model parameters using LoRA Hu et al. (2021), including standard LoRA mee-ttning and G-Retriever w/ LoRA He et al. 2024) combining retrieval augmentation with parameter-efficte tuning, GNN-RAG Mavromatis
& Karypis (2025).
Evaluation Metries. For ExplaGraphs and SceneGraphs, the performance is measured ing Accuracy, which calculates the percentage of correctly predicted answers. For WebQSP, we use the Hit metric, which measures the percentage of queries for which at least one of the top returned answers is correct. This metric is particularly suitable for multi-hop reasoning tasks, where the model must traverse multiple hops in a knowledge graph to retrieve the correct answer.
Experiment Settings. All experiments set the top-k for 0- and 1-cells to & = 3 on WebQSP; on SceneGraphs, we set sweep the top-k over l {0. 2, For reasoning, the number of layers is varied in (2,3, 3, 4, 5}, with a uniform dimensionality (input, hidden, and output). For generation, as the large language model backbone. When fine-tuning with LoRA Hu et al. (2021). ) we set the rank 8, alpha 16, and dropout rate 0.05; for prompt tuning, we use 10 virtual tokens. The maximum imput length is set to 512 tokens, and the maximum number of generated tokens is set to 32. We adopt the AdamW optimizer Loshchilov & Hutter (0017) with a learning rate of 1 x 10-5 a batch size of 8, and train for 10 epochs with early stopping (patience = 2).
conducted on two A6000-48G GPUs. For retrieval,
for O-cells
and & 5 for 1-cells. For 2-cells,
1024 across all layers employ the Llama-2-7B model Touvron et al. (2023)
5.2 EXPERIMENT RESULT
Main Results. As summarized Table I our model consistently outperforms baselines across datasets and configurations. We highlight three key findings:
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Table I: Performance comparison across ExplaGraphs, SceneGraphs, and WebQSP datasets under different configurations. The bold numbers indicate that the improvement of our model over the baselines is statistically significant with (p-value < 0.01), and the best baseline results are underlined
Sctting
Method
SceneGraphs
WebQSP
Zero-shot
0.5650
0.3974
41.06
Zero-Co T
0.5704
0,5260
51.30
Inference-only
CoT-BAG
0.5794
0.5680
39.60
KAPING
0.6227
0.4375
52.64
Prompt tuning
0.5763
0.6341
48.34
GraphToken
0,8508
0,4903
57.05
Frozen LLM w/ PT
G-Retriever
0.8516
0.8131
70.49
SubgraphRAG
0.8535
0.8074
86.61
TopoRAG (Ours)
0.8899
0.8362
87.10
LoRA G-Retriever w/ LoRA
0.8538
0.7862
66.03
0.8705
0.8683
73.79
Tuned LLM
GNN-RAG
0.8466
0.8149
85.70
TopoRAG w/ LoRA (Ours)
0.9151
0.8768
90.66
TopoRAG delivers the strongest overall performance. Compared to the best baseline, TopoRAG improves Expla aGraphs and SceneGraphs Accuracy by 5.12% and 0.98%, respectively; on WebQSP, increases the Hit metric by 4.67%. We attribute the improve- ments to the following reasons: Cellular Representation Lifting, which transforms tex- tual graphs into cellular complexes and explicitly encodes that support closed- loop relational reasoning; 2) topology-awan subcomplex retriever that selects query-relevant cellular complexes, supplying compact yet informative topological context; and 3) multi-dimensional topological reasoning that propagates information across 0-/1-/2-cells to enable structured, logic-aware inference tightly integrated with LLM rea- soning. Together, these components overcome the limitations node/edge-centric meth- ods and yield more accurate and robust QA over complex textual graphs.
structures
Graph-structured prompts effectively improve QA performance. All prompt-tuning approaches (e.g., Goken SubgraphRAG) outperform inference-only baselines (Zero-shot, Zero-CoT), underscoring the value of structured context. TopoRAG further improves upon these by grounding prompts in nigher-dimensional topological dependen- cies cies-beyond nodes and edges- theerby providing richer, loop-aware relational context, especially for queries involving multi-hop and eyelic dependencies.
Ablation Study. We conduct an ab- lation study to evaluate the contribu- tion of each component of TopoRAG. Specifically, we replace Cellular Rep- resentation Lifting (CRL) with a stan- dard edge-based graph structure, sub- stitute Topology-aware Subcomplex Re- trieval (TSR) with thortest-path-basse retrieval, and replace Mulii-dimensionl Topological Reasoning (MTR) with GCN for message passing.
Table 2: Ablation Study on ExplaGraphs and WebQSP Datasets.
Method
ExplaGraphs (Accuracy)
WehQSP (Hit)
w/o CRL w/o TSR w/o TopoRAG
0.8576
84.96
0.8524
84.23
0.8611
85.46
0,9151
90.66
1) Replacing Cellular Representation Lift- ing (CRL) with an edge-only graph representation removes the lifting of textual graphs into cellular complexes and, consequently, the explicit encoding of higher-dis diiheer-immesiooall structures (e.g.. cycles) that support closed-loop relational reasoning. This leads to a substantial performance drop, under- scoring the necessity of CRI. for modeling high-dimensional dependencies in RAG.

