Title: Interpretability Through Invertibility: A Deep Convolutional Network With Ideal Counterfactuals And Isosurfaces. Abstract: Current state of the art computer vision applications rely on highly complex models. Their interpretability is mostly limited to post-hoc methods which are not guaranteed to be faithful to the model. To elucidate a model’s decision, we present a novel interpretable model based on an invertible deep convolutional network. Our model generates meaningful, faithful, and ideal counterfactuals. Using PCA on the classifier’s input, we can also create “isofactuals”– image interpolations with the same outcome but visually meaningful different features. Counter- and isofactuals can be used to identify positive and negative evidence in an image. This can also be visualized with heatmaps. We evaluate our approach against gradient-based attribution methods, which we find to produce meaningless adversarial perturbations.  Using our method, we reveal biases in three different datasets. In a human subject experiment, we test whether non-experts find our method useful to spot spurious correlations learned by a model. Our work is a step towards more trustworthy explanations for computer vision.