Expanding Search Space with Diverse Prompting Agents: An Efficient Sampling Approach for LLM Mathematical Reasoning

Large Language Models (LLMs) have exhibited remarkable capabilities in many complex tasks including mathematical reasoning. However, traditional approaches heavily rely on ensuring self-consistency within single prompting method, which limits the exploration of diverse problem-solving strategies. This study addresses these limitations by performing an experimental analysis of distinct prompting methods within the domain of mathematical reasoning. Our findings demonstrate that each method explores a distinct search space, and this differentiation becomes more evident with increasing problem complexity. To leverage this phenomenon, we applied efficient sampling process that uniformly combines samples from these diverse methods, which not only expands the maximum search space but achieves higher performance with fewer runs compared to single methods. Especially, within the subset of difficult questions of MATH dataset named MATH-hard, The maximum search space was achieved while utilizing approximately 43% fewer runs than single methods on average. These findings highlight the importance of integrating diverse problem-solving strategies to enhance the reasoning abilities of LLMs.

Towards Efficient Visual-Language Alignment of the Q-Former for Visual Reasoning Tasks

Recent advancements in large language models have demonstrated enhanced capabilities in visual reasoning tasks by employing additional encoders for aligning different modalities. While the Q-Former has been widely used as a general encoder for aligning several modalities including image, video, audio, and 3D with large language models, previous works on its efficient training and the analysis of its individual components have been limited. In this work, we investigate the effectiveness of parameter efficient fine-tuning (PEFT) the Q-Former using InstructBLIP with visual reasoning benchmarks ScienceQA and IconQA. We observe that applying PEFT to the Q-Former achieves comparable performance to full fine-tuning using under 2% of the trainable parameters. Additionally, we employ AdaLoRA for dynamic parameter budget reallocation to examine the relative importance of the Q-Former's sublayers with 4 different benchmarks. Our findings reveal that the self-attention layers are noticeably more important in perceptual visual-language reasoning tasks, and relative importance of FFN layers depends on the complexity of visual-language patterns involved in tasks. The code is available at https://github.com/AttentionX/InstructBLIP_PEFT.