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92.0
0.885
WebQSP (Hil)
WebQSP (Hit)
92
ExplaGraphs (Accuracy)
0.96
91.5
SceneCraphs (Accuracy)
0.880
0.94
91.0
91
0.92
90.5
0.875
Accuracy
90
0.90
90.0
0.88
89.5
0.870
89
0.865
88
0.84
88.5
87
0.82
88.0
2
3
0.860
(a) Layers (L)
(b) top-k (k)
Figure 3: (a) Effect of layers (2,3,4, 4, on TopoRAG performance: WebQSP (Hit) and Expla- Graphs (Accuracy). (b) Effect of top-k k E {0, 1,,,,2,3) 3) on TopoRAG performance: WebQSP (Hit) and SceneGraphs (Accuracy).
2) Replacing Topology-aware Subcomplex Retrieval (TSR) with shortest-path retrieval restricts results to the 1-skeleton and removes 2-cells, thereby discarding digher-dimensional motifs and closed-loop constraints that are critical for capturing query-relevant structure, underscoring the im- portance of TSR for sustaining TopoRAG's effectiveness.
3) When removing Mulii-dimensionl Topological Reasoning (MTR), the performance TopoRAG drops significantly. This is due to the crucial role of MTR in enabling multi- ditinniimnniiall message passing using cellular complexes. Without MTR, the model loses the ability to effectively propagate information from high-dimensional cells to low-dimensional ones, resulting in the loss of important high-dimensional structural information during the message passing process.
Hyper-parameter Study. We study the sensitivity To to two key hyperparameters: the number of layers 7. and the top-k of 2-cell for subcomplex retrieval. The layer depth I, controls the model's s ability to capture hierarchical structures and long-range dependencies. Larger enhances the model's representational capacity but may lead to overfitting increased computational cost, while smaller L may limit structural information capture, causing underfitting. Figure 3 (a) shows the effect of different L values performance: reasoning ability improves L increases, but excessive depth reduces expressiveness. We also analyze the impact of the top-k parameter for 2-cells selection retrieval. Too small I causes information loss, while too large k introduces noise. Figure (b) illustrates the effect of different A {0, 1, 2, 3} values, showing that a moderate achieves a better balance between structural coverage and noise. Appendix we present an extended sensitivity analysis of the choice of k.
6 CONCLUSION
In this work, we introduced TopoRAG, capology-enhancee retrieval-augmennee generation frame- work for textual graph question answering. Unlike conventional GraphRAG approaches that mainly rely nodes and edges, TopoRAG explicitly incorporates higher-dimensional topological struc- tures by lifting textual graphs into cellular complexes. Through topology-aware subcomplex re- trieval mechanism, TopoRAG provides compact yet informative multi-dimensional contexts, while the proposed multi-dimensional topological reasoming module enables structured and logic-aware inference that captures eyclic and dimeen-aimeniional dependeneies beyond pairwise relations. Ex- perimental results demonstrate that ToGoRAG outperforms existing methods across three datasets from different domains.
ACKNOWLEDGMENTS
This work is supported in part by the Chongqing Municipal Education Commission (No. KJQN202500620), and General Program of Chongqing Municipal Fund (NO. CSTB2025NSCQ-
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GPX1297). The authors would like thank the anonymous reviewers for their valuable comments and advice.
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Table 3: Notation and definitions used in the TopoRAG framework.
Notation
Definition
G
The imput textual graph, defined G (V, E, {fa hev, (fe)eE)) The sets vertices (nodes) and edges in the graph G. The text attribules associated with node n E V and edge E E.
V.
tn. te
The regular cell complex constructed from the graph G. d-skeleton.
x
A k-dimensional cell in the complex (e.g.. a a O-cell, a²: I-cell).
zer ze
The d-dimensional embedding of node v (0-cell) and edge e (1-vell), obtained via Language Model (LM).
spanning tree of the graph G. used for cycle detection.
x
A 2-cell attached to fundamental cycle induced by non-tree edge E EXT.
The d-dimensional embedding of the input query Jig-
x
The of top-k retrieved d-cells (d 0,1, 2) based on semantic similarity or prize.
prize(x')
The prize (relevance score) assigned cell x² during retrieval.
X*
The final retrieved and connected subcomplex, X (0) (1) (2)
Oxx
The boundary operator; 0,æ gives the set (k 1) 1)-cllls on the boundary of k-cell
ni
The hidden representation of cell x at message passing layer 1.
F(x). C(x)
The set of faces floer-dimensiona. dimensional incident cells) of cell
boundary cells) and cofaces (higher-
m²)(2),,
m²( mmx(()).mm())
Messages aggregated from faces and cofaces of cell layer I.
hx
The final pooled representation of the entire subcomplex X"
hx.
