Learning Global Hypothesis Space for Enhancing Synergistic Reasoning Chain
Authors: Jiaquan Zhang
Chaoning Zhang
Shuxu Chen
Xudong Wang
Zhenzhen Huang
Pengcheng Zheng
Shuai Yuan
Sheng Zheng
Qigan Sun
Jie Zou
LIK-HANG LEE
Yang Yang
Venue: ICLR 2026 Poster (2026)
Keywords: Large Language Models，Complex Reasoning
Primary area: foundation or frontier models, including LLMs

Abstract: Chain-of-Thought (CoT) has been shown to significantly improve the reasoning accuracy of large language models (LLMs) on complex tasks. However, due to the autoregressive, step-by-step generation paradigm, existing CoT methods suffer from two fundamental limitations. First, the reasoning process is highly susceptible to early-stage errors, which tend to propagate and amplify without a global coordination and correction mechanism, thereby distorting the overall reasoning chain. Second, current CoT methods lack structured analytical frameworks for pruning redundant reasoning and identifying critical reasoning features, resulting in instability and reduced interpretability. To address these issues, we propose Global Hypothesis Structure via Topological Data Analysis (GHS-TDA), which constructs a semantically enriched global hypothesis graph that integrates and coordinates multiple candidate reasoning paths, thereby supporting global consistency refinement and error mitigation. GHS-TDA applies persistent homology-based topological data analysis to capture stable multi-scale structures, remove redundancy and inconsistencies, and extract a more reliable reasoning skeleton. By jointly leveraging reasoning diversity and topological stability, GHS-TDA achieves self-adaptive convergence, produces high-confidence and interpretable reasoning paths, and consistently outperforms strong baselines in terms of both accuracy and robustness across multiple reasoning benchmarks.

Published as a conference paper at ICLR 2026
LEARNING GLOBAL HYPOTHESIS SPACE FOR EN- HANCING SYNERGISTIC REASONING CHAIN
Jiaquan Zhang', Chaoning Zhang' Shuxu Chen', Xudong Wang', Zhenzhen Huang', Pengcheng Zheng' Shuai Yuan', Sheng Zheng", Qigan Sun', Jie Zou', Lik-Hang Lee ', Yang Yang!
I 'nniversity of Electronic Science and Technology of China
"Kyung Hee University The Hong Kong Polytechnic University
ABSTRACT
Chain-of-Thought (CoT) has been shown significantly improve the reasoning accuracy of large language models (LLMs) on complex tasks. However, due to the autoregressive, step-by-step generation paradigm, existing CoT methods suffer from two fundamental limitations. First, the reasoning process is highly suscep- tible to early-stage errors, which tend to propagate and amplify without a global coordination and correction mechanism, thereby distorting the overall reasoning chain. Second, current CoT methods lack structured analytical frameworks for pruning redundant reasoning and identifying critical reasoning features, resulting instability and reduced interpretability. To address these issues, we propose Global Hypothesis Structure via Topological Data Analysis (GHS-TDA), which constructs semantically enriched global hypothesis graph that integrates and co- ordinates multiple candidate reasoning paths, thereby supporting global consis- tency refinement and error mitigation. GHS-TDA applies persistent homology- based topological data analysis capture stable multi-scale structures, remove redundancy and inconsistencies, and extract more reliable reasoning skeleton. By jointly leveraging reasoning diversity and topological stability, GHS-TDA achieves self-adaptive convergence, produces high-confidence and interpretable reasoning paths. and consistently outperforms strong baselines in terms of both accuracy and robustness across multiple reasoning benchmarks.
INTRODUCTION
LLMs have demonstrated remarkable potential in tasks such logical reasoning, mathematical proof, and multi-hop question answering. A representative technique to elicit such capabilities is CoT prompting (Wei et al. 2022). which improves interpretability and accuracy by decomposing complex problems into coherent intermediate steps.
Despite these advances, CoT and its extensions fundamentally rely on an autoregressive, step-by- step generation paradigm, where each reasoning step conditions on previously generated outputs Cao et al. (2026). Such sequential dependency increases the susceptibility of the reasoning pro- cess to early- sttagg errors, which may propagate and compound throughout the reasoning trajectory Wang et al. (2025). Moreover, the incremental generation mechanism lacks structured analytical control to regulate redundancy and identify salient reasoning features Chu et al. (2024), resulting in unstable reasoning trajectories and limited interpretability. To alleviate these limitations, a series of structured extensions have been proposed. Approaches such as Tree-of-Thouus
(ToT) (Yao al. 2023a), Sraph-of-Thougee (GoT) (Besta et al. 2024), and Atom-of- Thought (AoT) (Teng et al, 2025) expand the reasoning space beyond single-par pathhe CoT and increase reasoning diversity. How- ever, while these methods expand the reasoning space, their ability to mitigate autoregressive de-
Corresponding author. Contact: 2szbxx221e@mail.cooo
Additional contacts: jiaquanchhagg2255@mmall. com, chaoningzhangg199066 com, ccccsx322egmal com, w12002038khu. ac alley10086@gmal. com, 7pc777@std uestc.edu.cn, sunq ganggigan0266egaa111 com,
jie. zou Questc. edu. bang.yangguestc.cem 1ik iihhang.

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Published as a conference paper at ICLR 2026
pendency remains limited. Interactions across hypotheses are not explicitly coordinated, which may allow errors to accumulate across branches. Other frameworks attempt to enhance efficiency and robustness. ReAct (Yao et al., 2023b) integrates reasoning with acting, AFlow (Zhang et al. 2024) applies Monte Carlo tree search to reasoning workflows, and ReCEval (Prasad et al. 2023) evalu- ates reasoning chains for correctness and informativeness. While these methods improve task-level performance, they primarily emphasize outcome optimization rather than structural regulation, and thus lack unified analytical framework for systematically characterizing reasoning chains. As ex- plicit representations of the reasoning process Xia et al. (2025), reasoning chains inherently encode the semantic and logical organization of problem solving. However, without a principled structural perspective to characterize the topology and dependency patterns within reasoning chains, global coordination and consistency regulation remain underdeveloped. As a result, error propagation and redundant reasoning cannot be systematically controlled, limiting the reliability and interpretability of reasoning outcomes.
To address these challenges, this work introduces a new perspective: the reliability of reasoning depends not only on the correctness locally generated results but also on the structural robustness exhibited by candidate paths within the global solution space. Unlike local heuristics, adopt a topological perspective to model the reasoning space. Fundamentally, the reasoning space con- stitutes high-dimensional complex structure formed by multiple interdependent candidate paths, which cannot be fully characterized by local indicators such as confidence scores or shortest-pan patt length alone. TDA capable of capturing stable connectivity and cyclic patterns across multiple scales, thereby providing a noise-insensitive and globally coherent structural measure. This per- spective enables us formalize concepts such as "logical backbones" and "self-consistent loops" as topological invariants, offering a principled basis for selecting and composing reasoning paths.
We propose GHS-TDA (Global Hypothesis Space with Topological Data Analysis), a two-stage framework that first constructs a global hypothesis graph through multi-role interactions to integrate diverse reasoning paths, and then applies topological analysis via persistent homology to extract sta- ble backhones and self-consistent loops for interpretable reasoning chains. In the construction stage, we introduce a multi-role agenda mechanism consisting of explorers, verifiers, and bridges to dy- namically generate and optimize Global Hypothesis Graph (GHS). This process enables systematic integration and interaction of diverse reasoning information. Through unification, conflict detection, and closure inference, GHS enhances semantic connections among nodes and overcomes the isola- tion of traditional path-based generation. In the analysis stage, we leverage TDA (Munch] [017]] Chazal & Michel, 2021), specifically persistent homology, extract robust reasoning skeletons and self-consistent cycles from the GHS. Analyzing the persistence of connected components (Ho) and loops (H₃) allows to systematically capture backbone reasoning paths and self- seff-verifiattion struc- tures, ultimately yiclding reasoning chains with high confidence and interpretability.
Our key contributions are follows:
We introduce TDA into the reasoning chain, leveraging its scale invariance and structural robustness to provide a new perspective for analyzing and improving complex reasoning.
We propose the GHS-TDA framework, a two-stage automated paradigm: the construction stage builds Global Hypothesis Graph (GHS) via multi-role agenda mechanisms, and the analysis stage employs persistent homology with Betti stability checks to extract robust Ho backbones and H, loops.
We validate GHS-TDA on benchmarks including GSM8K, MATH, OlympiadBench, Hot- potQA, MuSiQue, BBH, and LongBench, where it consistently outperforms existing meth- ods in accuracy, consistency, and interpretability.
2 RELATED WORK
2.1 LLM REASONING OPTIMIZATION
AI and LLMs Zheng et al. 2025 Brown et al. 2020): Zheng et al. (002bb) demonstrate remark- able potential in complex reasoning tasks such mathematical problem solving, logical deduction, and multi-hop question answering. However, their performance still heavily depends on carefully designed prompting strategies and reasoning structures (Achiam et al.
2023 Vaswani et al. 2017
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Zheng al. 2026a). A seminal advance in this direction is Chain-of- -froiuughh-Thhhtttt (CoT) prompting [Wei] et al. 2022). which shows that decomposing complex problems into explicit intermediate steps sig- nificantly improves both the accuracy and interpretability of reasoning. This finding establishes prompting as a critical factor in eliciting reasoning capabilities from I.LMs.
