Artificial intelligence systems based on neural networks—such as ChatGPT, Claude, DeepSeek or Gemini—are extraordinarily powerful, yet their internal workings remain largely a “black box.” To better understand how these systems produce their responses, a group of physicists at Harvard University has developed a simplified mathematical model of learning in neural networks that can be analyzed mathematically using the tools of statistical physics.Artificial intelligence systems based on neural networks—such as ChatGPT, Claude, DeepSeek or Gemini—are extraordinarily powerful, yet their internal workings remain largely a “black box.” To better understand how these systems produce their responses, a group of physicists at Harvard University has developed a simplified mathematical model of learning in neural networks that can be analyzed mathematically using the tools of statistical physics.[#item_full_content]