The projected subcomplex embedding, aligned to the LLM's hidden space via an MLP.
PY xx))
The conditional probability of generating answer Y, given the subcomplex X and query zg..
A NOTATIONS
The notations in the TopoRAG framework are summarized in Table
B ADDITIONAL RELATED WORK
Graphs and Large Language Models. In parallel, there has been surge of interest in combin-
ing graphs with LLMSs Pan et al. (2033); ; Li et al. (2023b); Jin et al. (2023): Wang et al. (2023):
/Zhang et al. (023). This line of research spans wide spectrum, from the design general graph
models Ye et al. (2023); Liu et al. ) Yu et al. (002bb; Lei et al. (2023); Tang et al. (2023): )
Perozzi et al. (2024). multi-modal architectures Li al. (202a)); Yoon al. (2023). and diverse
downstream applications.
Applications of Graph-augmented LLMs include fundamental graph reasoning Zhang 2023 ; hai et al. (2023); Zhao et al. (2023b), node classification He et al. (2023); HHang et al. (2023)) Sun al. 2023); Chen al.] et 2023al: Chen al. (2024); Qin al. (2023), and graph classif- cation/regression Qian et al. (2023 /hho et al. (2023a). Furthermore, LLMSs have been increasingly employed for knowledge graph-related tasks such as reasoning, completion, and question answer-
ing Tian et al. (2023) Jiang et al. 2023 Luo al. (2023).
Topological deep learning expands graph learning by modelling re- lations that exceed simple pairwise links. Early work in Topological Signal Processing (TSP) em- structure for signal and relational modeling Barbarossa &
Topological deep learning.
phasized the value of Sardellitti (2020); Schaub et al. (2021) Roddenberry et al. (2022); y: Sardellitti al. (221)) 1) prompting extensions of graph tools to richer discrete geometries such as simplicial and cell complexes. Theo- retical progress e.g., higher-dimensionall generalizations of the Seeefeiler-eemmae test-has clar-
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ified the expressive power required for distinguishing complex topologies and motivated message- passing schemes beyond traditional GNNs Bodnar et al. (2021c a..
On the modelling side, researchers have proposed numerous neural architectures that operate these higher-dimensionall domains, including convolutional-styy operators for simplicial and cell complexes Ebli al. (2020); Yang et al. (2022): Hajij et al. (2020); Yang & Isufi (2023); Rodden- berry et al. (2021): Hajii et al. (2022) and attention based formulations that incorporate incidence relations and coface interactions Goh et al., Giusti al. (2023). Efforts unify these variants led to
combinatorial-come
frameworks that generalize message passing to a wide class of combinato-
rial objects (simplicial complexes, CW complexes, hypergraphs) Hajij et al. (2023). Complementary lines of work use theaf-thherreti constructions to impose local consistency and handle heterophilous patterns, demonstrating another principled route to encode localized topological constraints Hansen
& Ghrist (2019): Hansen & Gebhart (2020): Bodnar et al. (2022): Battiloro et al. (2023 2024);
Barbero et al. (2022).
While these works have substantially advanced higher- ligher-dimeesiioall representation learning, current topological deep learning methods exhibit limited generalization to unseen graphs with substantially different topologies, a sensitivity that hinders their applicability in real-world scenarios where struc- tural variability is common. Moreover, they remain largely tied to static, pre-defined complexes and traditional graph formulations, leaving them ill ill-suited for reasoning in question answering tasks that require integrating textual graph inputs with large language models and dynamically incorporating external knowledge. In this work, address these limitations by introducing TopoRAG, frame- work that explicitly models multi-dimensional topological structures and couples topology-awe retrieval with large language models enable robust and context-sensitive reasoning over textual graphs.
C DATASETS
Following prior work He al. (2024), we use three existing datasets: WeboSP, ExplaGraphe and SceneGraphs, which are summarized in Table These datasets are standardized into uni- form format suitable for graph question answering, allowing consistent evaluation across diverse reasoning tasks. ExplaGraphs focuses on generative commonsense reasoning. The task requires predicting whether an argument supports or contradicts a given belief, evaluated using Aceuracy. SceneGraphs is visual question answering dataset. The task is to answer questions based on textualized scene graphs, requiring spatial reasoning and multi-step inference, evaluated by Accu- racy. WebQSP is large-scale multi-hop knowledge graph QA dataset, which contains facts within 2-hops of entities mentioned in the questions. Each question associated with a subgraph extracted from Freebase. The task involves multi-hop reasoning, evaluated using Hit for the top returned answer.
Table 4: Overview of datasets used in the GraphQA benchmark.
Dataset
Exp1 Fap1aGraphs
SceneSraphs
WebOSP
Number Graphs
2.766
100,000
4.737
Average Nodes
5.17
19.13
1,370.89
Average Edges
4.25
68.45
4,252.37
Node Features
Commonsense concepts
Object properties (e.g.. color, shape) Ohject interactions and spatial relations Scene graph QA Accuracy
Freebuse entities Freehase relations
Edge Features
Commonsense relations
Task Type
Commonsense reasoning
Knowledge graph QA Hit
Evaluation Metric
Accuracy
D COMPARISON METHODS
In our experiments, we consider three categories of baselines: 1) Inference-only, 2) Frozen LLM w/ prompt tuning (PT), 3) Tuned LLM. The details of each baseline described follows.