Building CoT, researchers propose range of structured extensions further enrich the rea- soning process. Thee-of-Thouuht (ToT) (Yao et al. (2023a). Braph-of-Thoughh (GoT) (Besta et al.] 2024), and Atom-of-Thought (AoT) (Teng al. (2025) introduce tree, graph, and atomic reasoning structures, respectively. These paradigms allow the model to explore multiple reasoning branches in parallel, reuse evidence across paths, and dynamically adjust reasoning trajectories, thereby alleviat- ing the limitations of single-path CoT reasoning. Beyond structural extensions, frameworks such as ReAct (Yao et al. 2023b) and AFlow (Zhang et al., 2024) further integrate reasoning with external actions or search mechanisms. By combining reasoning with environment interaction or systematic search, these methods achieve stronger robustness and higher efficiency in complex tasks such as multi-hop QA and interactive problem solving.
Despite these advances, existing approaches still rely primarily on local heuristics for path selection and conflict resolution. They lack mechanisms for globally integrating diverse hypotheses or sys- tematically analyzing the structural properties of reasoning chains, such as connectivity, consistency, and redundancy (Wang et al. 2022). This limitation often leads to fragmented reasoning, redundant exploration, or unstable convergence, especially in tasks that require reconciling multiple sources of evidence. Addressing these challenges motivates the development of new frameworks that combine global integration mechanisms with principled analytical tools for structural reasoning evaluation.
2.2 APPLICATIONS OF TOPOLOGICAT. DATA ANALYSIS
TDA provides powerful and principled framework for the structured analysis of high-dimennional data. Its core technique, persistent homology, captures the evolution of connected components and loops across multiple scales, thereby extracting structural features that remain stable under noise and local perturbations Munch] (2017); Chazal & Michel (2021). Over the past decade, TDA has achieved successful applications in diverse fields, including bioinformatics Nicolau et al. (201T). material science Hiraoka et al.) (2016), and neural network analysis Rieck et al. (2018) 8); Naitzat jet al. (2020). Beyond these domains, TDA also demonstrates broad potential feature extraction, representation learning, and robustness evaluation within machine learning pipelines Hofer et al.
(2177) : Carrière et al. (2020).
However, its potential for reasoning research remains largely unexplored (Munch 2017 Chazal & Michel 202T). Reasoning chains produced by LLMs naturally exhibit graph-structured or sequen- tial semantic and logical organization. Analyzing their topological properties through TDA offers the opportunity to identify stable connected components and self-consistent loops that persist across scales. These structures can then be mapped to backbone reasoning paths and consistency mecha- nisms, providing principled way to filter redundant hypotheses, highlight critical connections, and improve both the stability and interpretability of reasoning processes. This perspective opens up new line of inquiry into how topological robustness can complement semantic reasoning in LLMs.
3 METHOD
We propose GHS-TDA, a two-stage atonstruct-analyze"" reasoning framework (Figure I In the construction stage, multiple reasoning paths sampled from LLM are semantically aligned and merged into a unified Global Hypothesis Graph (GHS), which systematically integrates diverse in- formation and manages conflicts. In the analysis stage, topological data analysis (TDA) is applied to extract stable backbones and self-consistent loops from the GHS, yielding high-confidence and interpretable reasoning paths. The construction ensures coherent integration, while the analysis ex- ploits topological stability as a structural constraint and convergence criterion.
3.1 GLOBAL HYPOTIESIS SPACE MODELING
Problem setup. Given problem Q. we first sample N candidate reasoning paths
P (PI.... ........ Px], P. = (+ (6) (6)
(6)
3

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Global Hypothesia Space Medeling
alignuni morzing
Resweing Text
O-0-O-
>Siga2
OHOHO
P-..
SSupph
Q-C
Seppat
Impul
6-0
Exiiioker Nodas
Sanpling Keaceting paths
Ressoning
Skeleton Extraction
Analysis sopological reasoning spact
Avenge oige
Maali dinensseed feruse vector
Viarneelip Cample
l'lmation
Pereewer llomologe
plwepd kep Hrique
Statetoe Extration
Puins-Cloud Representation of Reasoning
Distunee Mitilo Griph Corsiraction
Periston Hanolog & Foatree Selection
Jawer Approgation
The method consists of two stages: (1) Global Hypothesis Space Modeling, where mul- tiple reasoning paths sampled from an LLM are semantically aligned and merged into unified Global Hypothesis Graph encoding adjacency, support, and refutation relations; and (2) Skeleton Extraction, where the graph is embedded into feature space, analyzed via Vietoris-Rip filtration and persistent homology, and reduced to stable backbones and self-consistent loops. The resulting skeleton provides both accurate answers and interpretable reasoning structures.
Figure 1:
where each P. denotes stepwise sequence of intermediate hypotheses with variable length mi These paths may differ substantially in surface form, semantic fidelity, and logical coverage. Our goal is to integrate them into single global structure that preserves diversity while eliminating redundancy.
Graph definition. We define the Global Hypothesis Graph (GHG) as
G = EV,
(2)
Each node V is represented
(text, canor, r),
(3)
where: (i) text stores the natural-language expression of the step: (ii) canor: is its canonical-
ized form (e.g., symbolic or normalized logical representation) used for equivalence testing: (iii) E [0, 1] is the confidence score estimated from the LLM aggregated statistics; (iv) [0, 1] a normalized progress indicator reflecting how far the step is from the final answer. Edges dependencies, typically arising from path adjacency, explicit usage (e.g., 8; uses 8y). or inferred support/refutation. We elaborate the definition of "sup- port" and "refutation" in the Appendix[A.. [A.2]
(v;, U2y) E represent semantic-
This construction yields a directed multigraph which all hypotheses generated by the model are placed into shared reasoning space.
Node alignment and merging. A central step is to align semantically equivalent hypotheses across different paths. For two nodes 8, and sú, compute the similarity of their canonicalized forms. If
(4) the two nodes merged into single representative vertex, inheriting all incident edges. This merging criterion ensures that semantically equivalent reasoning steps, possibly expressed in differ- ent surface forms (e.g., "2 + 2 4" "the sum is four"), are unified.
Sim canon (sb) 0 m
After merging, the confidence e the resulting node is computed as the average of its sources, while the progress assigned the maximum progress value among them to preserve downstream
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completeness. We also maintain record of provenance (i.e., which original paths contributed) to enable later attribution and evidence tracking.
Resulting properties. The resulting graph G compactly encodes the union of all sampled reasoning paths without duplication, while retaining their semantic and logical structure. preserves alterna- tive hypotheses in unified space, allowing systematic comparison of competing reasoning attempts and their interdependencies. At the same time, it provides a coherent foundation for subsequent topological analysis, where connected clusters naturally correspond stable reasoning backbones and cycles capture self-consistent or cross-validating structures within the reasoning process.
3.2 SKELETON EXTRACTION
Point-cloud representation. Each node e is embedded into a joint feature vector:
z, = e || @graph (u) || Ue
(5)
where: (i) e, is an L2-normalized semantic embedding; (ii) (g) encodes graph structure (progress To- BFS-based positional encoding, centrality). standardized per instance: (iii) u, log confidence, + 10-6) denotes uncertainty. All features are normalized to ensure balanced contributions.
Distance metric and filtration. We define mixed distance:
d(e,, Uÿ) = a(1 - (e), + 3 || - grapph (i)ll + v (ut + uy).
(6)
A k-nearest-neighbor graph (A: zs 15) is constructed and pruned by a global threshold (95th per- centile of distances). A Vietoris Pitoris-RRiss filtration is then built on this sparsified graph, which preserves salient topological features (Ho, H1) while reducing complexity.
Persistent homology and feature selection. We compute persistent homology up H1, obtaining barcodes for connected components (Ho) and loops (H2). Significant features are selected by lifes- pan I = death-birth (Top-q%). with Hu capturing major clusters and H1 reflecting self-consistent loops.
Operating scales and skeleton construction. To map features back into the graph, we precisely define operating thresholds:
Ho = median (dcath(b) b Bp), e, = 0.99 death(b), vb E B
This yields a thresholded subgraph ((s) for cluster and loop analysis:
Clusters and anchors. On G H,)), ). retain components C with |C| 3 that cover least two reasoning paths. Anchors are chosen as
SC = arg min Tay vEC
9C = arg max Tey
(8)
vEC'
corresponding to start and goal nodes.
Loop assignment. Each loop b E B, is localized at E, and assigned to the cluster with maximal overlap:
c(b) = arg max IV nc..
Skeleton buckbone. For each C, we compute the shortest path Pe from se ge the backbone. If a principal loop by is assigned, we reroute via pivot near median progress:
+ (tour of bc) + JC,
(10)
explicitly embedding a verification loop to enhance ceff-onsistennyy. Loops are instantiated by minimum-weight cycle basis (Horton's algorithm) by stitching heuristics if fragmented.
When multiple clusters are available, we prioritize: (i) clusters with principal loops; (ii) larger loop lifespan; (iii) larger cluster size; (iv) smaller backbone cost.
Answer aggregation. We use ceafiddecce/prrsssteeeewweee aggregating along the skeleton. If loops present, additional numeric substitution entailment
voting to get candidate answers
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checks applied. The final output includes the high-confidence answer, skeleton structure, and key statistics (e.g., contributing paths, average edge weight, loop lifespan).
Implementation details. Embeddings: text-embedding. 3-1azge; persistent homology: GUDHI (VR up to H1); random seeds: 5; temperature: 0.7; to 0.95; maximum LLM calls: 16 per example. Settings are fixed across baselines unless specified.
