大模型的第一性原理：（一）统计物理篇

Core Viewpoint - The article discusses the rapid advancements in large models, particularly in the AI field, highlighting the emergence of models like ChatGPT and DeepSeek, and the anticipated release of Google's Gemini 3, which is seen as a significant step towards Artificial General Intelligence (AGI) and Artificial Super Intelligence (ASI) [2][3]. Group 1: Large Model Developments - The investment in AI in the U.S. has surpassed the GDP of many countries, indicating a booming industry [2]. - DeepSeek has achieved remarkable performance with low training costs, further pushing the boundaries of AI capabilities [2]. - Gemini 3 is expected to challenge NVIDIA's ecosystem with its TPU training paradigm [2]. Group 2: Theoretical Foundations - The research paper "Forget BIT, It is All about TOKEN" aims to combine statistical physics, signal processing, and information theory to better understand the mathematical principles behind large models [4]. - The article emphasizes the need for a comprehensive understanding of large models beyond single-dimensional theories, which have limited insights into their underlying principles [3][4]. Group 3: Memory Capacity and Generalization - The memory capacity of large models increases exponentially with the linear growth of model parameters, suggesting that smaller models can still perform effectively but are prone to collapse if over-trained [8]. - The upper bound of generalization error in large models is linked to the absolute sum of logits, necessitating careful management during model reduction techniques like pruning and distillation [8][34]. Group 4: Causality and Prediction - The article posits that the ultimate goal of large models is to predict the next token, with the Transformer architecture being effective in achieving this [14][36]. - The reasoning behind large model capabilities is tied to Granger causality, indicating that while scaling laws will continue, true logical reasoning and concept abstraction may remain out of reach for these models [36][38]. Group 5: Future Directions - The article outlines plans for a series of articles that will delve deeper into the first principles of large models, focusing on statistical physics, signal processing, and information theory [4][39].