Inference-only. tion.
Using a frozen LLM for direct question answering with textual graph and ques-
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Zero-shot. In this approach, the model is given textual graph description and task de- scription, and immediately asked to produce the desired output. No additional examples demonstrations are provided.
Zero-CoT. Zero-shot Chain-of-thought (Zero-CoT) prompting (Kojima al. 2022 is follow-up to CoT prompting (Wei et al. 2022). which introduces an incredibly simple zero shot prompt by appending the words "Let's 's think step by step." to the end of question.
CoT-BAG. Build-a- Graph Prompting (BAG) (Wang et al. 2023) is a prompting technique that adds "Let's construct graph with the nodes and edges first." after the textual descrip- tion of the graph is explicitly given.
KAPING. KAPING (Baek al. 2023) zero-shot knowledge-augmente prompting method for knowledge graph question answering. It first retrieves triples related to the question from the graph, then prepends them to the input question the form of prompt, which is then forwarded to LLMs to generate the answer.
Frozen LLM w/ prompt tuning (PT). Keeping the parameters of the LLM frozen and adapting only the prompt.
GraphToken (Perozzi al. 2024). which is graph prompt tuning method.
G-Retriever He et al. (2024) an efficient and lightweight model that adapts frozen large
language model parameters to graph question answering tasks solely through trainable graph-structured soft prompts.
SubgraphRAG Li et al. (2025) is a retrieval-uugmented generation framework based on knowledge graphs, which effectively improves the accuracy, efficiency, and interpretability of question answering through lightweight subgraph retrieval and inference with an untuned large language model.
Tuned LLM. Fine-tuning the LLM with LoRA.
G-Retriever (w/ LoRA) He et al. (2024) is a high-precision model that fine-tunes large language model parameters using techniques such LoRA, enabling deep integration of graph structure information to enhance graph question answering performance.
GNN-RAG Mavromatis & Karypis 2025 is retreeevl-augmented generation framework based on graph neural networks, which efficiently retrieves multi-hop reasoning paths from knowledge graphs using GNNs and inputs them context to LLM, enhancing the curacy and efficiency of complex knowledge graph question answering.
E IMPACT OF DIFFERENT SPANNING TREE METHODS
We evaluate the sensitivity of our method to the choice of spanning tree by comparing different spanning tree construction strategies, including DFS, BFS, and Random spanning trees. As shown in T all variants achieve comparable performance across datasets, indicating that the proposed framework is largely insensitive to the specific spanning tree algorithm.
This robustness be explained from topological perspective. Although different spanning trees induce different fundamental cycle bases, they generate the same cycle space, corresponding to an identical first homology group. Consequently, while the specific 2-cells constructed from basis cycles may vary, the lifted complexes preserve the same global topological structure.
Table 5: Performance comparison of different spanning tree algorithms
Method ExplaGraphs (Accuracy) SceneGraphs (Accuracy)
WebQSP (Hit)
DFS
0.9151
0.8768
90.66
BFS
0.9025
0.8725
90.18
Random
0.9187
0.8698
90.03
18

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Published as a conference paper at ICLR 2026
F IMPACT OF TOP-K SELECTION ON SUBCOMPLEX RETRIEVAL
To further quantify the influence of k on subcomplex retrieval, we conduct supplementary exper- iments with & E {1, 2, 3) and report, on WebQSP and S SceneGraphs, the average numbers of O-, 1-, and 2-cells per retrieved subcomplex. As shown Table 6 larger h yields more retrieved 2-cells; the accompanying inclusion of
structures also increases the counts of O- and 1-cells, underscoring the trade-off that introduces between structural coverage and noise.
Table 6: Impact of Top- K Selection on Subcomplex Retrieval.
Number of Cells per Dimension
Dataset
O-cells
1-cells
2-cells
15
17
2
Web2sP
16
18
3
17
20
12
SceneGraphs
13
5
14
G DISCUSSION ON THE COMPLEXITY
Following prior work, TopoRAG adopts the LLM+X framework. which enhances LLMs with mul- timodal capabilities by integrating them with encoders from other modalities. In recent years, the LLM+X framework has been widely adopted in various RAG methods. Notable examples include: 1) KG+LLM approaches, such as RoG, ToG, StructGPT, and KAPING, and 2) GNN+LLM ap- proaches, including G-Retriever and GNN-RAG. These models have demonstrated strong perfor- mance in both efficiency and accuracy. Furthermore, we introduce Topo+LLM.
Regarding the integration of topological methods into RAG, does not significantly increase the time or computational complexity associated with LLM-based answer generation, as both cellular complex construction and subcomplex retrieval are implemented during the preprocessing phase.
