Core Insights - The core issue with large language models (LLMs) is not the amount of computational power but how that power is allocated during reasoning tasks [3][6]. - A phenomenon termed "Reasoning Miscalibration" is identified, where models often overthink less critical steps while underthinking crucial ones, leading to inefficiencies in reasoning [6][8]. Theoretical Breakthrough - The Budget Allocation Model (BAM) is proposed, which uses cognitive uncertainty to guide the allocation of computational resources during reasoning [9][14]. - BAM emphasizes that initial reasoning steps, which are often more uncertain, should receive more computational resources, while later steps, which are more certain, should receive less [12][17]. Plan-and-Budget Framework - The Plan-and-Budget framework is introduced as a practical application of BAM, designed to operate during the reasoning phase without requiring additional training [19][20]. - This framework consists of two main steps: planning the problem into structured sub-questions and allocating tokens based on the importance of each step [21][23]. Experimental Results - The Plan-and-Budget framework demonstrates higher pass rates across varying difficulty levels in reasoning tasks compared to traditional methods, indicating improved efficiency and accuracy [30][32]. - The E³ (Efficiency-aware Effectiveness Score) metric is introduced to evaluate reasoning methods, rewarding those that achieve better results with fewer tokens [36][38]. Significance and Outlook - The research highlights that effective reasoning is not solely dependent on computational power but on the strategic use of that power [41][42]. - The shift from focusing on reasoning length to reasoning value suggests a new paradigm in LLM deployment, particularly in cost-sensitive and time-sensitive applications [42][43].