Artificial intelligence systems based on neural networks—such as ChatGPT, Claude, DeepSeek or Gemini—are extraordinarily ...

Researchers use statistical physics and "toy models" to explain how neural networks avoid overfitting and stabilize learning in high-dimensional spaces.

Last week, Google Research held an online workshop on the conceptual understanding of deep learning. The workshop, which featured presentations by award-winning computer scientists and neuroscientists ...

A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used ...

In Chapter 1, verification is defined as the process of determining how accurately a computer program (“code”) correctly solves the equations of a mathematical model. This includes code verification ...

You can probably think of a time when you’ve used math to solve an everyday problem, such as calculating a tip at a restaurant or determining the square footage of a room. But what role does math play ...

In addition to ascertaining that the internal vitality of the mathematical sciences is excellent, as illustrated in Chapter 2, the current study found a striking expansion in the impact of the ...