4 EXPERIMENT
4.1 EXPERIMENTAL SETUP
Models. We select three representative LLMs as backbones for reasoning: GPT-4o-mini, Qwen- Turbo, and DeepSeck-V3. V3. These models differ in architecture and optimization strategies, which reduces bias from model-specific behaviors. All experiments run under unified decoding and budget constraints to ensure comparability.
Baseline models. We compare GHS-TDA with nine representative baselines that cover chain-based, tree-based, graph-based, forest-based, and atomic reasoning paradigms: CoT (Wei et al. 2022)
and its self-consiseency variant CoT-SC (Wang et al.] 2022). Self-Refine (Madaan et al. 2023
Analogical Prompting (Yasunaga et al. 2023), the search-based framework AFlow (Zhang et al.
2024), and the structured approaches ToT Yao et al. 2023a). GoT (Besta et al. 2024). FoT (Bi et al.
2024 and AoT (Teng al. 2025). Together, these baselines provide comprehensive benchmark for systematic comparison.
Datasets. We adopt eight widely used benchmarks covering arithmetic, mathematics, multi-hop, and long-context reasoning: GSM8K [oobe et al. (2021). (Henrrycs et al.) al.] (2021a), Olympiad-
Bench Zheng al. (2024), BBH Srivastava et al. (2022), MMLU-CF Hendryycss al. (2021b).
LongBench Bai et al. (2023). HotpotQA Yang et al. 2018) and MuSiQue Trivedi et al. (2022)
Evaluations. We report Exact Match (EM, %) and four auxiliary metrics. For interpretability. three trained annotators rate clarity, logical coherence, credibility, and conciseness on a 1-5 Likert scale following written rubric (IAA reported via Krippendorff's a). Node confidence is the model- reported step probability calibrated on held-out set; Confidence Stability is the standard deviation across steps on path (lower is better). Computation Cost is the average number of LLM calls per problem. Statistical significance is assessed via paired t-tests against AoT with 0.05 (per- dataset details Appendix).
4.2
MAIN RESULTS
We evaluate GHS- TDA on eight reasoning and question-answertt benchmarks, namely MATH, OlympiadBench, GSM8K, BBH, MMLU-CF, LongBench, HotpotQA, and MuSiQue. The com- parison involves nine representative baselines: CoT, CoT-SC, Self-Refine, Analogical Prompting, AFlow, ToT, Go', FoT, and AOT. Experiments are conducted across three backbone models: GPT- 4o-mini, Qwen-Turbo and DeepSeek-V3 The evaluation metric exact match (EM) accuracy.
As shown in Table I GHS-TDA consistently delivers the best or near-best results across datasets and backbones. On GPT-4o-mini, it achieves 83.9% on MATH, surpassing AoT by 0.3 percent- age points and CoT by 5.6 points. On Hotpot QA, it reaches 81 81.4%, improving over AFlow by nearly eight points. On MuSiQue, obtains 39.8%, outperforming ToT by 0.7 points and AoT by 1.4 points. On Qwen-Turbo, GHS- -DA achieves 87. 87.9% on BBH, exceeding GoT by 3.0 points and AOT by 2.5 points, and reaches 80.3% on Hotpot a gain of over seven points compared to AFlow. On DeepSeek-V3, it records 14.7% on 01 aBBench, surpassing GoT by one point, and achieves 81.7% on HotpotQA, slightly higher than AoT at 80.6%. In terms of over- all performance, GHS-TDA attains average EM scores of 68.0% on GPT-40 4onimii, 67.6% on Owen-Turbo, and 68.3% on DeepSeex-V3. These values consistently surpass the strongest baselines, with AoT reaching 66.9%, 66.8%, and 67.3% under the same settings. This demonstrates that the proposed global hypothesis framework outperforms representative multi multi-path reason- ing methods in overall accuracy.

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Table 1: Performance comparison across datasets (EM %6.
Method
OlympiudBench
gsm8k
LongBench
HolpotQA
MuSiQue
Avg
GPT--o-mini
COT
78.3
9.3
90.9
78.3
69.5
57.6
67.2
34.1
60.7
CoT-SC (x=5)
58.6
33.8
Self-Refine
78.7
9,4
91.7
80.0
69.7
58.2
68.3
35.1
61.4
Analogical Prompting
65.4
87.2
$2.9
32.8
AFlow
83.0
12.4
93.5
76.0
69.5
61.0
73.5
38.1
63.4
ToT
79.2
11.4
94,9
84.1
62.8
76.8
39.1
64.8
GoT
13.1
94.5
85.9
70.2
63.1
74.2
36.5
65.1
FoT (m==8)
82.5
12.5
94.0
82.4
70.6
59.1
66.7
35.8
63.0
95.0
70.9
68.5
38.4
GHS-TDA (Ours)
83,9
14.5
95,2
88,4
71.6
69.5
81.4
39.8
68.0
Qwen- Turbo
90.7
CoT-SC
81.4
9.9
91.5
K3.2
70.8
58.4
65.99
33.5
61.8
Self-Refine
35.0
Analogical Prompting
65.2
6.2
87.0
72.2
65.2
52.7
64.5
32.6
$5.7
AFlow
60.4
37.8
ToT
78.9
11.3
94.2
83.7
69.6
62.4
7644
38.4
64.4
GoT
82.7
13.0
93.8
84.9
70.1
62.8
74.0
36.4
64.7
FoT (n==)
82.2
12.3
93.9
M2.3
70.4
59.0
66.4
35.8
62.8
AoT
83.5
12.6
94.7
85.4
70.5
68.1
80.0
39.2
66.8
GHS-TDA (Ours)
83.7
14.4
94.8
87.9
71.2
68.6
80.3
39.6
DeepSeek-V3
CoT
78.5
9.5
91.3
78.5
69.9
57.7
67.4 4
34.2
60.9
CC (x=5)
92.1
Self Relf-Refine
78.9
9.5
91.9
80.4
70.1
58.4
69.1
35.1
61.7
Analogical Prompting
AFlow
83.4
12.5
93.6
76.4
69.8
61.4
74.0
38.2
63.7
ToT
79.1
70.4
63.2
39.4
GoT
83.2
13.7
94.5
86.2
70.3
63.4
74.2
36.7
65.3
FoT (n=88
82.7
12.6
94.2
82.6
70.5
59.3
66.8
36.2
63.1
AcT
84.0
13.1
95.1
86.1
70.8
68.7
80.6
39.6
67.3
GHIS-TA (Ours)
84.5
14.7
95.2
88.7
71.6
69.9
81.7
40.1
68.3
Table 2: Comparison of different path selection strategies within the Global Hypothesis Graph (GHS), combining quantitative evaluation and human- interpretability assessment.
Type
Accuracy
Avg. Length
Avg.
Clarity
Credibility
Conclseness
Shortest Path (GHS)
75.2
5.8
0.81
0.12
3.6
2.9
Max- Confidence Path (GHS)
$2.1
11.5
0.93
0.21
4.2
Human Hunsa--Sleeted Path (GHS)
83.6
9.2
0.88
0.07
4.6
TDA Skeleton (Ours)
83,9
8.7
0.90
0.07
4.5
4.3 PATII SELECTION ANALYSIS
We examine whether topology-an aware path selection outperforms local confidence-basee selection. As shown Table 2 we compare four strategies on the MATH dataset: shortest path, max- confidence path, human-selected path, and the TDA Skeleton from our GHS-TDA framework. Evaluation considered both quantitative indicators accuracy, path length, confidence, and stabil- ity ity-and and human judgments of clarity, coherence, credibility, and conciseness.
aware
accurat
The shortest path was most concise with an average of 5.8 steps, but accuracy dropped 75.2 percent and confidence was unstable with variance of 0.12. The max-confidence path reached the highest confidence of 0.93, yet required 11.5 steps and showed high variance of 0.21. The human- selected path balanced these trade-offs, achieving 83.6 percent accuracy with 9.2 steps and stable variance 0.07. The TDA Skeleton slightly outperformed it, with 83.9 percent accuracy, 8.7 steps, and the same low variance, yielding compact and reliable chains.
Human evaluation aligned with these findings. The shortest path was concise but incoherent, the max-confidence path moderately rated but verbose, while the human sulentselected path achieved the best overall scores. The TDA Skeleton closely matched human ratings, with clarity at 4.4, coherence 4.5, credibility 4.7, and conciseness 4.3.

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Birned Correct Rate vs. Hi Persidence (NI) Logadic Ftt
00-
04
Paraittece
Binned correct rate with logistic fit.
(h) Raw samples with binned means and logistic
Figure 2: Global relation between H₃ persistence and reasoning correctness.
These results show that topological analysis enables automatic extraction of reasoning chains that are nearly as accurate and interpretable as those chosen by humans, while avoiding both under- and over-extension.
As shown in Table we further evalu- ate the robustness of different path selec- tion strategies under adversarial perturba- tions. Specifically, reasoning steps were paraphrased with semantically equivalent but lexically altered expressions to intro- duce local noise. Results show that the path selected by GHS-TDA achieves an accuracy drop of only 2.4 points with answer change rate of 2.9%, significantly lower than the 7.4% observed for the Max-Confidence baseline. This indicates that paths identified by topological stability exhibit stronger internal logical connectivity and less sensitive to superficial wording variations, whereas confidence-basee paths are more vulnerable to semantic perturbations. These findings highlight the robustness advantage of structural evaluation beyond local heuristics.
Table 3: Robustness under adversarial perturbations.
