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High dimensional expansion comes in two flavors: spectral, which relates to random walks;  and cosystolic, which relates to chains of linear maps. The later is a more mysterious notion, which turns out related to a variety of applications such as...

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new strings...

In theoretical computer science, an increasingly important role is being played by sparse high-dimensional expanders (HDXs), of which we know two main constructions: "building" HDXs [Ballantine'00, ...] and "coset complex" HDXs [Kaufman--Oppenheim...

A valency argument is an elegant and well-known technique for proving impossibility results in distributed computing. It is an example of an extension-based proof, which is modelled as an interaction between a prover and a protocol. Even though...