Datasets:
Predicting the activation VALUE, not just whether it fires
prog_L06F08045_value.py — the George feature (GPT-2 small, layer 6
resid_pre, feature 8045) as a program that returns a number instead of a
1, because the magnitude turns out to encode which George is meant:
"...under President [George] W. Bush..." ~50 the US president
"...Chancellor [George] Osborne..." ~40 a notable public figure
"...[King George] III..." ~30 royalty
"...Russell Westbrook, Paul [George]..." ~20 the NBA player
"...the [St George] flag..." ~15 a place name
The binary gate is unchanged from the last-token program, so its F1 is identical; only the returned number is new.
Scores, disjoint test data
| canonical 10k test split | 12k trigger-enriched sample | |
|---|---|---|
| binary F1 | 0.9721 | 0.9951 |
| value R² (on firing positions) | 0.6782 | 0.6858 |
| value MAE | 6.24 | 5.66 |
| MAE, always-emit-the-mean | 10.88 | 9.97 |
| R² over all positions | 0.9535 | 0.9598 |
R² here is over positions where the feature truly fires, so the plain binary
program scores exactly 0 on it — emitting the feature's mean is
predicting the mean. That makes it a clean 0-to-1 scale on the thing being
added. R² over all positions is also given, but firings are under 1% of
positions so it starts at 0.87 for the binary program and flatters it.
How good is 0.68?
- A gradient-boosted model over the same left-context information scores 0.616 — worse than this readable rule, while overfitting (train 0.842).
- The same model allowed to peek at the following token scores 0.834.
So most of the remaining error is the surname — "George W. Bush" vs "George" ending a sentence — which sits to the right of the trigger and no left-context program can see. The practical ceiling for a legal rule is ~0.70.
Honest note on how the constants were set
The structure (which words belong to which sense group, the 5-token window, the fading weights) was read off the data by hand. The numbers (the base values, the six point levels, the repeat drop) were fitted by least squares on train. Hand-picked constants scored 0.648; fitted ones score 0.678.