Markov chain

A Markov chain decides what happens next by looking only at the current state, completely ignoring the path that led there. Think of forecasting tomorrow's rain by looking only at today's weather, with no regard for what happened yesterday or the day before.

The appeal of this approach is its simplicity. Instead of remembering and weighing the entire past, you only need to look at the single preceding state, which makes guessing the next step much faster. In AI systems that generate text character by character, this kind of calculation is used to quickly guess the next character based on just the few characters right before it.

In practice, though, this simple rule is usually layered and refined by combining multiple such rules, so that the model captures some influence from several nearby elements rather than relying on just one immediately preceding state.

In the article about Liquid AI's DSpark, the draft model is described as using "a lightweight sequential head that recovers dependencies between neighboring tokens via a rank-256 Markov chain to boost acceptance rates in the latter part of a block." It's easy to mistake the Markov chain here for some cutting-edge AI technique introduced in this article, but it's actually a concept that has long been used in probability and statistics, applied here as just one of several components for speeding things up.

Try asking a chatbot this to get a feel for it: "Build a very simple text generator that predicts the next word based only on the single preceding word's probabilities, and explain why this approach produces fast but unnatural-sounding sentences." The answer will give you a sense of how much memory of the past trades off against speed and naturalness.