# A Dual Representation of Influence Functions for Linearizable Models

arXiv: https://arxiv.org/abs/2605.11239 · HTML: https://mlsanity.com/paper/2605.11239/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 13 of 13)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Certified Data Removal from Machine Learning Models](https://mlsanity.com/paper/1911.03030/) (2019)
- [Studying Large Language Model Generalization with Influence Functions](https://mlsanity.com/paper/2308.03296/) (2023)
- [A Survey of Machine Unlearning](https://mlsanity.com/paper/2209.02299/) (2022)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [Neural Tangents: Fast and Easy Infinite Neural Networks in Python](https://mlsanity.com/paper/1912.02803/) (2019)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [Infinite attention: NNGP and NTK for deep attention networks](https://mlsanity.com/paper/2006.10540/) (2020)
- [Fast Finite Width Neural Tangent Kernel](https://mlsanity.com/paper/2206.08720/) (2022)
- [On the infinite width limit of neural networks with a standard parameterization](https://mlsanity.com/paper/2001.07301/) (2020)
- [Fast Neural Kernel Embeddings for General Activations](https://mlsanity.com/paper/2209.04121/) (2022)

## Built on by (most cited first, 1 of 1)

- [Estimating Population-Risk Curves Along Nonconvex Gradient Flows from the Training Sample](https://mlsanity.com/paper/2608.30261/) (2026)

## Abstract (arXiv)

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.