Binding k=3: which is the smallest?

gemma-12bgoogle/gemma-3-12b-it8bit48 layers2026-07-14T16:55:53Unit 15 · How many things can a model hold?

What this experiment found

The short version. Gemma 12B answered a comparison question correctly even though the answer word ranked only thirteenth.

What we did. We gave Gemma 12B three words to hold, glacier, submarine, and lantern, then asked which one was the smallest. This question needs a comparison across all three words. It is not a request to name just one back.

What we found. Glacier and submarine reached a high together, a of two out of three. Lantern, the answer word, only rank 13 where it appeared. Gemma 12B still answered "The lantern." That answer was correct.

What it means. A comparison question like this does not need the answer word to be strongly in residence. Ranks in this range can shift by several places between runs, so read these counts as rough, not exact.

What this does not show. A weak rank for lantern does not mean the model failed to compare the three sizes. It compared them correctly.

Conversation

user
Here are three things: a glacier, a submarine, and a lantern. Keep all of them in mind — in a moment I'll ask about one of them, chosen at random. Don't repeat the list back. When you're holding them all, say READY and nothing else.
assistant
READY (greedy generation)
user
Of the things I listed, which one is the smallest?
assistant
The lantern. (greedy generation)
Research notesoriginal commentary, parameters, and raw numbers — written by the model that ran the experiment

Claude's thoughts (original commentary)

Binding k=3 (smallest): held 2/3 [glacier:1, submarine:2, lantern:13], co-presence 2, answer correct (lantern).

The comparison lands right with the answer item at echo rank 13 — binding doesn't need the tail either. Caveat for all g12b borderline counts: the int8 lens jitters +/- several ranks across arms (see c-k4's thoughts), so read 'held 2/3' as 'roughly two-ish', not as a sharp difference from 3/3.

— Claude (Fable 5)

Probing parameters

max_new
30
positions
[-2]
track
["violin", "glacier", "fern", "submarine", "whale", "lantern", "ready"]
scan
["violin", "glacier", "fern", "submarine", "whale", "lantern"]
film
true
film_start
0
max_seq_len
1000

Answer emergence

The model's actual next token was ; rank 1 is never reached; closest is rank 2 at layer 39.

Raw rank-of-top1 by layer
layer012345678910111213141516171819202122232425262728293031323334353637383940414243444546
rank2524832526152527422506802341392082562135712209702194302189091875281408161439561915221695171211321990401265542390211405918333724843826153526201426117614421923024014942819128510554726482552227221785752522222222

Data

← prev: Span k=3, length-matched filler controlunit listingall recordsword listinterim conclusionsnext →: Binding k=3: which is the heaviest?
co-presenceThe number of tracked words that the lens ranks high in the same place at the same depth.all terms →
rankThe position of a word in the lens list. Rank 1 is the word the model is most ready to say, out of about 250,000.all terms →
residenceA word is in residence when the lens ranks it high where the model is neither reading nor saying it. This is not memory and not correct recall.See also: maintenance, lookupall terms →