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Learning Global Hypothesis Space for Enhancing Synergistic Reasoning Chain

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Chain-of-thought training and analysis · 0 citations (OpenAlex)

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Proposes GHS-TDA, which merges multiple sampled LLM reasoning paths into a global hypothesis graph and uses persistent homology to extract a reasoning skeleton (backbone and loops) for answer selection.

Problem

Chain-of-thought reasoning is susceptible to early-stage error propagation and lacks global coordination and structured filtering of redundant reasoning steps.

Approach

Build a global hypothesis graph by aligning and merging nodes across multiple sampled reasoning paths (with LLM-inferred support/refutation edges), then apply Vietoris-Rips persistent homology (H0 backbones, H1 self-consistent loops) to extract a skeleton used for answer aggregation.

Key results

• GHS-TDA averages 68.0% EM on GPT-4o-mini vs. 66.9% for the strongest baseline AoT across eight benchmarks.
• On GPT-4o-mini MATH, GHS-TDA reaches 83.9% vs. AoT 83.6% and CoT 78.3%.
• H1 persistence reaches ROC-AUC 0.74 for predicting reasoning correctness, with global Spearman rho 0.349.

Surprising findings

• Reported LLM-call budget of 19 per problem is listed as fixed, yet CoT-SC uses 16 calls and the paper's own call counts for ToT/AoT are reported as varying per dataset, with GHS-TDA's token use exceeding GoT/AoT on GSM8K and MATH-scale tasks in some cases.
• Gains over strongest baselines are small (often under 1 point), and the paper's averages and tables show internal inconsistencies (e.g., GHG vs GHS naming, duplicate parameter sections).

Limitations

• Gains over the strongest baseline (AoT) are small, often under one point.
• Reliance on LLM-inferred support/refutation labels and canonicalization adds cost and possible noise; the paper reports no code or data release.

Experimental setup

Datasets: GSM8K MATH OlympiadBench BBH MMLU-CF LongBench HotpotQA MuSiQue

Benchmarks: GSM8K MATH OlympiadBench BBH MMLU-CF LongBench HotpotQA MuSiQue

Metrics: exact match LLM calls token consumption Likert ratings (clarity, coherence, credibility, conciseness ROC-AUC Spearman correlation

Baselines: CoT CoT-SC Self-Refine Analogical Prompting AFlow ToT GoT FoT AoT

Builds on: Chain-of-Thought Tree-of-Thought Graph-of-Thought Atom-of-Thought Vietoris-Rips filtration

Closest papers by meaning

• Topology of Reasoning: Understanding Large Reasoning Models through Reasoning Graph Properties (NeurIPS 2025 · similarity 0.88)
• Reasoning on Graphs: Faithful and Interpretable Large Language Model Reasoning (ICLR 2024 · similarity 0.87)
• System-1.5 Reasoning: Traversal in Language and Latent Spaces with Dynamic Shortcuts (NeurIPS 2025 · similarity 0.87)
• Graph-constrained Reasoning: Faithful Reasoning on Knowledge Graphs with Large Language Models (ICML 2025 · similarity 0.87)
• Metastable Dynamics of Chain-of-Thought Reasoning: Provable Benefits of Search, RL and Distillation (ICML 2025 · similarity 0.86)
• Boule or Baguette? A Study on Task Topology, Length Generalization, and the Benefit of Reasoning Trace (NeurIPS 2026 · similarity 0.86)