Interactive lab

The grid explorer

How to read the toy

Start by fixing the mental model: rows are possible training worlds and columns are evaluation slices. Once that is in place, the rest of the interface is about moving between nearby rows, nearby columns, or nearby perturbations and asking what changed.

How to read this grid

Rows are training worlds, columns are evaluation slices, and the rings only mark the cells used by the current comparison.

Simple modeReference gridShapley valueShapley phi: 0.5208
Question
Focus tokensi
Single-point modes keep one focus chip active so the question stays about one contributor at a time.
Scene
Training worldi
Evaluation slicei
Toy universe sizei
4
Cell scorei
Current score means: overlap divided by union.
Workspace
Reference gridShapley valueReference grid locked
Stay here when you want the cleanest distillation: one reference grid, the essential scene controls, and the explanation of the active question.
PresetsGuided starts
5 built in
Load a preset to jump straight to a useful scene instead of building one from scratch.
Active questionAverage one point's marginal contribution across many worlds
Shapley phi: 0.5208

Across every partial training world and fixed eval A, how much does adding A help on average?

8 row-pairs contribute to this estimate. The rings show the exact before-and-after comparisons.
Train world
A
Evaluation slice
A
Focus
A
Score rule
Jaccard
Selected cell
1.000
f(A, A)
Shapley phi
0.5208
8 row-pairs contribute to this estimate. The rings show the exact before-and-after comparisons.
Pair count
8
Matched partial worlds with and without A.
Counterfactual grid

Rows are worlds; columns are slices.

JaccardTrain AEval AShapley value
0∅
1A
2B
3C
4D
5AB
6AC
7AD
8BC
9BD
10CD
11ABC
12ABD
13ACD
14BCD
15ABCD
0∅
1A
2B
3C
4D
5AB
6AC
7AD
8BC
9BD
10CD
11ABC
12ABD
13ACD
14BCD
15ABCD
On the active evaluation column, amber rings mark partial worlds S and cyan rings mark the matching worlds S + A.
White outline: selected cell. Ochre ring: comparison source. Sage ring: comparison partner.
Axis labels: each header shows the subset id and the specific instance letters in that world or slice.
Shapley phi(A) averages the marginal change from adding A across 8 paired rows on eval A.
Inspector

Statistic details

Shapley value
Average many local moves
Shapley does not trust any single row pair. Instead it walks through every partial world on the active evaluation slice and averages the marginal contribution of the focus point.
Shapley phi(A) averages the marginal change from adding A across 8 paired rows on eval A.
Focus pointA
Evaluation sliceA
phi0.5208
Paired worlds8
|S|Avg marginal delta#pairs
01.00001
10.50003
20.33333
30.25001
Reading help

Quick answers stay nearby so you can recover the mental model without leaving the grid.

Why are there so many rows and columns?
This toy enumerates every subset of A, B, C, and so on so you can see the whole space of training worlds and evaluation slices. Real systems rarely compute the full grid; the powerset here is a teaching scaffold.
What is the difference between the focus chips and the selected row?
The row chooses which training world you are looking at right now. The focus chips choose which point or group the question talks about. Picking B does not move you to row B; it tells leave-one-out, group, or Shapley views which member to value.
Do I need to read every highlighted cell?
No. Start with the selected row, selected column, and question card. The amber and cyan rings only mark the cells the current statistic compares, so they are there to narrow your attention rather than widen it.
Why do some answers come out as zero?
A zero often means the selected point or group is not actually present in the chosen training world, so removing it changes nothing. In scaling mode, the headline average may also stay flat when many same-size worlds behave similarly.
What changes in Operator view?
Operator view applies toy edits like poisoning or added noise before the grid is rendered. Real world always shows the untouched reference matrix, even if the edit toggles are still switched on.