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 analysed mathematically using the tools of statistical physics.

“Toy models”, like the one presented in the study just published in the Journal of Statistical Mechanics: Theory and Experiment (JSTAT), provide researchers with a controlled theoretical laboratory for investigating the fundamental mechanisms of neural networks. A deeper understanding of how these systems work could help design artificial intelligence systems that are more efficient and reliable, while also addressing some of the current challenges.

A model developed by Washington State University researchers can predict how transmission towers might fail and collapse in extreme wind events. The work, reported in the journal, Engineering Structures, could someday help power companies identify the most vulnerable transmission towers in extreme wind events and determine which should have retrofits to reduce the power outage risks.