Their representation is a key-value store that they embed via a tensor product to reconstruct the vectors the model produces. The catch is that it works best if the key-value mapping is task-specific. So if you already know how to solve the task the model is performing and can transform the input into a data structure that makes it easy to just read off the answer, you can probably also recover the model output.

That in itself is of course not super useful for tasks that we don't already know to do symbolically, but it's nice to see that they can manipulate the keys and values of their representation somewhat independently. So at least some of what LLMs do internally seems to involve a bit more structure than just linear combinations of some overcomplete dictionary.

The interesting question is whether this can be used to interpret the operation of a single layer by lifting it to operate on key-value stores instead, replacing matrix-vector products with reading from some keys and then writing to others. That could potentially move the balance of power more towards CPU inference instead of GPUs.