LogicTree: Structured Proof Exploration for Coherent and Rigorous Logical Reasoning with Large Language Models

Large language models (LLMs) have achieved remarkable multi-step reasoning capabilities across various domains. However, LLMs still face distinct challenges in complex logical reasoning, as (1) proof-finding requires systematic exploration and the maintenance of logical coherence and (2) searching the right combination of premises at each reasoning step is inherently challenging in tasks with large premise space. To address this, we propose LogicTree, an inference-time modular framework employing algorithm-guided search to automate structured proof exploration and ensure logical coherence. Advancing beyond tree-of-thought (ToT), we incorporate caching mechanism into LogicTree to enable effective utilization of historical knowledge, preventing reasoning stagnation and minimizing redundancy. Furthermore, we address the combinatorial complexity of premise search by decomposing it into a linear process. The refined premise selection restricts subsequent inference to at most one derivation per step, enhancing reasoning granularity and enforcing strict step-by-step reasoning. Additionally, we introduce two LLM-free heuristics for premise prioritization, enabling strategic proof search. Experimental results on five datasets demonstrate that LogicTree optimally scales inference-time computation to achieve higher proof accuracy, surpassing chain-of-thought (CoT) and ToT with average gains of 23.6% and 12.5%, respectively, on GPT-4o. Moreover, within LogicTree, GPT-4o outperforms o3-mini by 7.6% on average.

Prompt-Based Bias Calibration for Better Zero/Few-Shot Learning of Language Models

Prompt learning is susceptible to intrinsic bias present in pre-trained language models (LMs), resulting in sub-optimal performance of prompt-based zero/few-shot learning. In this work, we propose a null-input prompting method to calibrate intrinsic bias encoded in pre-trained LMs. Different from prior efforts that address intrinsic bias primarily for social fairness and often involve excessive computational cost, our objective is to explore enhancing LMs' performance in downstream zero/few-shot learning while emphasizing the efficiency of intrinsic bias calibration. Specifically, we leverage a diverse set of auto-selected null-meaning inputs generated from GPT-4 to prompt pre-trained LMs for intrinsic bias probing. Utilizing the bias-reflected probability distribution, we formulate a distribution disparity loss for bias calibration, where we exclusively update bias parameters ($0.1\%$ of total parameters) of LMs towards equal probability distribution. Experimental results show that the calibration promotes an equitable starting point for LMs while preserving language modeling abilities. Across a wide range of datasets, including sentiment analysis and topic classification, our method significantly improves zero/few-shot learning performance of LMs for both in-context learning and prompt-based fine-tuning (on average $9\%$ and $2\%$, respectively).