Strategy
Before (%)
After (%)
Change (%)
Max-Contie Confidence GHS-TDA (Ours)
82.1
77.1
7.4
81.5
4.4 ROBUSTNESS AND INTERPRETABILITY OF REASONING PROCESSES
We examine whether the proposed framework produces reasoning processes that interpretable. We systematically evaluate the association between topological persistence and rea- soning correctness across diverse tasks and difficulty levels. As shown in Fig. ??, we analyze pooled samples from multiple datasets under a unified framework. The left panel aggregates instances into bins with logistic regression fit, revealing clear monotonic trend: higher persistence consistently predicts higher accuracy. The right panel confirms this result using raw samples with binned means, showing that the trend is robust and not an artifact of binning. This global analysis indicates that topological persistence serves as principled, task-agnostic signal of reasoning reliability.
robust and
shown in Fig. 3 we further validate the predictive value of topological persistence through both distributional and classification analyses. The boxplot analysis (Fig. 3a) demonstrates that correct reasoning chains consistently exhibit higher Hi persistence values than incorrect ones, indicating that persistent topological structures capture stronger logical robustness. The ROC analysis (Fig. 3b) quantifies this effect, with persistence alone reaching an AUC of 0.74. These results confirm that Hi persistence not only provides discriminative power but also enhances robustness and interpretability
of reasoning processes. More detailed, per-dataset visualizations are presented in Appendix A.3 further illustrating the consistency of these findings across diverse benchmarks.
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by
Perastonce
Janno
00
6.40
2.2
(a) Distribution of H₁ persistence by outcome.
(b) ROC curve using H₁ persistence.
Figure 3: Validation of the predictive role of topological persistence. Left: correct reasoning chains have consistently higher H₃ persistence values than incorrect ones. Right: ROC analysis shows persistence alone achieves an AUC of 0.74.
Table 4: Predictive power H, persistence for reasoning correctness. Higher persistence consis- tently correlates with better performance.
Analysis Item
Value
Interpretation
Global Spearman P
0,349 (p =e 0)
Moderate positive correlation
Logistic regression (std. H,)
1.247 (OR = 3.48)
Strong effect: +1 SD = ~3.5x odds
ROC-AUC (H₃ only)
0.74
Good discriminative ability
Per-dataset ROC-AUC
GSM8K
0.748
Robust
MATH
0.704
Robust
OlympiadBench
0.703
Robust
BBH
0.729
Robust
MMLU-CF
0.733
Robust
LongBench
0.737
Robust
HotpotQA
0.778
Strongest
MuSiQue
0.709
Robust
4.5 CORRELATION BETWEEN TOPOLOGY AND REASONING ACCURACY
We investigate whether topological persistence quantitatively associated with reasoning correct- ness. As shown in Table 4 Hj persistence emerges as strong predictor. A global Spearman correlation 0.349 confirms a significant positive relationship: more persistent topological features correspond to higher accuracy. Logistic regression further shows that one-standare deviation in- crease in persistence raises the odds of correctness by roughly 3.5 times, indicating a substantial effect size. Using persistence alone, ROC analysis yields an AUC of 0.74, demonstrating solid discriminative power.
This effect is consistent across all eight benchmarks. Per-dataset AUC values remain within the 0.70-0.78 range, with HotpotQA reaching 0.778. Such stability across arithmetic, symbolic, and multi-hop reasoning indicates that topological persistence provides task-agnostic and statistically significant signal of reliability, offering principled way to estimate correctness beyond ground-truth supervision.
4.6 ABALATION STUDY
As shown in Table 5 we conduct ablation study the distance weights under the constraint
a + 3 + = The full model with weights (0.6, 0.3, 0.1) achieves an average accuracy of 83.9%. Removing the structural term (B 0) reduces the accuracy to 81 81.2%, while removing the

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Published as a conference paper at ICLR 2026
semantic term (a 0) causes the largest drop, down to 77.4%, indicating its dominant contribution. Removing the uncertainty term (y = 0) results in an accuracy of 83.5%. suggesting a smaller but consistent gain in robustness. Overall, semantic similarity is the most critical factor, structural features provide complementary benefits, and the uncertainty term, although lightweight, improves stability.
Table 5: Ablation study of distance weights under the constraint +
Method
Ct
7
Accuracy (Avg.)
GHS-TDA (Ours)
0.6
0.3
0.1
83.9%
Without 9
0.9
0,0
0.1
81.2%
Without
0.0
0.9
0.1
77.4%
Without y
0.7
0.3
0.0
83.5%
4.7 EFFICIENCY PERFORMANCE EXPERIMENT
As shown in Table our method maintains a stable and fixed upper bound of M.. calls across all tasks, substantially reducing inference cost compared with existing mulli--atth reasoning approaches. Under the same settings, GHS-TDD reduces the number of calls by approximately 25%-30% rel- ative to ToT and 40% relative AoT, indicating that our discriminative relation inference effectively replaces the large amount of recursive generative evaluation used in prior work.
Since the actual computational cost of LLMs is more closely tied token usage than call count alone, we further report total token consumption in Table 7 The results show that GHS-TDA uses about 26.8% fewer tokens than ToT and 35.7% fewer tokens than AoT on average, confirming the efficiency advantage of our approach in reducing redundant generation and improving overall reasoning efficiency.
Table Comparison of LLM Call Computational Costs
Method
MATH
Olymp.
GSM8K
BBH
MMLU-CF
LongB.
HotpotQA
MuSiQue
CoT
1
CoT-SC
16)
16
16
16
16
ToT
25.8
27.2
13.5
24.1
19.3
14.2
20.7
26.4
GoT
21.6
23.5
14.8
22.9
18.4
13.9
17.8
20.3
AoT
29.7
32.4
17.2
28.6
24.9
16.8
23.5
29.1
GHS-TDA (Ours)
19
19
19
19
19
Table 7: Comparison of token consumption.
Method
MATH
OlympiadBench
GSMSK
BBH
MMLU-CF
LongBench
HolpotQA
MuSiQue
CC
36640
73440
4448
10272
19760
1328
20880
7760
23208
GoT
64303
140225
5349
19112
29541
1500
30198
12799
AoT
68013
148716
4782
18361
30752
1394
30668
14114
GIIS TDA
51411
83309
7709
15793
28862
1685
28358
10263
CONCLUSION
In this work, we present GHS-TDA, a two-stage framework that integrates Global Hypothesis Graph construction with topological data analysis for robust reasoning. By unifying diverse reasoning paths into a coherent hypothesis space and extracting stable backbones and self-consistent loops via persistent homology, the framework improves both accuracy and interpretability. Experiments across multiple benchmarks demonstrate consistent gains over strong baselines, while analysis of topological persistence establishes it task-agnostic indicator of reasoning reliability. This work highlights the value of combining structural integration with topological robustness, providing a principled foundation for more reliable and transparent reasoning systems.
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6 ACKNOWLEDGMENTS
This work was partially supported by the National Natural Science Foundation of China under grants 62220106008, and 62572104.
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A
APPENDIX
A.1
ACKNOWLEDGE
This article used large language models (such as ChatGPT) as an auxiliary tool in the language polishing process, but did not use them in research conception and academic content generation.
A.2 DEFINITION OF SUPPORT AND REFUTATION
To efficiently incorporate logical relations into the TDA distance, we avoid evaluating all (((V)) node pairs. Instead, we construct reduced candidate set L Liong U Lim consisting of two types of pairs. The longitudinal set Liong contains existing derivation edges (m;, Uy) in the GHG, which correspond to potential "premise conclusion" relations. The lateral set L includes unconnected node pairs (Va, 18) that satisfy
(r(va) - r(v))] <,,
which typically represent competing hypotheses at the same reasoning stage and may potentially contradict each other.
The resulting candidate set has size K << |V|2, To infer logical relations efficiently, we partition into C' chunks of size S (e.g., S = 20) and process each chunk with a single LLM call. For each node pair (i,, uy), the model assigns one three labels: SUPPORT, REFUTE, or NEUTRAL, yielding a logical code R(v,, u,). The inferred logical relation is then integrated as an additional term into the TDA distance function:
d(u,, 0y) = (1 (e), + 11ogrrphh (i) @graph (i)ll, + v(u; + uy) 8 R(u,, vy).
Specifically, if pair is labeled REFUTE, we R(V;, uj) +M, where M is a large positive constant, thereby pushing the corresponding nodes far apart in the embedding space. If pair is labeled SUPPORT, we set R(v, 02) W (e.g.. W 1), which draws the nodes closer and encourages logically coherent connections. If pair is labeled NEUTRAL or does not belong to the candidate set, we set R(v, 0,) 0, reducing the distance its original form.
A.3 PERSISTENCE-ACCURRC ANALYSIS ACROSS DATASETS
Figure presents logistic fits of reasoning accuracy function of H1 persistence, with binned means overlaid. Across all eight datasets, we consistently observe monotonic increase, demon- strating that more persistent topological loops reliably predict higher correctness. The effect is most
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Figure 4: Overall results across eight experimental settings.
pronounced in the wow-to-moderate persistence regime (H1 E [0, 2)), where small increases in per- sistence correspond sharp gains in accuracy. At higher values, curves gradually saturate, reflecting a ceiling effect once loop stability is sufficient.
Arithmetic and short-chain reasoning. On GSM8K, the curve rises steeply and quickly saturates near perfect accuracy. This suggests that persistent loops in arithmetic tasks effectively function as self-verification mechanisms (e.g., numeric substitution equation consistency checks). Similarly, MATH exhibits monotonic increase but with a smoother slope, indicating that more complex derivations require higher persistence levels to capture the complete reasoning backbone.
