Current logical reasoning evaluations of Large Language Models (LLMs) primarily focus on single-turn and static environments, such as arithmetic problems. The crucial problem of multi-turn, strategic reasoning is under-explored. In this work, we analyze the multi-turn strategic reasoning of LLMs through text-driven complete- and incomplete-information gaming, e.g., board games (Tic-Tac-Toe, Connect-4) and poker games (Texas Hold’em Poker). Specifically, we consider two distinct scenarios: 1) Online Racing, featuring multiple LLMs/agents to facilitate direct competition and comparison; 2) Offline Probing, constructing targeted questions with verified ground truth to evaluate LLMs’ strategic behaviors. Experimental results demonstrate that existing state-of-the-art LLMs and reasoning schemes are largely ineffective for strategic reasoning tasks. To mitigate these limitations, we propose a simple yet effective Recursively Thinking-Ahead (ReTA) agent, incorporating a recursive prompting mechanism that automatically analyzes the opponents’ future moves/actions and assigns reward signals for these situations, to strengthen the strategic reasoning of LLMs. We hope our work could spur further research and exploration in the multi-turn strategic reasoning of LLMs. The code is available at https://github.com/jinhaoduan/ReTA.

Large Language Models (LLMs) show promising results in language generation and instruction following but frequently “hallucinate”, making their outputs less reliable. Despite Uncertainty Quantification’s (UQ) potential solutions, implementing it accurately within LLMs is challenging. Our research introduces a simple heuristic: not all tokens in auto-regressive LLM text equally represent the underlying meaning, as “linguistic redundancy” often allows a few keywords to convey the essence of long sentences. However, current methods underestimate this inequality when assessing uncertainty, causing tokens with limited semantics to be equally or excessively weighted in UQ. To correct this, we propose Shifting Attention to more Relevant (SAR) components at both token- and sentence-levels for better UQ. We conduct extensive experiments involving a range of popular “off-the-shelf” LLMs, such as Vicuna, WizardLM, and LLaMA-2-chat, with model sizes extending up to 33B parameters. We evaluate various free-form question-answering tasks, encompassing domains such as reading comprehension, science Q&A, and medical Q&A. Our experimental results, coupled with a comprehensive demographic analysis, demonstrate the superior performance of SAR. The code is available at https://github.com/jinhaoduan/SAR.