Explaining the influence of training data on deep neural network predictions is a critical tool for debugging models through data curation. A recent tractable and appealing approach for this task was provided via the concept of Representer Point Selection (RPS), i.e. a method the leverages the dual form of $l_2$ regularized optimization in the last layer of the neural network to identify the contribution of training points to the prediction. However, two key drawbacks of RPS are that they (i) lead to disagreement between the originally trained network and the RP regularized network modification and (ii) often yield a static ranking of training data for the same class, independent of the data being classified. Inspired by the RPS approach, we propose an alternative method based on a local Jacobian Taylor expansion (LJE) of the Jacobian.We empirically compared RPS-LJE with the original RPS-$l_2$ on image classification (with ResNet), text classification recurrent neural networks (with Bi-LSTM), and tabular classification (with XGBoost) tasks.Quantitatively, we show that RPS-LJE slightly outperforms RPS-$l_2$ and other state-of-the-art data explanation methods by up to 3\% on a data debugging task. Qualitatively, we observe that RPS-LJE provides individualized explanations for each test data point rather than the class-specific static ranking of points in the original approach. Overall, RPS-LJE represents a novel approach to RPS that provides a powerful tool for data-oriented explanation and debugging.

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.

Contributions were made while the author was at the University of Toronto.

Explaining the influence of training data on deep neural network predictions is a critical tool for debugging models through data curation. A recent tractable and appealing approach for this task was provided via the concept of Representer Point Selection (RPS), i.e. a method the leverages the dual form of l_2 regularized optimization in the last layer of the neural network to identify the contribution of training points to the prediction. However, two key drawbacks of RPS are that they (i) lead to disagreement between the originally trained network and the RP regularized network modification and (ii) often yield a static ranking of training data for the same class, independent of the data being classified. Inspired by the RPS approach, we propose an alternative method based on a local Jacobian Taylor expansion (LJE) of the Jacobian.We empirically compared RPS-LJE with the original RPS- l_2 on image classification (with ResNet), text classification recurrent neural networks (with Bi-LSTM), and tabular classification (with XGBoost) tasks.Quantitatively, we show that RPS-LJE slightly outperforms RPS- l_2 and other state-of-the-art data explanation methods by up to 3\% on a data debugging task. Qualitatively, we observe that RPS-LJE provides individualized explanations for each test data point rather than the class-specific static ranking of points in the original approach.

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.

This paper proposes a decomposition of the pre-activation prediction (the values of the last intermediate layer in a NN) into a linear combination of activations of the training points. The weights in this linear combination are called representer values. Positive representer values represent excitatory signals that contribute to the prediction of the particular sample in the corresponding class, while negative representer values inhibit the prediction to that particular class. The representer values can be used to better understand the prediction of the model. The experimental section shows how this technique can be used in several explanatory analyzes, such as: * Data debugging: for a MNIST dataset, consider some of the labels being interchanged in the dataset (in the example used some 1s become 7s).

Several instance-based explainability methods for finding influential training examples for test-time decisions have been proposed recently, including Influence Functions, TraceIn, Representer Point Selection, Grad-Dot, and Grad-Cos. Typically these methods are evaluated using LOO influence (Cook's distance) as a gold standard, or using various heuristics. In this paper, we show that all of the above methods are unstable, i.e., extremely sensitive to initialization, ordering of the training data, and batch size. We suggest that this is a natural consequence of how in the literature, the influence of examples is assumed to be independent of model state and other examples -- and argue it is not. We show that LOO influence and heuristics are, as a result, poor metrics to measure the quality of instance-based explanations, and instead propose to evaluate such explanations by their ability to detect poisoning attacks. Further, we provide a simple, yet effective baseline to improve all of the above methods and show how it leads to very significant improvements on downstream tasks.

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. Papers published at the Neural Information Processing Systems Conference.