In contrast to G-Retriever, we use a more complex Multi-dimensional Topological Reasoning to capture high-dimensional topological structures, which introduces some additional time over- head. However, the benefits achieved outweigh the costs. To validate this, we conducted experi- ments using two A6000-48G GPUs with Llama2-7b as the LLM, training on Expl ExplaGraphs and ScerrGraphs. Detailed experimental settings are provided in Appendix C. The results in Table show that, compared to baseline methods, our approach incurs only a slight increase in runtime, yet significantly improves model performance.
Table Performance and Efficiency Comparison of To and G-Retriever on ExplaGraphs and SceneGraphs Datasets.
Explace AapaaGrahhs
SceneGraphs
Sctting
Method
Hit
Time
Accuracy
Time
G-Retriever TopoRAG
0.8516
2.6 min/epoch
0.8131
267 min/epoch
Frozen LLM w/ PT
0.8899
3.0 min/cpoch
0.8362
300 min/epoch
G-Retriever w/ LoRA
0.8705
3.0 min/epoch
0.8683
285 min/epoch
Tuned LLM
TopoRAG w/ LoRA
0.9151
3.3 min/epoch
0.8768
310 min/epoch
19

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Published as a conference paper at ICLR 2026
H ALGORITTMM
Cellular Representation Lifting Algorithm. We present Algorithm which formally describes the Cellular Representation Lifting process outlined in Section 4. The algorithm takes a textual graph 9 and lifts into a regular cell complex X endowed with feature representations for all its cellular substructures. The algorithm proceeds in two main phases.
The first phase (Lines 1-15) constructs the 1-skeleton (X(") of the complex. initializes the sets of O-cells (X(()) and 1-cells (x(1) and their corresponding feature dictionaries (Z", Zz). For each vertex E V, O-cell æ is instantiated, and its representation 2 is obtained by encoding the vertex's 's text attribute t, using a pre-trained language model (LM). Similarly, for each edge e E E, 1-cell z is created, attached to the O-cells of its endpoints, and its representation ze is computed from the edge text te.
The second phase (Lines 16 28) augments the 1 1-skeleton with 2-cells to capture topological information. A spanning tree T of G is computed, whose complement Enon-tree defines the set of fundamental cycles in the graph. For each non-tree edge E Pron-tree. the algorithm identifies the corresponding fundamental cycle by finding the unique path between the endpoints of in T and appending itself (as detailed in the subroutine Algorithm 2). A 2-cell x is then created and attached to this cycle. The initial representation =2 for the 2-cell is computed by aggregating (e.g., via mean pooling) the representations of all the O-cells and 1 1-cells that constitute its boundary cycle. This provides an inductive bias that initializes the feature of higher-dimensional cavity based on the features of its lower-dimensional boundaries.
Finally, the complete cell complex X is formed by the union of all cells across dimensions (Line 30). The algorithm returns both the topological structure X and the associated features Z Z _ Z2, which serve the input for subsequent cellular message- paggggg networks (Bodnar et al. 2021b). This lifting procedure effectively transforms a plain graph into a richer topological domain, explicitly encoding relational cycles as tangible geometric entities.
Topology-awart Subcomplex Retrieval Algorithm. A formalizes the Topology-awan Subcomplex Retrieval process outlined in Section 4.2 The algorithm takes as input the cell complex X with precomputed cellular embeddings, textual query Iq.. and parameters i and C2. It returns a connected subcomplex X that maximizes the relevance prize under topological constraints. The procedure operates in three distinct phases.
The first Phase is Query-based Cell Retrieval (Lines 1-7). The algorithm begins by encoding the query Fig into embedding 2g using the language model (LM). It then computes the cosine simi- larity between 2, and the embeddings of all O-cells and 1-cells. The top-k most similar cells from each dimension are selected, forming the initial sets of highly relevant candidates, x and x!".
The second Phase is Multi-dimensional Prize Assignment (Lines 9-26). This phase assigns a prize value to each cell, quantifying its incentive for inclusion in the final subcomplex. Prizes for the top-k O-cells and 1-cells are assigned in descending order based on their similarity ranking (e.g., the highest-ranked cell receives a prize of k). For a 2-cell x² its prize is computed inductively as the sum of the prizes of all its boundary O-cells and 1-cells, minus cost penalty cost(z²) |0 C2 that discourages the selection of overly large faces. This design propagates relevance signals from lower-dimensional cells to the higher-dimensional structures they define. Finally, the top-k 2-cells
by prize, denoted x(2) are selected.
The last phase is Prize- Prize-CCole Steiner Subcomplex Extraction (Lines 28-34). The core challenge to extract connected subcomplex that includes high-prize cells while respecting the boundary consistency constraints (i.e., if a 2-cell is selected, all its boundary cells must also be included). We model this as a Prize-Collecting Steiner Tree (PCST) problem on a hypergraph representation Ghyper of the cell complex, where 2-cells are modeled as hyperedges. The set Riemmnnass consists of the top-k cells from all dimensions, and the prize function P is defined from the previous phase. Solving this generalized PCST problem yields a connected subcomplex X that approximates the optimal trade-off between total collected prize and the cost of the required connecting cells. We employ a near- lanear time approximation algorithm (Hegde et al. 2015) to ensure computational feasibility.
