# Explanations for Neural Networks by Neural Networks
## 5 Related Approaches  
Various methods to interpret black-box models have been proposed in the past decades. Overviews from different perspectives can be found in [1; 7; 9]. According to the taxonomy of [PERSON] [7], our approach can be classified as global, post-hoc, and model specific, with an intrinsically interpretable model (i.e., a polynomial function) as interpretation. Therefore, we focus on global interpretation methods with the goal of uncovering the decision-making process of the model based on the impact of the learned parameters (e.g., weights and biases of a neural network) on its features [7]. Global explanations therefore allow us to better understand the relationship and interactions between the features within the learned model. In contrast, local explainability methods such as LIME [13] or SHAP [3] only generate explanations for the models' prediction on a single instance. Therefore, they aim for local fidelity, which means that the explanation only accounts for this specific instance of interest and does not claim to have a high fidelity for further instances. This is fundamentally different from the goal of global interpretability, where we want to find an interpretation that has a high fidelity for the complete model and not only for a specific instance. There is a wide range of active research in the field of global interpretability. One part of global interpretability research focuses on uncovering the impact of a feature or a set of features on the model's predictions, as in, for instance, partial dependency plots (PDP) [14; 15], feature interaction [16; 17; 18], or (permutation) feature importance [19]. Another area of global interpretability is concerned with finding data points that are representative for the learned model in order to increase the interpretability, as in, for instance, prototypes and criticisms [7]. While the previously mentioned approaches are similar to \(\mathcal{I}\)-Nets as global interpretability methods that can be applied post-hoc, they differ significantly in the results of the interpretation method. As it presents an intrinsically interpretable model as a result of the interpretation, the most relevant work for our paper is work on global surrogate models. Global surrogate models, according to [PERSON] [7], are defined as an interpretable model trained to  
Figure 7: \(\mathcal{I}\)-Net performance evaluation on noisy data. The plot displays the mean absolute error between the \(\lambda\)-Nets and the functions predicted by the \(\mathcal{I}\)-Net for different levels of noise and numbers of variables. approximate the predictions of a black-box model. Thus, interpretability is achieved by inspecting the parameters of the surrogate model. In the literature, surrogate models are considered as model-agnostic and are trained based on the prediction of the model we want to interpret [1, 7]. Existing approaches usually differ only in the type of surrogate model that is chosen and the training procedure of the model. Different types of surrogate models have been explored, including mathematical functions [5, 20], decision trees [21, 22, 23], or rule sets [24, 25]. While the result of the interpretation (i.e., an intrinsically interpretable model) of global surrogate models matches our approach, there are also major differences. All mentioned approaches require an optimization process during interpretation, whereas our approach transforms the interpretation task into a machine learning problem that is solved using neural networks up-front. Additionally, existing approaches generate interpretations based on samples from the model to be interpreted, making them model-agnostic. In contrast, the \(\mathcal{I}\)-Net uses the network parameters of the \(\lambda\) network as the basis for generating explanations; therefore, this approach is model-specific by definition.