Long-context and multi-hop reasoning. Datasets such as HotpotQA, LongBench, and MuSiQue show the steepest slopes low persistence and saturate earlier than other tasks. This pattern highlights the importance of stable loop structures for integrating multiple evidence sources and maintaining coherence across extended reasoning chains. HotpotQA, in particular, reaches near-perfect accuracy once persistence exceeds moderate values, reflecting the decisive role of struc- tural consistecy in cross crossent reasoning.
For MMLU-CF, persistence provides strong positive signal, with accuracy steadily rising as loops become more stable. The trend indicates that persistence mitigates the effects of noisy uncertain knowledge retrieval reinforcing structurally coherent reasoning paths.
Knowledge-intensive tasks.
Challenging and creative reasoning. OlympiadBench exhibits clear upward trend but with slightly lower plateau compared to other datasets. This suggests that while loop persistence improves correctness, certain Olympiad-level problems involve creative steps or lengthy derivations that may not be fully captured by first-order topological features alone. Nonetheless, persistence remains robust predictor of accuracy.
Summary. Taken together, these results confirm that H1 persistence serves task-agnostic reliability signal across diverse benchmarks. In arithmetic tasks it captures self-verification, in long- context reasoning it enforces multi-evidence integration, and in knowledge-intensive settings it sup- presses noisy paths. We therefore recommend persistence-awes path selection strategies, using thresholding (e.g., H1 2 1) or weighted scoring, enhance both robustness and interpretability of reasoning chains.
A.4 STABILITY ANALYSIS
To assess the stability of the proposed GHS-TDA pipeline, we evaluate both its computational cost and the robustness of the resulting topological features. In our experiments GSM8K and MATH, each problem instance produces roughly 80-120 nodes, with the KNN neighborhood size fixed at 15. End-to-end graph construction canonicalization, node merging, node embedding, and
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KNN graph building-requrres only 25-60 15-60mm ms per instance system equipped with an RTX 4090 GPU and 32 GB of CPU memory, with embedding computation and KNN construction dominating the runtime. The subsequent Vietoris- Rips filtration, computed up to the first homology group, operates on these sparse graphs and exhibits a peak memory usage of 150-400 MB for graphs with around 100 nodes, and remains below GB even when the graph size grows to approximately 200 nodes. Pensistent-homologs computation is also efficient: computing the zeroth and first homology groups with GUDHI takes 10-25 ms per instance, corresponding only 10-30% of the overall pipeline time. These results indicate that the method scales well within typical LLM-reasoning workloads.
We further evaluate numerical stability by perturbing node embeddings with isotropic Gaussian noise of magnitude between 0 and 0.1 and recomputing the persistence diagrams. The resulting bot- tleneck distances lie in the range 0.01-0.10 10, depending on the noise level, and remain significantly smaller than the lifetimes of the dominant first-ooollgy features, which typically range from 0.3 to 0.8. This demonstrates that the extracted topological signatures are highly robust to embedding per- turbations, consistent with the theoretical stability properties of persistent homology. Overall, the pipeline exhibits low computational overhead, favorable scaling behavior, and strong robustness, supporting its suitability for large-scale multipath reasoning analysis.
A.5 GENERALIZATION
The Table shows that GHS-GHD delivers consistent and significant improvements on both models. On Llama 3-8B, it achieves average score of 63.88, outperforming CoT, ToT, and AoT by 6.9, 3.0, and 1.1 points, respectively. On Qwen2-14h3 14B, it reaches 62.35, with gains of 6.75, 2.7, and 1.5 points the corresponding baselines. Notably, these improvements supervision or external knowledge, indicating that the benefits come from the reasoning mechanism itself rather than model size. Overall, while all methods improve as the base model scales from 8B to 14B, the relative gains of GHS-TDA remain stable, demonstrating strong transferability and robustness across model sizes and architectures.
obtained without any additional
Table 8: Generalization ability of GHS-TDA.
Backhone
Method
OlympiadBench GSM8K
MMLU-CF
LongBench
HotpotQA
MuSiQue
Avg
CsT
72.04
8.37
87.26
74.38
65.42
51.57
63.17
31.71
56.99
ToT
72.86
10.26
91.10
79.89
65.71
58.40
72.19
36.36
60.85
LJama 3-8B
GoT
76.36
11.79
90.72
81.61
65.99
58.68
69.75
33.95
61.10
76.91
10.89
81.70
63.71
35.71
GHS-TDA
77.19
13.05
91.39
83.98
67.30
64.64
76.52
37.01
63.88
CoT
60.80
6.40
86,70
75.80
65.10
$2.70
64.90
32.40
55.60
ToT
65.00
7.20
89.80
79.70
67.60
59.30
70.80
37.90
59.66
Qwen
GoT
80.40
39.62
AoT 66.20
7,80
90.80
80.90
68.90
61.20
73.40
37.30
60.81
GHS-TDA
9.70
91.20
82.50
We conducted additional experiments with GHG-TDA on different base large language models, using GPT-4o and Claude 3.5 Sonnet.
The Table 9 shows that GHG-TDA consistently achieves the best overall performance on both mod- els. with an average score of 72.4 on GPT-4o and 72.8 on Claude 3.5 Sonnet, outperforming AoT, GoT, ToT, and CoT on all benchmarks. The consistent gains across different datasets and model backbones indicate that the effectiveness of GHG-TDA is not tied to single powerful LLM, but instead stems from its graph-guided hierarchical reasoning mechanism. These results demonstrate the strong cross-model generalization capability of the proposed method.
A.6 CORRELATION ANALYSIS
Tables 10 and 11 present the statistical analysis of the relationship between Hi persistence and reasoning correctness. Table 10 shows correlation metrics across our primary dataset collection, while Table II provides the same analysis specifically for the deepseek-V? model. The tables report global correlation measures and dataset-specific discrimination ability, quantifying how topological features in reasoning traces relate successful problem-solving across diverse reasoning tasks.
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Table 9: Performance comparison of different reasoning methods on two base models.
Base Model
Method
MATH
OlympiallSench
GSMEK
MMLUUCF
LongBench
HorpotOA
MuSiQue
Ave
CoT
85.4
12.5
92.7
82.0
72.1
62.0
71.9
36.2
61.4
GPT-4o
GoT
88.4
15.3
95.2
90.3
73.2
66.8
80.4
39.6
68.7
AoT
89.1
15.0
96.5
92.0
74.3
72.6
86.0
42.1
71.0
GBG-TDA
COT
$4.1
12.9
93.5
84.2
73.0
61.7
72.8
37.1
64.9
ToT
86.0
14.8
96.2
90.8
74.1
66.4
83.3
41.5
68.9
Sonner
92.1
AoT
88.0
15.7
96.8
93.4
75.2
72.2
86.7
43.2
71.3
GHG-TDA
89.1
19.0
97.1
95.4
75.9
73.5
58.0
44.6
72.8
Table 10: Correlation between H1 persistence and reasoning correctness across datasets.
Analysis Item
Result
Interpretation
Global Spearman correlation (p)
0.314 (p 0)
Moderate correlation with correctness.
Logistic regression coefficient
0.736 (OR 2.09 per 11SD
+ISD nearly doubles correctness odds.
ROC-AUC (Hı persistence only)
0.671
Good discrimination ability.
Dataset-level AUC
Stable across tasks.
GSMSK
0.699
Robust.
MATH
0.597
Robust.
OlympiadBench
0.686
Robust.
BBH
0.663
Robust.
MMLU-CF
0.703
Robust.
LongBench
0.764
Robust.
HotpotQA
0.617
Robust.
MuSiQue
0.627
Robust.
A.7 PARAMETER SETTINGS AND TUNING STRATEGIES
Hyperparameter settings directly affect both the degree structural compression in the Global Hy- pothesis Graph (GHG) and the sensitivity of the topological analysis. The key parameters include:
node merging threshold m hybrid distance weights (a,3,7), number of significant topo- logical features K, loop embedding threshold 8.
These are designed under the principle of "semantics-domina structure-assisted, uncertainty- corrected" reasoning.
Hybrid distance construction.
We constrain
a + +
So that semantic similarity, structural consistency, and uncertainty are comparable on the same scale. The default setting is (a, ,,,7) = (0.6, 0.3, Semantic similarity (a) dominates clustering, thus receives the highest weight. Structural consistency (3) crucial in multi-hop cross-document reasoning. Uncertainty (π) down-weights low-confidence nodes and acts as regularization.
Tuning guideline: Increase a for arithmetic short logical inference. Increase 3 for long-chain or cross-document reasoning. Increase under noisy outputs or fluctuating confidence.
Node merging threshold. The default m 0.85 balances redundancy removal and connec- tivity. Too low (< 0.8): risk of merging non-equivalent expressions. Too high (> 0.9): graph becomes sparse, losing connectivity. Empirically: Use 0. 0.75-0.8 in noisy tasks, Use 0.9 in precise reasoning (math, code).
Number of significant topological features. We use by default to capture diverse back- bones without redundancy. Too small K: omits plausible reasoning chains. Too large K: intro- duces noisy cycles, weakening interpretability. Practical range: K [3, 8), tuned by task complexity and candidate path size.
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Table 11: Correlation analysis between H1 persistence and reasoning correctness across datasets, deepseek-V3.
Analysis Item
Result
Interpretation
Global Spearman correlation (p)
0.391 (p 0)
Moderate correlation with correctness.
Logistic regression coefficient
1.046 (OR x 2.847 per 11SD)
+ISD triples correctness odds.
ROC-AUC (H) persistence only)
0.726
Good discrimination ability.
