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Explaining the predictions of a deep neural network is a nontrivial task, yet high-quality explanations for predictions are often a prerequisite for practitioners to trust these models. Counterfactual explanations aim to explain predictions by finding the ''nearest'' in-distribution alternative input whose prediction changes in a pre-specified way. However, it remains an open question how to define this nearest alternative input, whose solution depends on both the domain (e.g. images, graphs, tabular data, etc.) and the specific application considered. For graphs, this problem is complicated i) by their discrete nature, as opposed to the continuous nature of state-of-the-art graph classifiers; and ii) by the node permutation group acting on the graphs. We propose a method to generate counterfactual explanations for any differentiable black-box graph classifier, utilizing a case-specific permutation equivariant graph variational autoencoder. We generate counterfactual explanations in a continuous fashion by traversing the latent space of the autoencoder across the classification boundary of the classifier, allowing for seamless integration of discrete graph structure and continuous graph attributes. We empirically validate the approach on three graph datasets, showing that our model is consistently high-performing and more robust than the baselines., Comment: Published at Northern Lights Deep Learning Conference 2025

The analysis of data such as graphs has been gaining increasing attention in the past years. This is justified by the numerous applications in which they appear. Several methods are present to predict graphs, but much fewer to quantify the uncertainty of the prediction. The present work proposes an uncertainty quantification methodology for graphs, based on conformal prediction. The method works both for graphs with the same set of nodes (labelled graphs) and graphs with no clear correspondence between the set of nodes across the observed graphs (unlabelled graphs). The unlabelled case is dealt with the creation of prediction sets embedded in a quotient space. The proposed method does not rely on distributional assumptions, it achieves finite-sample validity, and it identifies interpretable prediction sets. To explore the features of this novel forecasting technique, we perform two simulation studies to show the methodology in both the labelled and the unlabelled case. We showcase the applicability of the method in analysing the performance of different teams during the FIFA 2018 football world championship via their player passing networks.

Latent representations are used extensively for downstream tasks, such as visualization, interpolation or feature extraction of deep learning models. Invariant and equivariant neural networks are powerful and well-established models for enforcing inductive biases. In this paper, we demonstrate that the inductive bias imposed on the by an equivariant model must also be taken into account when using latent representations. We show how not accounting for the inductive biases leads to decreased performance on downstream tasks, and vice versa, how accounting for inductive biases can be done effectively by using an invariant projection of the latent representations. We propose principles for how to choose such a projection, and show the impact of using these principles in two common examples: First, we study a permutation equivariant variational auto-encoder trained for molecule graph generation; here we show that invariant projections can be designed that incur no loss of information in the resulting invariant representation. Next, we study a rotation-equivariant representation used for image classification. Here, we illustrate how random invariant projections can be used to obtain an invariant representation with a high degree of retained information. In both cases, the analysis of invariant latent representations proves superior to their equivariant counterparts. Finally, we illustrate that the phenomena documented here for equivariant neural networks have counterparts in standard neural networks where invariance is encouraged via augmentation. Thus, while these ambiguities may be known by experienced developers of equivariant models, we make both the knowledge as well as effective tools to handle the ambiguities available to the broader community., Comment: This paper was updated to reflect the version accepted to ICML 2024