Some questions require a small image region; others require a long path or several separated regions. In this experiment, coding agents receive requests about the size and shape of the regions their inverse programs use. We measure these regions by masking parts of the image.
Three scales × three shapes
Rows describe spatial extent. Columns describe geometry. Select a cell to see recorded examples from worlds with that measured pattern.
The colored shapes are schematic illustrations of each pattern, not measurements. A pattern can occur anywhere in an image.
Which labeled tile contains a completely filled 2-by-2 cyan square? Answer A, B, C, or D.
C
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which half of the centered dashboard visibly contains the steering wheel? Answer left or right.
left
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Does the one dark track contain a closed route? Ignore the colored dots. Answer yes or no.
yes
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
The dark trail is one connected thin stroke. How many separate pale pockets does its complete route enclose: one pocket or two pockets?
one pocket
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Do the two visible irises have the same color? Answer yes or no.
yes
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Do the top coral interval and bottom blue interval share any horizontal values? Answer yes or no.
yes
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which symbol is hidden by the texture: a circle or a diamond?
circle
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Apply the marked clockwise spiral and adjacent-pair XOR. Is the resulting bitmap A) LOOP or B) DIAMOND? Answer A or B.
A
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which colored bead lies on the only closed loop of the cyan rail?
violet
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
How many times does the cyan trace cross the dashed reference line? Answer with a number.
4
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which labeled card has four cyan dots at the corners of a rectangle? Answer A, B, C, or D.
C
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
How many complete colored rings are visible in the sports emblem? Count each colored closed loop once.
4
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Do all four arms of the single colored plus sign extend equally far from its center? Answer yes or no.
yes
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which candidate has the same five-station height profile as the reference when read from right to left?
A
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Trace the navy route. Which matching-color checkpoint pair is farther apart when distance is measured along the route: cyan or orange?
cyan
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Following the single dark cord from START to END, do the five large colored beads read the same forward and backward? Answer yes or no.
yes
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which color has the same left-to-right rank in both strips? Answer red, teal, or violet.
red
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
Which candidate has the same complete clockwise bead-color order as R after its left-right reflection?
B
The world matched its requested pattern. 100% pattern agreement across 6 measured scenes.
These examples come from worlds that passed replay and had complete measurements, a stable pattern, and a pattern matching the request. Each label summarizes measurements across several scenes. The individual image shown here may have a different measured pattern.
How patterns are measured
The pattern grid above has 3×3 cells. The measurement below uses a separate 8×8 probe grid to test regions of each image.
Select a square to see which region would be masked.
This illustration shows the mask location only. It does not run the inverse program or show whether masking that region changes its answer.
Run the inverse program on the unmodified image.
Replace pixels with the median color of the image’s outer three-pixel border. Each probe extends one quarter-cell beyond its nominal boundary on every side.
A position is affected if the answer changes or the inverse raises an error. An error on a masked image is evidence of sensitivity; an error on an unmodified verification image still fails verification.
Measure the extent and shape of affected positions. Repeat across four to six distinct scenes, then aggregate their geometry to assign a world-level pattern.
Focal: normalized span below 0.30.
Regional:
0.30 to below 0.65.
Distributed: 0.65 or
above.
Multipart: at least two four-connected
components.
Pathlike: otherwise, elongation ≥
2.75 or bounding-box fill ≤ 0.55 with nonzero span.
Compact:
all remaining cases.
Four-connected positions share a horizontal or vertical edge. Elongation describes how stretched the affected region is; fill measures how much of its bounding box is occupied. These rules operate on measured probe geometry, not on the objects’ semantic meaning.
Complete measurement: at least two thirds of analyzed scenes expose an affected region. Stable pattern: at least two thirds of all analyzed scenes receive the aggregate pattern. The world pattern uses median geometry across scenes; completeness and stability are separate conditions.
From measurement to generation
The controller chooses a target pattern before an episode. The coding agent receives the request alongside its reasoning instructions, implementation demonstrations, and campaign history.
An example request for where the answer’s evidence should lie.
The agent writes the question, sampler, renderer, forward program, and inverse program.
A separate masking analysis assigns the observed pattern.
A mismatch does not reject a world that otherwise passes acceptance. A rejected submission can still receive a pattern measurement.
The controller keeps at most three worlds per pattern. Its fixed request rule favors patterns with fewer stored worlds, more past target matches or fewer observations, and patterns not requested in the preceding episode. It penalizes repeated misses.
Because the controller keeps at most three worlds per pattern, these stored examples are far fewer than all accepted worlds.
Observed results
| Population | Total | Measured | Matches | Match rate |
|---|---|---|---|---|
| All episodes | 1,179 | 981 | 918 | 93.6% |
| Accepted worlds | 903 | 902 | 860 | 95.3% |
| Replay-verified worlds | 875 | 874 | 835 | 95.5% |
Match rates use the measured population as their denominator. One replay-verified world had an incomplete measurement. Steered campaigns produced 3.35 accepted worlds per episode-hour, compared with 4.95 without steering.
Steered and unsteered campaigns were run separately, so these differences in coverage and throughput are descriptive, not causal. Masking shows which regions the inverse program depends on, not which regions a person needs.
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