Last Layer Logits to Logic: Empowering LLMs with Logic-Consistent Structured Knowledge Reasoning

TL;DR

This work tackles logic drift in KGQA with LLMs by introducing Logits-to-Logic, a last-layer logits–level framework that maps KG and question logic into an NFA and uses three modules—logic compiling, logits strengthening, and logits filtering—to enforce logic-consistent reasoning. The objective is to maximize alignment of the LLM's next-token distribution with structured knowledge, formalized as $\igl\{ s_{+}^{e^{topic}} \bigr\} \propto \mathcal{D}_{q,G} \sim {\underset{\mathcal{D}_{\theta}}{argmax}} P_{\theta}(a|q,G)$. Empirical results across multiple KGQA benchmarks (including WebQSP, CWQ, GrailQA, and Simple Questions) show state-of-the-art performance, with ablations confirming the necessity of both logits strengthening and filtering. The method transfers robustly to unseen KBs (QALD10-en, T-REx, Zero-shot RE) and various tasks (multi-hop, single-hop, slot filling), while demonstrating favorable efficiency characteristics such as reduced token counts and near one-API-call inference in some settings. Overall, Logits-to-Logic provides a flexible, transferable approach to achieve logic-consistent structured knowledge reasoning in LLMs, with practical implications for trustworthy KGQA systems.

Abstract

Large Language Models (LLMs) achieve excellent performance in natural language reasoning tasks through pre-training on vast unstructured text, enabling them to understand the logic in natural language and generate logic-consistent responses. However, the representational differences between unstructured and structured knowledge make LLMs inherently struggle to maintain logic consistency, leading to \textit{Logic Drift} challenges in structured knowledge reasoning tasks such as Knowledge Graph Question Answering (KGQA). Existing methods address this limitation by designing complex workflows embedded in prompts to guide LLM reasoning. Nevertheless, these approaches only provide input-level guidance and fail to fundamentally address the \textit{Logic Drift} in LLM outputs. Additionally, their inflexible reasoning workflows cannot adapt to different tasks and knowledge graphs. To enhance LLMs' logic consistency in structured knowledge reasoning, we specifically target the logits output from the autoregressive generation process. We propose the \textit{Logits-to-Logic} framework, which incorporates logits strengthening and logits filtering as core modules to correct logical defects in LLM outputs. Extensive experiments show that our approach significantly improves LLMs' logic consistency in structured knowledge reasoning and achieves state-of-the-art performance on multiple KGQA benchmarks.

Figures (8)

• Figure 1: Logic Drift ratio of current approaches.
• Figure 2: Logic Drift in LLM's output. Orange highlights reasoning paths/tokens semantically irrelevant to the question's logic. Gray highlights reasoning paths/tokens inconsistent with structured KG logic (i.e., hallucinated paths that LLMs output but don't exist in the KG).
• Figure 3: Overview of our Logits-to-Logic framework.
• Figure 4: Left: Error analysis of Logits-to-Logic and advanced methods ToG, DoG, KG-CoT, and GCR. Lighter colors indicate Question-Inconsistent Logic Drift, while darker colors indicate KG-Inconsistent Logic Drift. Right: Impact of strength value in the logits strengthening module on reasoning performance.
• Figure 5: Visualization of LLMs output logits distribution and question, KG logical distributions. X-axis shows reasoning steps, Y-axis shows token logits rankings. Red colors indicate higher logits values. Green-bordered textured boxes are desired correct tokens (logically consistent with question and KG). We want green boxes to rank higher with redder colors.