# Representer Point Selection for Explaining Deep Neural Networks

arXiv: https://arxiv.org/abs/1811.09720 · HTML: https://mlsanity.com/paper/1811.09720/

## Key facts

- Cited by 187 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Nov 2018.

## Built on by (most cited first, 30 of 187)

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- [Scaling Up Influence Functions](https://mlsanity.com/paper/2112.03052/) (2021)
- [Human-Centered Explainable AI (XAI): From Algorithms to User Experiences](https://mlsanity.com/paper/2110.10790/) (2021)
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- ["Help Me Help the AI": Understanding How Explainability Can Support Human-AI Interaction](https://mlsanity.com/paper/2210.03735/) (2022)
- [Post hoc Explanations may be Ineffective for Detecting Unknown Spurious Correlation](https://mlsanity.com/paper/2212.04629/) (2022)
- [PUMA: Performance Unchanged Model Augmentation for Training Data Removal](https://mlsanity.com/paper/2203.00846/) (2022)
- [Leveraging Explanations in Interactive Machine Learning: An Overview](https://mlsanity.com/paper/2207.14526/) (2022)
- [Simfluence: Modeling the Influence of Individual Training Examples by Simulating Training Runs](https://mlsanity.com/paper/2303.08114/) (2023)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [Measuring the Effect of Training Data on Deep Learning Predictions via Randomized Experiments](https://mlsanity.com/paper/2206.10013/) (2022)
- [Interactive Label Cleaning with Example-based Explanations](https://mlsanity.com/paper/2106.03922/) (2021)
- [Intriguing Properties of Data Attribution on Diffusion Models](https://mlsanity.com/paper/2311.00500/) (2023)
- [The Journey, Not the Destination: How Data Guides Diffusion Models](https://mlsanity.com/paper/2312.06205/) (2023)
- [Revisiting Methods for Finding Influential Examples](https://mlsanity.com/paper/2111.04683/) (2021)
- [HYDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks](https://mlsanity.com/paper/2102.02515/) (2021)
- [Combining Feature and Instance Attribution to Detect Artifacts](https://mlsanity.com/paper/2107.00323/) (2021)
- [DISSECT: Disentangled Simultaneous Explanations via Concept Traversals](https://mlsanity.com/paper/2105.15164/) (2021)
- [Self-Influence Guided Data Reweighting for Language Model Pre-training](https://mlsanity.com/paper/2311.00913/) (2023)
- [An Empirical Comparison of Instance Attribution Methods for NLP](https://mlsanity.com/paper/2104.04128/) (2021)
- [First is Better Than Last for Language Data Influence](https://mlsanity.com/paper/2202.11844/) (2022)
- [ORCA: Interpreting Prompted Language Models via Locating Supporting Data Evidence in the Ocean of Pretraining Data](https://mlsanity.com/paper/2205.12600/) (2022)

## Abstract (arXiv)

We propose to explain the predictions of a deep neural network, by pointing to the set of what we call representer points in the training set, for a given test point prediction. Specifically, we show that we can decompose the pre-activation prediction of a neural network into a linear combination of activations of training points, with the weights corresponding to what we call representer values, which thus capture the importance of that training point on the learned parameters of the network. But it provides a deeper understanding of the network than simply training point influence: with positive representer values corresponding to excitatory training points, and negative values corresponding to inhibitory points, which as we show provides considerably more insight. Our method is also much more scalable, allowing for real-time feedback in a manner not feasible with influence functions.