Quantum-Inspired Trace-Augmented Evidence Selection for Reasoning over Structured Hypothesis Spaces

Large language models are increasingly applied to high-risk domains such as law, yet complex legal reasoning remains limited by two structural challenges. First, existing RAG and GraphRAG methods emphasize lexical or semantic similarity while overlooking normative relations among legal provisions. Second, vanilla Chain-of-Thought prompting may generate plausible rationales without enforcing the normative structure of legal reasoning. To deal with the bottleneck of pipelines in the legal reasoning domain, we propose LEGO, a dual-module framework that synergizes Legal Expert GraphRAG and expert Chain-of-thought for complex legal reasoning. ExpertGraphRAG uses an expert-annotated civil code graph encoding these normative relations with a greedy normative-coverage retrieval algorithm to dynamically extract instance-specific provision subgraphs, while ExpertCoT organizes the retrieved provisions and case facts into structured Provision-Fact-Conclusion reasoning. With a Qwen3-8B backbone, LEGO achieves 40.53% exact-match accuracy on LawExamQA_Civil, outperforming the evaluated RAG and CoT baselines and performing comparably to the evaluated larger models, while remaining robust on multi-hop questions. It also achieves the best results among the evaluated baselines on the open-ended benchmarks. Ablation studies confirm the individual and complementary contributions of both modules, demonstrating LEGO's effectiveness in improving LLMs' complex legal reasoning ability. Code and dataset can be found in the link: https://github.com/BLK-WHT/LEGO

Retrieval-augmented question answering depends on selecting evidence passages that jointly support answer generation. However, many RAG pipelines rely on top-$k$ ranking, where passages are selected mainly by individual relevance scores, even though multi-hop questions often require complementary evidence satisfying multiple information requirements. Recent LLM-based selectors address this by treating retrieval as set selection, but using an LLM for this intermediate stage can be costly and difficult to scale. In this work, we formulate evidence selection as a Quadratic Unconstrained Binary Optimization (QUBO) problem. Given a question, candidate passages, and decomposed information requirements, our method constructs an energy function that balances relevance, requirement coverage, support strength, redundancy, complementarity, and compactness. Low-energy solutions correspond to compact evidence subsets that cover the needed requirements while avoiding unnecessary or repetitive context. The selected passages are then passed to a downstream language model for answer generation, separating combinatorial evidence selection from semantic answer generation. We evaluate the proposed QUBO selector on HotpotQA and compare it with LLM-based set selectors and non-LLM baselines including BM25, relevance top-$k$, maximal marginal relevance, hybrid lexical--semantic ranking, greedy coverage, and random selection. The QUBO selector achieves competitive exact-match and token-F1 performance relative to LLM-based selectors while providing a solver-compatible formulation for structured evidence selection. These results suggest that multi-hop evidence selection can be cast as discrete optimization, opening a path toward RAG pipelines where LLMs are reserved for semantic processing and answer generation, while context selection is handled by Ising/QUBO-compatible solvers.

Large Language Models (LLMs) explore problems through chain-of-thought, but this exploration is buried in unstructured prose. On high-stakes tasks, users cannot tell which steps are well-supported, which alternatives were seriously considered, or how the final conclusion compares to those the model discarded. We propose a framework that ensembles the reasoning structure, not just the answers, of multiple LLMs by weighted merging of Directed Acyclic Graphs (DAGs) extracted from reasoning chains. We weight each step by how many traces independently attest to it, to return "Consensus Reasoning". Across six benchmarks spanning statutory interpretation, graduate-level science, narrative multi-hop reasoning, and first-order logic, our ensemble outperforms a matched-budget majority-vote baseline, with a maximum accuracy gain of 3.1% on MuSR-MM (narrative multi-hop reasoning). On a single model, the framework matches or exceeds self-consistency at the same trace budget while additionally exposing an inspectable consensus reasoning graph. Ensemble weights correlate with LLM-judge rankings of reasoning quality at Spearman $ρ= 0.30$-$0.51$, and consensus subgraphs are preferred over alternatives leading to the majority-vote answer in 54.4-65.4% of head-to-head comparisons across five of six datasets. We observe that our framework can also be used to analyze diverse reasoning perspectives for a problem.