Equation 5 · Part 8 · The Hardest Unsolved Problems in Mechanistic Interpretability
=
=
What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
Leask, Nanda and colleagues then tested the assumption directly with two new techniques, and the result undercuts the idea that there is a “right” dictionary size waiting to be found by scaling further. Stitching the dictionaries of differently sized sparse autoencoders together, they show that larger dictionaries recover latents genuinely missing from smaller ones — the smaller dictionary is incomplete. Training a second, “meta” sparse autoencoder on the decoder directions of a first one, they show that what looks like a single, atomic feature in a large dictionary is itself well approximated by a sparse combination of directions from a smaller one — a reported example decomposes an…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
Open the illustrated equality: what the equals sign claims guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.