Dataset-level AUC
Consistent across tasks.
GSM8K
0.641
Robust discrimination.
MATH
0.770
Robust discrimination.
OlympiadBench
0.689
Robust discrimination.
BBH
0.690
Robust discrimination.
MMLU-CF
0.791
Robust discrimination.
LongBench
0.770
Robust discrimination,
HotpotQA
0.741
Rohust discrimination.
MuSiQue
0.734
Robust discrimination.
Loop embedding threshold. The default = 0.15 controls which loops are embedded into the backbone. We further adopt adaptive scaling:
8= A co.
A E (..1,
where is the persistence scale of loop features. Large 8: may introduce noisy, distant loops. Small d: may discard important verification loops.
Summary. The default hyperparameters provide a balanced configuration for general tasks. Prac- tical tuning follows the order: 1. Fix + 3 + 7 1, redistribute according to task. 2. Tune mergg and via grid search. Set adaptively using G scaling.
This strategy ensures robustness and reproducibility across diverse reasoning scenarios.
A.8 PARAMETER SETTINGS AND TUNING STRATEGIES
Hyperparameters affect both graph compression and topological sensitivity. The key ones are the node merging threshold Imerges distance weights (a:, 3))), number of topological features K, and loop threshold 6, designed under the principle of "semantics-dominnn,, structure-assisted, umcertainty-coorectted"" reasoning.
Hybrid distance. We constrain a + 3 + with default (0.6, 0.3, 0.1). Semantic similarity (a) dominates, structure (3) supports long multi-hop tasks, and uncertainty (r) regularizes noise. Adjust by increasing a for precise reasoning, 3 for long dependencies, and for noisy outputs.
We tested various combinations of Hybrid distance. As shown in Table 12 our node representation integrates semantic embeddings, graph-struse graph-structural features, and an uncertainty term. This design enables TDA to simultancously capture semantic coherence, structural consistency, and potential sources of noise. The confidence component is defined as uい = log (confiidenc)) and is assigned small weight in the hybrid distance metric (y 0.1). Thus, even if the confidence estimates are imperfect, their overall influence remains limited. Moreover, persistent homology is inherently robust local perturbations: erroneous confidence values lead only to short-lived topological fea- tures, which are automatically filtered out and do not appear in the final skeleton. As a result, the final reasoning outcome is determined primarily by topological persistence and structural consis- tency rather than by confidence itself. Consequently, imperfect confidence scores neither distort node representations nor degrade.
Node merging. Default @merge = 0.85 balances redundancy and connectivity. Use 0.85-0.8 for noisy tasks, 0.9 for precise domains (e.g., math, code).
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Table 12: Study of the distance metric.
(Semantic)
(Structural)
Y (Uncertainty)
Accuracy (%)
0.60
0.30
0.10
83,9
0.90
0.00
0.10
77.4
0.00
0.90
0.10
75.2
0.70
0,30
0.00
82.6
0,53
0.27
0.20
83.4
0.70
0.20
0.10
83.7
0.50
0.40
0.10
82.9
We examine how the node-merging threshold influences the construction of the Global Hypothe- sis Graph. The results are shown in Table 13 A low threshold (around the 0.70 range) induces overly aggressive consolidation, where semantically different reasoning steps are forced into a sin- gle node. This leads to semantic collapse, reduced path diversity, and weakened topological struc- ture, ultimately degrading accuracy. As the threshold moves into a moderate region (approximately 0.80 (.800).90), semantically aligned steps merged reliably while the graph remains well connected. In this regime, the resulting structure preserves both diversity and coherence, enabling persistent HO backbones and HI verification loops to be detected consistently. This balance produces the most stable and accurate reasoning performance across datasets. When the threshold becomes overly conservative (around the 0.95 range), the graph becomes fragmented due to insufficient merging of near-equivalent steps. Such sparsity reduces the emergence of meaningful topological features and limits the ability of TDA extract coherent reasoning skeletons. These observations collectively indicate that moderate thresholds naturally yield the best trade-off between semantic integration and structural robustness.
Table 13: Effect of the node-merging threshold mergg on EM accuracy.
Omerge
EM Accuracy (%)
0.70
72.6
0.80
83.1
0.85 (default)
83,9
0.90
83.4
0.95
78.3
Topological features. Default captures diverse backbones without noise; practical range 3-8, tuned by task complexity.
Loop threshold. Default 0.15, with adaptive scaling
x X (0.1,
where eb loop persistence. Larger risks noisy loops; smaller may drop useful ones.
Summary. Defaults are balanced for general use. Tuning priority: (1) redistribute (a, 8); (2) grid search Omenge, K; (3) adapt 5 via persistence scaling.
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A.9 PSEUDOCODE
Algorithm GHS-TDA: Construct-Analyze Pipeline
Require: Problem Q; number of sampled paths N: merge threshold Omerge: distance weights
(v): KNN size k; truncation percentile т; topological feature budget K; loop-embedding
threshold
Ensure: Final answer reasoning skeleton
I: P t- SAMPLEPATHS(Q) N)
ML-M-asedd sampling of candidate reasoning paths Global Hypothesis Graph with merged equivalent
2: G
BUILDGHG(P, mmerge)
nodes
3: (Eo + EMBEDNODES(G)
P 2, = e, || @graph (v) || uu Hybrid distance over (e, graph
4: d((,)) + a(1- - (1. + B1| + v((
5: GKNN + BBULLDKNN ). d, k); 9r TRUNCATE(GKNV
6: VR VIETORISRIPS d)
D Filtration sparsified metric graph
7: (DHg: DH,)= + PERSUSTENTHONOLGGGYYYY
D Persistence diagrams/harcodes Top-K significant features E Büj: Ab Bi: S < 0.99 ddeah(bb)
8: B Bi -SELECCTTOPBYLLFESPPNNNN Ho: DH K)
9: HH + mediaa
(b) (eetha)(detth(()
10: S + EXTRACTSKKLEEON E.o (eE) 5)
11: à + AGGREGATRANNSEERSSS)
D Confieeneeperisteeee-wweiie voting with validation
12: return (ā,
Algorithm BUILDGHG: Construct Global Hypothesis Graph with Node Alignment
Require: Paths p {P.) merge threshold mmerge
Ensure: Graph G EV.
1: V < 0. E +-
2: for = 1 to do
3: for 1 to m, do
4:
+ (i).
(text(s), c(s) ANNOTATE(S)
5:
v* arg max Sim(canon(s), canon(u))
b Search best canonical match
6:
if V = 9 or Sim(canon(s), canon(u")) < m then
7:
Unew + (text(s), canon(s), c(s), r(s));
V [Unew)
8:
INTPPROENANCC Unnww
(n i,
9:
else
10:
8² + MERGEEU",
Avg confidence; max progress; provenance union
11:
end
12:
if j
> 1 then
Add (1)_1
Temporal/dedductie edge along P;
end ir
15:
end for
end for
17:
return (V, E)
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Algorithm 3 EXTRACTSKELETON Backbone and Loop Embedding
Require: Graph G (V,E), distance d; cluster scale 'H loop scales {et]; loop set Bi; embed-
ding threshold 5
Ensure: Reasoning skeleton 8
d, 1: ( <- TTHRESHOLLDGRAPPHH d
2: {Cm] +- CRONECCTDCCMMPONETTSICCC....
3: Cheep 6 { [[Cl > 3 A COVERSATTLESTTTTWOPPSSSSC.C
4: for each C. E Ckeep do
5:
SC +- arg mingge Tv
D Tie-broken by minimum avg. distance in C
6:
9c t arg max,eC Te
7: Pc + SHORTESTPATI((; sc, edge weights dıj)
>> Backbone
8:
Bc -
9:
for each b E B do
((=t) THRESHOLDGRAPPH(G..
11:
V,, 4 LOCALLZEL
(()))
[V, n C| maximal among clusters then
13:
Be t Bc {6}
Assign loop b to C
14:
end
15:
end for
16:
if
Bc + 0 then
17:
by arg maxseBe L(b)
Principal loop by lifespan
18:
v* + arg Vig r. medianfr, E C)
Pivot near median progress
19:
tour + MINWEGGICCYCLEBBSSTTOORR.. Embed loop if mill aEPo d(v, u) <
B Horton-based restricted cycle
20:
Pc < SPLICE(Pe, v", tour, 8)
end if
22:
Add Pa to skeleton set S
end for
24: return S t UPc
Algorithm 4 AGGREGATEANSWERS
Coatfidennc//ersssteccewwiieeisp Voting
Require: Skeleton S; node confidences {c,}; node degrees (deg(v))
Ensure: Final answer à
1: for each node E S do
2: Wy f-
Downht highly connected hubs
deg(v)
3: end for
4: à f- arg max, Eves, Wy
5: return
We provide pseudocode for the full GHS-TDA pipeline to complement the formal description in Section A.9 The pseudocode explicitly specifies data flow, intermediate representations, and ter- mination criteria, ensuring clarity and reproducibility. Each subroutine corresponds directly to one of the methodological components: Global Hypothesis Graph construction, point-cloud embedding and hybrid distance, Vietoris-Rips filtration and persistent homology, skeleton extraction with loop embedding, and final answer aggregation.
Overall pipeline. Algorithm | summarizes the two-stage "construct-analyze" procedure. It be- gins with sampling multiple reasoning paths and building the Global Hypothesis Graph (GHG) by merging semantically equivalent hypotheses. The graph is then mapped into a joint metric space that integrates semantics, structural encodings, and uncertainty. A sparsified k-nearest-neighhor (KNN) graph with global truncation serves the foundation for Vietoris filtration, upon which per- sistent homology is computed. Significant features (H, clusters and H₃ loops) are selected by lifespan, and operating scales are determined adaptively. The final skeleton is extracted by combin- ing shortest-patt backbones with loop embeddings, and candidate answers are aggregated through persistence- and aaafidence-weightee voting.
