# Sample based Explanations via Generalized Representers

arXiv: https://arxiv.org/abs/2310.18526 · HTML: https://mlsanity.com/paper/2310.18526/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 62 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 30 of 47)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [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)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [Data Shapley: Equitable Valuation of Data for Machine Learning](https://mlsanity.com/paper/1904.02868/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Estimating Training Data Influence by Tracing Gradient Descent](https://mlsanity.com/paper/2002.08484/) (2020)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [Interpretable machine learning: definitions, methods, and applications](https://mlsanity.com/paper/1901.04592/) (2019)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [TRAK: Attributing Model Behavior at Scale](https://mlsanity.com/paper/2303.14186/) (2023)
- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Influence Functions in Deep Learning Are Fragile](https://mlsanity.com/paper/2006.14651/) (2020)
- [On Completeness-aware Concept-Based Explanations in Deep Neural Networks](https://mlsanity.com/paper/1910.07969/) (2019)
- [Datamodels: Predicting Predictions from Training Data](https://mlsanity.com/paper/2202.00622/) (2022)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [Beta Shapley: a Unified and Noise-reduced Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2110.14049/) (2021)
- [The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective](https://mlsanity.com/paper/2202.01602/) (2022)
- [Counterfactual Memorization in Neural Language Models](https://mlsanity.com/paper/2112.12938/) (2021)
- [Explaining Black Box Predictions and Unveiling Data Artifacts through Influence Functions](https://mlsanity.com/paper/2005.06676/) (2020)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [Training Data Influence Analysis and Estimation: A Survey](https://mlsanity.com/paper/2212.04612/) (2022)
- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [A Kernel-Based View of Language Model Fine-Tuning](https://mlsanity.com/paper/2210.05643/) (2022)
- [FastIF: Scalable Influence Functions for Efficient Model Interpretation and Debugging](https://mlsanity.com/paper/2012.15781/) (2020)

## Built on by (most cited first, 10 of 10)

- [Evolving Interpretable Visual Classifiers with Large Language Models](https://mlsanity.com/paper/2404.09941/) (2024)
- [Helpful or Harmful Data? Fine-tuning-free Shapley Attribution for Explaining Language Model Predictions](https://mlsanity.com/paper/2406.04606/) (2024)
- [Interpretation Meets Safety: A Survey on Interpretation Methods and Tools for Improving LLM Safety](https://mlsanity.com/paper/2506.05451/) (2025)
- [Towards Explainable Artificial Intelligence (XAI): A Data Mining Perspective](https://mlsanity.com/paper/2401.04374/) (2024)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [Equivariant Neural Tangent Kernels](https://mlsanity.com/paper/2406.06504/) (2024)
- [Data-centric Prediction Explanation via Kernelized Stein Discrepancy](https://mlsanity.com/paper/2403.15576/) (2024)
- [How Video Meetings Change Your Expression](https://mlsanity.com/paper/2406.00955/) (2024)
- [Integrated Influence: Data Attribution with Baseline](https://mlsanity.com/paper/2508.05089/) (2025)
- [Latent Space Guided Scenario Sampling for Multimodal Segmentation Under Missing Modalities](https://mlsanity.com/paper/2605.20372/) (2026)

## Abstract (arXiv)

We propose a general class of sample based explanations of machine learning models, which we term generalized representers. To measure the effect of a training sample on a model's test prediction, generalized representers use two components: a global sample importance that quantifies the importance of the training point to the model and is invariant to test samples, and a local sample importance that measures similarity between the training sample and the test point with a kernel. A key contribution of the paper is to show that generalized representers are the only class of sample based explanations satisfying a natural set of axiomatic properties. We discuss approaches to extract global importances given a kernel, and also natural choices of kernels given modern non-linear models. As we show, many popular existing sample based explanations could be cast as generalized representers with particular choices of kernels and approaches to extract global importances. Additionally, we conduct empirical comparisons of different generalized representers on two image and two text classification datasets.