Clustered Influence Functions

Miklós Máté Badó, Kristian Fenech
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:4844-4865, 2026.

Abstract

Influence functions are a standard tool for data debugging and unlearning, but they become impractical for high-query subset workloads such as large-$K$ cross-validation, repeated resampling, or interactive what-if analysis as each subset query typically requires an expensive inverse-curvature solve. We introduce Clustered Influence Functions (CiF), which turns subset influence into an amortized subset oracle. We build a compact cache once by clustering training gradients, solve a damped Generalised Gauss-Newton system only for cluster means, and answer new subset queries by a linear recombination using cluster membership counts. This yields per-query cost of $O(Cp)$ linear in the cache size $C$, and the number of model parameters $p$. We further provide a diagnostic error bound that decomposes approximation error into a clustering scatter term and a solver residual term, making the accuracy-compute tradeoff explicit through the cache budget and solver tolerance. Evaluations across MNIST, CIFAR-10 show that CiF matches per-query influence rankings while significantly reducing the total runtime in high-$Q$ regimes, enabling influence-based workflows that are otherwise computationally prohibitive.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-bado26a, title = {Clustered Influence Functions}, author = {Bad\'{o}, Mikl\'{o}s M\'{a}t\'{e} and Fenech, Kristian}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {4844--4865}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/bado26a/bado26a.pdf}, url = {https://proceedings.mlr.press/v306/bado26a.html}, abstract = {Influence functions are a standard tool for data debugging and unlearning, but they become impractical for high-query subset workloads such as large-$K$ cross-validation, repeated resampling, or interactive what-if analysis as each subset query typically requires an expensive inverse-curvature solve. We introduce Clustered Influence Functions (CiF), which turns subset influence into an amortized subset oracle. We build a compact cache once by clustering training gradients, solve a damped Generalised Gauss-Newton system only for cluster means, and answer new subset queries by a linear recombination using cluster membership counts. This yields per-query cost of $O(Cp)$ linear in the cache size $C$, and the number of model parameters $p$. We further provide a diagnostic error bound that decomposes approximation error into a clustering scatter term and a solver residual term, making the accuracy-compute tradeoff explicit through the cache budget and solver tolerance. Evaluations across MNIST, CIFAR-10 show that CiF matches per-query influence rankings while significantly reducing the total runtime in high-$Q$ regimes, enabling influence-based workflows that are otherwise computationally prohibitive.} }
Endnote
%0 Conference Paper %T Clustered Influence Functions %A Miklós Máté Badó %A Kristian Fenech %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-bado26a %I PMLR %P 4844--4865 %U https://proceedings.mlr.press/v306/bado26a.html %V 306 %X Influence functions are a standard tool for data debugging and unlearning, but they become impractical for high-query subset workloads such as large-$K$ cross-validation, repeated resampling, or interactive what-if analysis as each subset query typically requires an expensive inverse-curvature solve. We introduce Clustered Influence Functions (CiF), which turns subset influence into an amortized subset oracle. We build a compact cache once by clustering training gradients, solve a damped Generalised Gauss-Newton system only for cluster means, and answer new subset queries by a linear recombination using cluster membership counts. This yields per-query cost of $O(Cp)$ linear in the cache size $C$, and the number of model parameters $p$. We further provide a diagnostic error bound that decomposes approximation error into a clustering scatter term and a solver residual term, making the accuracy-compute tradeoff explicit through the cache budget and solver tolerance. Evaluations across MNIST, CIFAR-10 show that CiF matches per-query influence rankings while significantly reducing the total runtime in high-$Q$ regimes, enabling influence-based workflows that are otherwise computationally prohibitive.
APA
Badó, M.M. & Fenech, K.. (2026). Clustered Influence Functions. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:4844-4865 Available from https://proceedings.mlr.press/v306/bado26a.html.

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