I'm behind on a couple of posts I've been planning, but am trying to post something every day if possible. So today I'll post a cached fun piece on overinterpreting a random data phenomenon that's tricked me before.

Recall that a random walk or a "drunkard's walk" (as in the title) is a sequence of vectors _x_1, x_2, ldots_ in some _mathbb{R}^n_ such that each _x_k_ is obtained from _x_{k-1}_ by adding noise. Here is a picture of a 1D random walk as a function of time:

A random walk is the "null hypothesis" for any data with memory. If you are looking at some learning process that updates state to state with some degree of stochasticity, seeing a random walk means that your update steps are random and you're not in fact learning. If you graph some collection of activations from layer to layer of a transformer [...]

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