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Global Hypothesis Graph construction. Algorithm details the GHG construction process. It systematically unifies reasoning steps across sampled paths by canonical-fome similarity. controlled by merge threshold merge. Provenance tracking ensures that each merged node retains information about its original sources, supporting later interpretability. Edge inheritance preserves deductive and temporal relations, yielding compact but comprehensive graph.
Skeleton extraction. A deescrbbes how sigmificant topological features are mapped back to the graph. For each cluster, we identify anchor nodes based on progress values and compute a shortest-path backbone. Loops are localized feature-specific scales and embedded into the backbone if sufficiently close under the hybrid metric. This ensures that the extracted skeleton captures both the global flow of reasoning and local self-consistency structures.
Answer aggregation. the skeleton weighted by node confidence while penalizing highly connected hubs. This de- sign balances precision and robustness, yielding a single high-confidence answer supported by topologically stable skeleton.
@ssorthhm4ppeeeee the final aggregation stage. Candidate answers along
Complexity and guarantees. The pipeline is polynomial in the number of nodes. GHG con- struction is (()V in the worst case but optimized by approximate nearest-neighbor search in canonical space. Persistent homology is computed up to dimension one (H1), which tractable on the sparsified KNN graph. Loop embedding relies polynomial-time Horton implementation. Conflict resolution in node merging satisfies the (1-1/e) approximation bound for hitting set.
mainmmum-weigh cycle basis with a known
Reproducibility. Default hyperparameter settings are provided Appendix ??, together with rec- ommended ranges for task-speciff tuning. Full prompts, random seeds, and environment details are included the supplementary material.
A.10 A GHS-TDA ANALYSIS EXAMPLE
Reasoning Log for Problem: n2² + |-1lm. n!!
Problem Statement Given integer 2 determine all such that n² n!.
Final Answer No solution exists. For all n 2 1, n² + 1f
Reasoning Log (Multi-Path Traces)
Path 1. Small cases: n 1: n 2 = 1 3!; 1:: 17 4!. -Fo 5. any prime divisor of + with p > n cannot divide n!. Exammpe: = 7, n +1= 50 = 2.52 but (7!)
Conclusion: no solution.
Path 2. Exhaustive check for = 1,2, 4: none valid. For n 2 5, p > n divides n² + 1, contradiction. Otherwise, prime exponent condition fails (e.g., case). Conclusion: no solution.
Path 3. - Explicitly verify n = 1, 2,4,4,,,66 7, all fail. For general prime factors of n²² + either too large (p n) or require higher multiplicities than available in n!. Conclusion: no solution.
Path 4. -Cross-checked small values: all fail. Structural fact: if p n² + 1, then n² = -1 (mod p). so order of n mod p is 4, implying p = (mod 4). Such primes are often larger than n, so cannot appear in n!. Conclusion: no solution.
Small cases 1, all fail. For 2 5, prime exponent mismatch occurs (e.g., n with factor 52 but 0y (7!) = -o.oCclcus:on: no solution.
Path 5.
Global Hypothesis Graph (GHG) and TDA Extraction
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Clusters. -Small-n check cluster: 1, 4.l.,4alll fail. Sttuuttral cluster: p |n²+1 p (mod 4). Counterexample cluster: n = 6 (37 > 6), n = (exponent deficit for 5?). General
obstruction: either p exponent deficit.
Skeleton Path (TDA Backbone). Example backbone extraction:
V = - 71 = 2 + n. = 3 - structural fact - = 6 + = 7 general obstruction - final conclusion.
Conclusion Nodes. Z1: No solution (supported by all clusters). Zz: {1,2,3} (false candidate,
rejected). Final skeleton selects Z1.
Consolidated Conclusion All reasoning paths converge:
No integer 2 satisfies n² n!!
A.11 ANALYSIS OF REPRESENTATIVE FAILURE CASES
Failure cases can be broadly categorized into two main types. Semantic ambiguity, illustrated us- ing examples from the HotpoiQA dataset. For instance, in the question "Did the actress who starred in The Ring also appear in King Kong?". the base model forms incorrect semantic clusters due to ambiguity between the Japanese and U.S. versions of The Ring. leading to an erroneous answer. Numerical perturbation, illustrated using GSM8K. In some arithmetic problems, the model oc- casionally generates minor numerical mistakes (e.g., writing "9" instead of "7"),, and the resulting structural similarity between intermediate steps causes such clusters to be incorrectly merged.
These errors primarily stem from ambiguities in the underlying LLM and the inherent stability properties of persistent homology, rather than from structural deficiencies in our framework. As noted in the revised manuscript, increasing sampling diversity (e.g., n 10) substantially reduces the frequency of such enrors.
A.12 QUALITATIVE ANALYSIS AND HUMAN-CENTEREE INTERPRETABILIT (SUCCESS CASES)
Complementary to the failure case analysis in the appendix, we further provide representative qual- itative examples to illustrate how GHS-TDA behaves well-posed scenarios and how its topolog- ical mechanism successfully suppresses noisy reasoning paths while preserving globally consistent structures. These examples demonstrate how the proposed framework identifies concise, coherent, and numan-preferred reasoning structures from multiple -.L--rgeertedd trajectories.
MATH: Extracting Concise and Expert-Like Reasoning Skeletons We first examine a repre- sentative problem from the MATH dataset. When prompted with this problem, the underlying LLM generates multiple correct but heterogeneous reasoning trajectories, and high-confidence baselines often produce verbose and logically tangled solutions that mix derivation with verification in- troduce unnecessary "guess-and-check" steps. In contrast, the GHS-TDA framework aggregates all sampled trajectories and identifies the most persistent structural cluster in the global hypothesis space. The resulting skeleton corresponds to canonical case-splitting strategy typically used by hu- man solvers: it separates the equation into the non-negative and negative cases, solves each branch, and filters the resulting solutions using appropriate domain constraints. This extracted reasoning path is shorter, logically cleaner, and more closely aligned with standard mathematical reasoning practices. The example illustrates how the TDA component suppresses locally confident yet logi- cally noisy steps while preserving the globally stable reasoning core.
HotpotQA: Capturing Robust and Self-Consistent Multi-Hop Reasoning We also examine multi-hop question from HotpotQA, where the model must retrieve and verify information across multiple entities. Among the sampled trajectories, unreliable paths (e.g., hallucinating directors, skipping verification steps, or producing incomplete hops) form weakly connected, low-persistence components in the GHS representation. In contrast, paths that correctly retrieve and cross-validate both film directors and their birthplaces form a highly persistent H₃ loop. This loop captures a struc- turally robust pattern: multiple independent paths reconverge the same factual nodes (e.g., the same director and birthplace). Such cross cross-path path consistency is naturally expressed as stable topo- logical cycle, enabling TDA distinguish reliable reasoning from brittle speculative alternatives.
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Interpretability We evaluate interpretability through human annotations along four criteria: conciseness, logical coherence, necessity of steps, and faithfulness to human rea- soning practices. Across both MATH and HotpotQA examples, annotators consistently judged the TDA-extracted skeletons to be more interpretable than high-confidence baselines. They noted that GHS-TDA effectively removes redundant or noisy steps, enforces appropriate structural con- straints (such as case conditions and entity verification), and highlights cross-path consistency that aligns with human intuitions about trustworthy reasoning. Taken together, these qualitative assess- ments demonstrate that GHS-TDA provides not only improved accuracy but also topologically grounded and entrreraatter summary of multipath reasoning. By isolating persistent struc- tural components-suce that are concise, coherent, and robust, thereby offering clear interpretive advantages over confidence- based or single-path approaches.
