The Core Question
Machine learning models learn from data. But what happens if we change the data?
What if we remove a data point? Add noise? Use a different subset?
A data counterfactual is a "what if" question about training data:
"What would the model's performance be if we trained on different data?"
This simple question connects many different research areas: data valuation, influence functions,
data poisoning, scaling laws, and algorithmic collective action.
The Grid Metaphor
Imagine a giant matrix. Each row represents a possible training set.
Each column represents a possible evaluation set.
Each cell contains the model's performance when trained on that row's data
and evaluated on that column's data.
A tiny example with 4 data points: A, B, C, D
A
B
C
D
AB
0.85
0.72
0.45
0.38
ABC
0.88
0.80
0.75
0.52
ABCD
0.92
0.88
0.85
0.82
ACD
0.78
0.55
0.82
0.80
Rows = training sets, Columns = evaluation points, Cells = performance scores
This grid contains all possible data counterfactuals. Every question about
how data affects performance is answered somewhere in this grid.
Leave-One-Out
The simplest counterfactual: what if we removed one data point?
Compare two rows in the grid—one that includes a point, and one that doesn't.
The difference tells you how much that point matters.
Comparing ABCD vs ACD (leaving out B)
A
B
C
D
ABCD
0.92
0.88
0.85
0.82
ACD
0.78
0.55
0.82
0.80
Gold row = with B, Cyan row = without B. Notice how removing B hurts performance on B.
This is the foundation of influence functions and data attribution—measuring
how much each data point contributes to the model.
From Points to Patterns
Once you understand leave-one-out, you can extend the idea:
- Group effects: What if we remove multiple points together? (Data strikes)
- Shapley values: Average a point's contribution across all possible subsets
- Scaling laws: Average performance across all training sets of size k
- Data poisoning: What if we corrupt points instead of removing them?
- Data selection: Which subset gives the best performance?
All of these are just different ways of navigating the same grid—asking different
counterfactual questions and aggregating the answers differently.
Why It Matters
Data counterfactuals help answer practical questions:
- Data valuation: How much is my data worth to this model?
- Debugging: Which training examples cause this prediction?
- Security: How vulnerable is this model to data poisoning?
- Fairness: How would performance change for different groups?
- Collective action: What leverage do data creators have?
Explore Further
The interactive Grid explorer lets you manipulate a toy dataset and see counterfactual effects in real time.
Try different tutorials, change the focus set, and watch how the grid responds.