Core Viewpoint - Salesforce AI Research has introduced two open-source tools, Elastic Reasoning and Fractured Sampling, which significantly enhance the efficiency and accuracy of large language models (LLMs) in reasoning tasks. Group 1: Elastic Reasoning - Elastic Reasoning replaces the traditional "think as you go" approach with a "think as much as you can, answer as much as you can" method, resulting in a 30% reduction in output time while maintaining or even improving accuracy [1][4]. - This method explicitly separates the reasoning process into thinking and problem-solving phases, allowing for token budget allocation for each phase [7][8]. - The model trained using this method, E1-Math-1.5B, achieved a 35.0% accuracy rate on the Math dataset, significantly outperforming the previous model L1, which had a 27.1% accuracy [13]. Group 2: Fractured Sampling - Fractured Sampling allows models to "think less and answer sooner," redefining the cost-performance frontier of reasoning by enabling strong inference with lower computational costs [2][4]. - This method samples across three dimensions: the number of reasoning paths (n), the number of answers per path (m), and the depth of thinking (H), with a focus on optimizing H for better performance [21][26]. - Experiments showed that increasing the thinking depth (H) was more effective in improving accuracy than changing the number of answers (m), with a slight accuracy increase observed when H was set to 16 compared to the standard setting [29].