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PreprintCC BY 4.0arXiv

A Dual Representation of Influence Functions for Linearizable Models

  • Zhenhuan Sun
  • Shahrokh Valaee
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Abstract

In this paper, we present a dual representation of influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an efficient alternative to the original influence functions for estimating changes in parameters, model outputs and loss due to data point removal, when model size is large relative to dataset size, or when evaluating the original influence functions in parameter space is infeasible. The dual representation, however, is limited to linearizable models, which are models whose behavior can be approximated by their linearizations throughout training, and requires materializing a matrix, whose size grows with the product of model output dimension and dataset size.

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Cite

BibTeXRIS
BibTeX
@misc{sun2026dual,
  title = {{A Dual Representation of Influence Functions for Linearizable Models}},
  author = {Zhenhuan Sun and Shahrokh Valaee},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.11239},
  eprint = {2605.11239},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.11239},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Dual Representation of Influence Functions for Linearizable Models
AU  - Zhenhuan Sun
AU  - Shahrokh Valaee
PY  - 2026
DA  - 2026/09/25
PB  - arXiv
DO  - 10.48550/arxiv.2605.11239
UR  - https://arxiv.org/abs/2605.11239
AB  - In this paper, we present a dual representation of influence functions, whose computational complexity scales with dataset size rather than model size. Both analytically and experimentally, we show that this representation can be an efficient alternative to the original influence functions for estimating changes in parameters, model outputs and loss due to data point removal, when model size is large relative to dataset size, or when evaluating the original influence functions in parameter space is infeasible. The dual representation, however, is limited to linearizable models, which are models whose behavior can be approximated by their linearizations throughout training, and requires materializing a matrix, whose size grows with the product of model output dimension and dataset size.
ER  -