Large Language Models (LLMs) have demonstrated impressive capabilities in reasoning tasks, yet their reliance on static prompt structures and limited adaptability to complex scenarios remains a major challenge. In this paper, we propose the **Deductive and Inductive (DID)** method, a novel framework that enhances LLM reasoning by dynamically integrating both deductive and inductive reasoning approaches. Drawing from cognitive science principles, DID implements a dual-metric complexity evaluation system that combines Littlestone dimension and information entropy to precisely assess task difficulty and guide decomposition strategies. DID enables the model to progressively adapt its reasoning pathways based on problem complexity, mirroring human cognitive processes. We evaluate DID’s effectiveness across multiple benchmarks, including the AIW, MR-GSM8K, and our custom Holiday Puzzle dataset for temporal reasoning. Our results demonstrate great improvements in reasoning quality and solution accuracy - achieving 70.3% accuracy on AIW (compared to 62.2% for Tree of Thought), while maintaining lower computational costs.

In the rapidly evolving field of image generation, achieving precise control over generated content and maintaining semantic consistency remain significant limitations, particularly concerning grounding techniques and the necessity for model fine-tuning. To address these challenges, we propose BayesGenie, an off-the-shelf approach that integrates Large Language Models (LLMs) with Bayesian Optimization to facilitate precise and user-friendly image editing. Our method enables users to modify images through natural language descriptions without manual area marking, while preserving the original image’s semantic integrity. Unlike existing techniques that require extensive pre-training or fine-tuning, our approach demonstrates remarkable adaptability across various LLMs through its model-agnostic design. BayesGenie employs an adapted Bayesian optimization strategy to automatically refine the inference process parameters, achieving high-precision image editing with minimal user intervention. Through extensive experiments across diverse scenarios, we demonstrate that our framework outperforms existing methods in both editing accuracy and semantic preservation, as validated using different LLMs including Claude3 and GPT-4.