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Published as a conference paper at ICLR 2026
The algorithm's output, X", provides coherent, query-focused topologiaa summary of the original complex, which can be directly utilized for downstream tasks such as reasoning or explanation generation.
Algorithm Cellular Lifting of Textual Graphs
Require: Textual graph 9 = (V, E, (ter fee)e pre-trained language model LM(-).
Ensure: A regular cell complex X with cellular embeddings {2,), f2, {
Step 1: Construct the 1-Skeleton and Compute Initial Embeddings
2: ( <- 0, (1) 0 {Initialize sets of O-cells and I-cells)
3: Z + (). z +- 0 (Initialize dictionaries for embeddings)
4: for V do
5: Create a O-cell z for vertex v
6: x
< x()) U {z
7:
20
(t.)t) 2/
{Encode vertex text attribute)
8:
7 ("100
9: end for
10: for e (u, v) E do
Create a 1-cell z attached zy and z
(
- -x(0) U (x2)
13: I 4LM((()) (Encode edge text attribute]
Z
+
15: end for
x(1) < X x (The I-skeleton is complete)
17:
Step 2: Augment with 2-Cells Capture Higher-Dimensiona. Structures 19: (2) +- 0
20: Z !
21: T < SpanningTreed (e.g.. using BFS DFS)
22: Emon-tree t T
23: for Emon.tree do
24: 1. - endpoints(e)
') 26: {cycle is the unique path from u to in T plus edge e}
25: cycle FindFunddmentalCyylee
Create a 2-cell _²²
28:
Attach x to the 1-skeleton via the attaching map Pe UD - cycle
29:
(²) xx U {x²}
2 AggregadCycleEmieeddnnsss/yy
Z", Z
31:
[e.g., mean/max pooling of embeddings of all 0/1 0/1-cells in the cycle)
32:
Z' 1
+- 2
33:
end for
34:
35:
X x U (2)
(The final cell complex)
36:
37: return X, Z Z zz
Algorithm 2 Find Fundamental Cycle
Require: Non-tree edge (u, v), spanning tree T.
Ensure: An ordered list of O-cells and 1-cells forming the fundamental cycle.
I: path to +- GetUniqudaahhnnTeeeeuu v, T)
2: cycle vertices < path u to vo.vv.vert v.vertices
3: cycle_edges path_u_tt uath___tto____ w_to_tteteeeeeeeeeeeeeeeeee
edges
v.dgge
4: cycle waaeeeddes..pppene e) { [Add the non-tree edge to complete the cycle)
5:
6: return healeveeriicss.ccl..eee...
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Published as a conference paper at ICLR 2026
Algorithm 3 Topology-Aware Subcomplex Retrieval
Require: Cell complex X = XX (xx() with embeddings Z", Z' Z²: query zy parameters
k, C2.
Ensure: A connected, topology-awe aware subcomplex X C X.
1: Step I: Encode Query and Retrieve Top-k Cells
2: 2g + LM(x,,) {Encode the query)
3: 5 - CompureCosinnSiiillrty Zqy 7 {.50 a list of (cell, score) pairs for all O-cells)
4: 5t <- CompuieCCosineSiiilrrttyty.. Z {St a list of (cell, score) pairs for all 1-cells)
5: _ ArgTopK(S", k) {Set of top-k relevant O-cells)
6: X + ArgTopK(S' k) (Set of top-k relevant 1-cells}
7:
8: Step 2: Prize Assignment
9: P < (} (Initialize a prize dictionary for all cells}
10: // Assign prizes to top-k 0/1-cells based on ranking
rank {-
12: for x²" E =x (in descending order of similarity) do
13: 'P[x"]] t k rank
14: rank 4- rank +
15: end for
rank +-0
17: for x E xx (in descending order of similarity) do
18: ]]x='] t rank
19: rank +- rank +1
20: end for
21: // Compute prizes for 2-cells based on boundary cells
22: for x² E X (2) do
23: boundary prize +-
24: for each N:0 0ga?2 do boundary-prizz
boundary-priae -prize + P-get(x0) (x. 0)
25: for each x² E 0₁ do boundary -prize--rzeeee +- boundary-prizz + P (ge (z)
cost + |0 (Penalize larger faces]
27: P[a3] t boundary
cost
end for
29: x + (rPT)p for x xx()),)) (Select top-k 2-cells by prize}
30:
31: Step 3: Prize- Collectnn Subcomplex Selection
32: V + -x(0) (1) U (2) {Candidate cells across all dimensions}
33: R + x ( X (Top-k cells as prize terminals]
34: // Assign prizes to 0- and 1-cells based on query similarity
35: // Compute 2-cell prizes from boundary consistency with selected cells
36:
37: X <- ApproXPCSTComplee X, R,P)
38: (Solve generalized PCST over cell complex with multi-dimensional prizes}
// Enforce boundary consistency: any 2-cell in X* must share boundary with chosen 0- and 1-cells
41: return X*
1 STATEMENT
Ethics Statement. This research follows the ICLR Code of Ethics) The work does not involve experiments with human participants, collection of personal data, or sensitive information. All datasets employed are publicly released and widely used in prior studies. The proposed framework is intended to advance topology-awan retrieval and reasoning in textual graphs for question answering, and do not anticipate direct societal risks or harmful misuse. Potential biases have been carefully considered, and we adopt standard practices to minimize unintended artifacts. No external funding sources conflicts of interest influenced the conduct of this work.
