The speaker's motivation is to identify when a neural network represents a clean algorithmic structure and distinguish algorithmic computation from lookup-table behavior.

“We want to know when,”

“like if a network is representing something as a sort of clean algorithmic structure,”

“like we want to know and what distinguishes like an algorithm from,”

“you know, a lookup table, say.”

“is that it's sort of it's like the difference between sort of zero-th and first-order logic like it quantifies there's there's a there's a space over which it has coherent operation and if you can't learn space if you can't learn subspaces like this then you will never be able to like properly understand like which which things are algorithmic and which things are sort of look-up table like”

“So that's sort of the deep motivation here is how do we find out like true algorithmic structure when it exists?”