# 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.