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arXiv · 2506.20481

Counterfactual Influence as a Distributional Quantity

Matthieu Meeus·Igor Shilov·Georgios Kaissis·Yves-Alexandre de Montjoye
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Abstract

Machine learning models are known to memorize samples from their training data, raising concerns around privacy and generalization. Counterfactual self-influence is a popular metric to study memorization, quantifying how the model's prediction for a sample changes depending on the sample's inclusion in the training dataset. However, recent work has shown memorization to be affected by factors beyond self-influence, with other training samples, in particular (near-)duplicates, having a large impact. We here study memorization treating counterfactual influence as a distributional quantity, taking into account how all training samples influence how a sample is memorized. For a small language model, we compute the full influence distribution of training samples on each other and analyze its properties. We find that solely looking at self-influence can severely underestimate tangible risks associated with memorization: the presence of (near-)duplicates seriously reduces self-influence, while we find these samples to be (near-)extractable. We observe similar patterns for image classification, where simply looking at the influence distributions reveals the presence of near-duplicates in CIFAR-10. Our findings highlight that memorization stems from complex interactions across training data and is better captured by the full influence distribution than by self-influence alone.

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Matthieu Meeus, Igor Shilov, Georgios Kaissis, Yves-Alexandre de Montjoye. 2025-06-25. Counterfactual Influence as a Distributional Quantity. https://arxiv.org/abs/2506.20481

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