Yixuan Liu

A rough sketch of a portrait: a few confident lines define the shape, but the details are not yet refined. That is how a parametric model, such as vector autoregression (VAR), describes a time series: it captures the main structure, but if the real data deviate from its assumptions, the portrait comes out distorted.

A language model is a multi-layered structure where each layer processes words in its own way. At the start of training, layers are chaotic, but gradually they organize into two teams. The first team works simply: its internal geometry smooths out, becoming less tangled. The second remains complex and intricate.

An ordinary free-electron laser is like a musical instrument with a single string: it can play only one note until you change its design. To get a different wavelength, you have to retune magnets or accelerate electrons harder. That's expensive and bulky.