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Published as a conference paper at ICLR 2026
Reproducibility Statement. To support reproducibility, all datasets are publicly available and preprocessing procedures are documented in the main text or supplementary material. We provide complete implementation part of the supplementary package, which enables replication of our experiments without additional dependencies. Hyperparameters, training configurations, and evalu- ation protocols are described in detail to facilitate verification and future extensions.
LLM Usage. We acknowledge the use of large language models (LLMs) as auxiliary tools for improving readability and clarity of writing. The conceptual development, methodology design, experimental setup, and analysis were entirely conducted and validated by the authors. LLMs were used generate novel research ideas nor contribute technical content.
23


Reviews:
[{"review_id": "UtbNPwdiq1", "reviewer": "Reviewer_DqYh", "summary": "This paper proposes TopoRAG, a topology-enhanced retrieval-augmented generation framework for\ntextual graph question answering.\nThe key novelty lies in lifting textual graphs into regular cell complexes—representing nodes, edges, and\nhigher-order cycles as 0-, 1-, and 2-cells—and retrieving relevant subcomplexes conditioned on the query.\nA topology-aware retrieval mechanism selects query-relevant cells by generalizing the Prize-Collecting\nSteiner Tree (PCST) formulation to multi-dimensional complexes, and a multi-dimensional reasoning\nmodule propagates information across these 0/1/2-cells.\nFinally, the subcomplex representation is integrated into a frozen LLM (Llama-2-7B) via prompt tuning or\nLoRA.\nExperiments on ExplaGraphs, SceneGraphs, and WebQSP show strong improvements (≈ +5 % Acc/Hit\nover GraphRAG baselines).", "questions": "N/A", "limitations": "", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "Introducing cell complex topology into RAG for textual graphs is new. Prior GraphRAG methods (e.g., G-\nRetriever, GNN-RAG, SubgraphRAG) restrict reasoning to pairwise edges, while TopoRAG models cyclic\nand higher-order relations. For a formal introduction. the paper carefully defines cell complexes,\nhomology, and the lifting procedure, demonstrating a strong understanding of topological deep learning\nfoundations. Besides, the whole pipline proposed in the paper provides a systematic way to inject\nstructured topology into frozen LLMs. Clear improvements over all categories of baselines (prompt-tuned,\nLoRA, and pure inference) across multiple datasets. The ablations are detailed and show the contribution\nof each module.", "weaknesses": "While using cell complexes for retrieval is novel, the reasoning stage (message passing with faces/cofaces)\nresembles existing simplicial or cell complex GNNs (e.g., CWN, SAN, CellNN). It would be better to\nintegrate clarification about how its update scheme differs algorithmically from those prior works.\nBuilding and storing cell complexes (especially identifying all 2-cells from cycles) may be expensive for\nlarge textual graphs.\nWhile topology sounds interpretable, the paper lacks visualizations or examples showing which cycles or 2-\ncells are retrieved and how they affect reasoning.\nAblations remove modules but not the dimensional component (e.g., keeping only 0- and 1-cells).\nShowing how much 2-cell reasoning alone contributes quantitatively would help isolate the topological\nbenefit.\ntypo:\nLine 123: intersecting\nLine 148: eq. 2", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hmVikj2cs3", "reviewer": "Reviewer_A3xA", "summary": "This paper proposes TopoRAG, a framework for textual graph question answering that explicitly models higher-dimensional topological structures. The framework introduces: (i) cellular representation lifting that transforms graphs into cell complexes capturing 0-cells (nodes), 1-cells (edges), and 2-cells (cycles) for closed-loop reasoning; (ii) topology-aware subcomplex retrieval extending Prize-Collecting Steiner Tree to multi-dimensional complexes; (iii) multi-dimensional topological reasoning with message passing across cellular dimensions; and (iv) integration with LLMs for generation. Experiments on three benchmarks (WebQSP, ExplaGraphs, SceneGraphs) show improvements of up to 5.12% accuracy over GraphRAG baselines.", "questions": "1. Many fundamental cycles may be semantically irrelevant. Has the paper considered the impact of such low-quality cycles on performance? Are there methods to further reduce their influence?\n\n2. Could the authors add experiments on acyclic or purely chain-style reasoning datasets to verify the method’s performance and generalizability in non-cyclic tasks?\n\n3. Different spanning trees lead to different 2-cell sets. Have the authors tested the impact of tree choice on final performance? If there is an impact, how should it be balanced?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is the first to introduce cellular complexes into the GraphRAG framework, explicitly modeling 2-cells to capture closed-loop topological dependencies that are ignored by traditional node-and-edge paradigms.