stable clusters and cycles- the framework yields reasoning skeletons
23


Reviews:
[{"review_id": "0LahE6Jc8s", "reviewer": "Reviewer_Ucj2", "summary": "This paper propose GHS-TDA, a novel method for improving the reliability and interpretability of LLM reasoning. It operates in two steps: first, it integrates diverse reasoning paths from an LLM into a Global Hypothesis Graph (GHS). Then, it uses Topological Data Analysis (TDA) to analyze this graph, identifying the most stable and consistent reasoning structures. Across multiple reasoning benchmarks, GHS-TDA is shown to substantially outperform strong baselines in both accuracy and robustness.", "questions": "See weakness above.", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- GHS-TDA offers a new approach to reasoning by replacing existing methods with a global mechanism. This mechanism integrates and coordinates various reasoning hypotheses, while also using structured analysis techniques to effectively filter out redundant information and extract the most crucial reasoning features.\n\n- Testing on multiple reasoning benchmarks demonstrated GHS-TDA's strong performance.", "weaknesses": "- Motivation for Point Cloud Representation is Unclear: The paper does not adequately explain the rationale for using a point cloud representation of the reasoning. Specifically, it is unclear why this representation is necessary for the Global Hypothesis Graph during the skeleton extraction process.\n\n- Missing Technical Specifications: Essential technical details are absent. For instance, the paper fails to describe how the refutation and support relations are constructed within the Global Hypothesis Graph during the global hypothesis space modeling stage.", "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": "jtdl9lCYv1", "reviewer": "Reviewer_sw5k", "summary": "This paper introduces GHS-TDA, a novel framework that enhances complex reasoning in LLMs by first constructing a Global Hypothesis Graph and then applying Topological Data Analysis to extract robust reasoning backbones and cycles. Extensive experiments demonstrate its superior performance across diverse benchmarks, validating the effectiveness of this approach.", "questions": "Q1: On the Distance Metric\nThe hybrid distance metric is a key contribution of the work. However, the weights (α, β, γ) appear to be set empirically. Did the authors perform ablation studies to quantify the individual contribution of each component (semantic, structural, uncertainty) to the final performance? Furthermore, was the exploration of more complex, non-linear distance functions considered?\nQ2: On the Robustness of Graph Construction\nThe node merging process heavily relies on the \"canonical form\" and the threshold θ_merge. Is the method sufficiently sensitive to steps that are semantically similar but logically distinct (e.g., \"Assume X is true\" vs. \"Therefore we have proven X\")? Could the authors discuss the potential risks and consequences of incorrect node merging?\nQ3: On Computational Cost\nThe GHS-TDA framework involves multiple LLM calls for path generation, embedding computation, and confidence scoring. Compared to other multi-call baselines like AoT or ToT, could the authors provide a more detailed computational overhead analysis (e.g., total token consumption or latency)? For resource-constrained applications, are there components within the framework that could be streamlined or simplified?\nQ4: On Generalizability\nThe methodology seems to be agnostic to the underlying LLM. Have the authors tested GHS-TDA on smaller or open-source models (e.g., the Llama series)? If the performance gains are heavily dependent on a powerful base model like GPT-4, how might this affect the perceived generalizability and accessibility of the proposed method?\nQ5. Diversity of Multiple Reasoning Paths: You use the same LLM to generate multiple reasoning paths, hoping to obtain diverse ones. However, it cannot be guaranteed that the multiple reasoning paths are diverse. The reasoning tokens generated multiple times by the same LLM are actually similar, and diversity cannot be guaranteed. Consequently, the subsequent similarity calculations can hardly play a key role.\nQ6. Node Representation in Global Hypothesis Graph: Why is the embedding formula defined like this? confidence_v is the LLM's confidence in that step. If the LLM's confidence is incorrect, will the node hypothesis be affected, and will it affect the global reasoning?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 3, "strengths": "1.\tHigh Novelty: This work is the first to introduce Topological Data Analysis (TDA) into LLM reasoning chains, innovatively formalizing concepts such as \"logical backbones\" and \"self-consistent loops\" as topological invariants.\n2.\tStrong Methodological Effectiveness: The proposed multi-role agenda mechanism for constructing the Global Hypothesis Graph enables effective integration and interaction across multiple reasoning paths.\n3.\tConvincing Experimental Results: The comprehensive experiments demonstrate the method's effectiveness and generalizability, showing superior performance over recent strong baselines across multiple datasets and various LLM backbones.", "weaknesses": "1.\tThe claimed novelty is questionable：There are already many methods for multi-path integrated reasoning, and the problem you raised of 'lacking global integration across hypotheses' does not hold.\n     - Barkan O, Elisha Y, Toib Y, et al. Improving LLM Attributions with Randomized Path-Integration[C]//Findings of the Association for Computational Linguistics: EMNLP 2024. 2024: 9430-9446.\n     - Wei Y, Lin Y, Gao H, et al. Path-LLM: A Multi-Modal Path Representation Learning by Aligning and Fusing with Large Language Models[C]//Proceedings of the ACM on Web Conference 2025. 2025: 2289-2298.\n     - Li X, Xian K, Wen H, et al. PathGen-LLM: A Large Language Model for Dynamic Path Generation in Complex Transportation Networks[J]. Mathematics, 2025, 13(19): 3073.\n\n2.\tThe method incurs substantial computational and time overhead： Firstly, for the same problem,\n     - generating diverse reasoning paths requires multiple queries (and there is no guarantee that multiple paths from the same LLM are diverse),\n     - secondly, for node merging, the M reasoning steps in the N reasoning paths are traversed sequentially, meaning it is repeated N*M times. Although the authors proposed algorithmic acceleration, they did not provide further details, such as building an index, and vaguely did not give the real number of computations in the experiment.\n     - In addition, the entire process involves repeatedly generating paths, merging them to generate a global hypothesis graph, then converting it into embeddings, and using topological structure to extract a reasoning skeleton. The process is very complex for the reasoning stage, making it difficult to ensure computational and time overhead.\n\n3.\tKey methodological details are ambiguously described：The paper's descriptions are vague. For example, how to perform conflict detection is only vaguely described as \"Through unification, conflict detection, and closure inference, GHS enhances semantic connections among nodes and overcomes the isolation of traditional path-based generation\". There is no detailed explanation of the specific algorithm, making it hard to believe the paper's contribution. There is also no specific description of how the method performs canonicalization. The correctness of the canonicalization plays a key role in the subsequent merging step.\n\n4.\tLack of Theoretical Foundation: The paper's central claim that the persistence of topological features like H₀ and H₁ characterizes reasoning reliability—lacks support from a theoretical model. Currently, this claim resembles a hypothesis retroactively inferred from experimental data, rather than a deduction derived from first principles, which weakens the theoretical grounding of the method. The concept of \"reasoning reliability\" is vaguely defined and is largely equated with final-answer correctness. We suggest the authors provide a more formal, process-oriented definition of reasoning reliability. Building upon this, they could then formally argue that the persistent topological features extracted by TDA serve as a effective proxy for this defined 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": "8ZgtqlcLft", "reviewer": "Reviewer_XVaz", "summary": "The paper proposes GHS-TDA, a two-stage framework for LLM reasoning. Stage 1 constructs a Global Hypothesis Graph (GHG) by sampling multiple reasoning paths, aligning semantically equivalent steps, merging them into nodes , and encoding adjacency/support/refutation relations. Stage 2 embeds the graph into a joint metric space and applies Vietoris–Rips filtration with persistent homology to extract stable H0 backbones and H1 loops, producing an interpretable “reasoning skeleton” and a confidence/persistence-weighted vote for the final answer. The manuscript positions TDA as a scale-robust, noise-insensitive structural lens for selecting and composing reasoning paths, and reports gains across several benchmarks.", "questions": "As above.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "1. The paper reframes multi-path reasoning as a global topological object and uses TDA to identify backbone chains and self-consistent cycles that persist across scales—going beyond local heuristics like per-node confidence or shortest paths. \n\n2. The GHG node/edge definition, semantic merging criterion, and skeleton-extraction pseudocode are explicitly provided, aiding reproducibility. \n\n3. The method surfaces stable H0/H1 structures and aggregates answers with a principled weighting that down-weights high-degree hubs, yielding human-auditable outputs. \n\n4. The claim is that GHS-TDA improves accuracy/consistency/interpretability on benchmarks such as GSM8K, MATH, OlympiadBench, HotpotQA, MuSiQue, BBH, and LongBench.", "weaknesses": "1. The rationale that topological persistence reflects reasoning stability is intuitively argued but not theoretically guaranteed.\n\n2. Some recent structured-search or reliability-oriented methods are not clearly included. There is a lack of sufficient comparisons of related work: thought tree combined with Monte Carlo, graph neural network combined with LLM, first-order logic combined with LLM.\n\n3. Complexity considerationsand numerical stability are not paired with measured time/memory curves or failure modes. Correctness under scale is therefore only partially substantiated.\n\n4. Given multiple datasets/baselines, include multiple-comparison corrections and effect sizes; detail inter-annotator agreement for human evaluations.", "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": "Ta9QxMe8cF", "reviewer": "Reviewer_rfA4", "summary": "The paper presents GHS-TDA, a two-stage framework designed to enhance the reasoning capabilities of LLMs. It addresses limitations of existing Chain-of-Thought (CoT) methods, which often lack a global mechanism for integrating and validating multiple reasoning paths. The proposed approach first constructs a Global Hypothesis Graph (GHS) that unifies diverse reasoning hypotheses into a coherent semantic structure. Then, it applies Topological Data Analysis (TDA), specifically persistent homology, to identify stable reasoning paths and self-consistent. Experimental results across eight reasoning benchmarks (including GSM8K, HotpotQA, and MATH) show consistent improvements over strong baselines such as CoT, ToT, GoT, and AoT, with further analysis showing a high correlation between persistence and reasoning correctness.", "questions": "1. The paper would benefit from a more detailed discussion of hyperparameter choices, such as the node-merging threshold and distance metric weights. It is better the paper also elaborates on the design rationale and sensitivity of the distance metric used.\n2. Could the authors provide additional qualitative analysis examples and elaborate on the human-centered interpretability assessment?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "1. The paper effectively addresses the global integration of reasoning paths and proposes GHS-TDA. It introduces a new methodological perspective by incorporating topological data analysis into reasoning chain evaluation.\n2. The extensive experimental results across multiple benchmarks demonstrate the effectiveness and robustness of the proposed approach.\n3. The analyses on interpretability, including the observed correlation between topological persistence and reasoning correctness, provide empirical support for the framework’s validity and its contribution to more interpretable reasoning processes.", "weaknesses": "1. The experiments are conducted on three LLMs, which, while representative, do not include the most recent or larger-scale models. Evaluating GHS-TDA on newer models would better demonstrate its generalizability.\n2. The proposed framework introduces multiple components, including graph construction, merging, and topological filtering, which increase complexity compared to baseline methods. A detailed computational cost or scalability analysis would clarify the trade-off between performance and efficiency.\n3. The paper presentation and writing could be further improved. Certain sections (e.g. Related Work) could benefit from improved clarity and consistency in citations.", "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)