\n\n2. The method design is logically clear, with a coherent pipeline progressing from cellular lifting to topology-aware retrieval, multi-dimensional reasoning, and generation.", "weaknesses": "1. All fundamental cycles—regardless of semantic relevance—are lifted into 2-cells, which may introduce noise or spurious dependencies due to meaningless loops.\n\n2. The experiments use datasets that involve multi-hop reasoning, but their graph structures inherently contain many cyclic dependencies. The paper does not evaluate on purely chain-like or acyclic reasoning tasks, making it unclear whether TopoRAG remains advantageous or introduces redundancy in non-cyclic scenarios.\n\n3. The impact of spanning tree choice is not analyzed: 2-cells depend on the tree construction, yet the paper does not assess how different trees (BFS, DFS, random) affect results, raising concerns about robustness.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "hiiJul5thG", "reviewer": "Reviewer_JK3r", "summary": "This paper proposes Topology-enhanced Retrieval-Augmented Generation (TopoRAG), a novel framework for textual graph question answering. TopoRAG retrieves not just at the node, edge, or triple level, but also incorporates higher-dimensional topological structures. The authors evaluate TopoRAG on three textual graph QA datasets with three different settings and conduct ablation studies on the number of layers in the reasoning module, the K value of the retrieval module, and other factors.", "questions": "- In equation 15, will the $x^d (d \\in \\{1,2,3\\})$ have an overlap? For example, if an edge was selected and the circle that contains this edge is also selected, how can such overlapping be addressed?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "- The proposed retrieval method enables retrieval at different granular levels, which can capture higher-dimensional topological and relational dependencies.", "weaknesses": "- **Comparing Methods are Not SOTA Models.** The authors compare with models like G-Retriever, SubgraphRAG, and GraphToken, but these are not state-of-the-art (SOTA). Some related work with better performance, such as DoG [1] and GCR [2], is not cited or compared. These models achieved better results on WebQSP than the proposed TopoRAG.\n\n- **Selected Datasets and Their Suitability.** The selected datasets (ExplaGraphs and SceneGraph) may not adequately demonstrate TopoRAG's ability to capture high-dimensional topological and relational dependencies. Since these datasets usually require less than 2-hop reasoning, they might not be the most suitable for demonstrating the need for \"higher-dimensional topological structures\" to answer questions. The authors should consider datasets that require multi-hop (>3-hop) reasoning.\n- **Sufficiency of 2-Cell.** The paper does not explain why (or if) a 2-cell is sufficient to capture higher-dimensional topological structures. Furthermore, there is no analysis of how the top-k 0/1/2 cells contribute to the results.\n\n\n[1] Kun Li, Tianhua Zhang, Xixin Wu, Hongyin Luo, James R. Glass, and Helen M. Meng. 2025. Decoding on Graphs: Faithful and Sound Reasoning on Knowledge Graphs through Generation of Well-Formed Chains.\n\n[2] Linhao Luo, Zicheng Zhao, Chen Gong, Gholamreza Haffari, and Shirui Pan. Graph-constrained\nreasoning: Faithful reasoning on knowledge graphs with large language models. ICML 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LbjupnKuwS", "reviewer": "Reviewer_gvvE", "summary": "The paper introduces a topology-aware retrieval-augmented generation framework that represents textual graphs as cell complexes to capture higher-order relations such as cycles and loops beyond standard nodes and edges. It retrieves relevant multi-dimensional subcomplexes and performs topological reasoning across dimensions to guide an LLM in generating answers.", "questions": "- Can the topological retrieval appriach be adapted to handle multimodal graphs?\n- Could the proposed topological framework be used for reasoning tasks that do not explicitly involve graph structures  (eg. scientific question answering or commonsense reasoning)?\n- What is the intuition behind describing the graph as a cellular representation? \n- Instead of adding high dimensional knowledge, can't we instead find the relevant 0- and 1- dim and let any reasoning model to reason over this? My intuition is that doing this will have many benefits - limited training, more robust to graph changes etc. Although this won't result in better answers when using a smaller model.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- A novel approach to include more relevant higher dimensional information in the RAG pipeline\n- Mathematically strong paper. \n- The approach does improve upon the existing baselines.\n- The approach provides interpretable reasoning traces", "weaknesses": "- The computational and memory cost of building and reasoning over high-dimensional cell complexes is not quantified or compared with simpler baselines.\n- The approach still has its limitations - including more higher dimensional knowledge in case of incomplete/noisy graphs could lead to worse results. Moreover the approach will be very difficult to adapt in cases of dynamic graphs where new nodes/edges are added from time to time.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)