FRInGe: Distribution-Space Integrated Gradients with Fisher--Rao Geometry

Gradient-based attribution methods are model-faithful and scalable, but Integrated Gradients (IG) can be brittle because explanations depend on heuristic baselines, straight-line paths, discretization, and saturation. We propose Fisher--Rao Integrated Gradients (FRInGe), which defines both the reference and interpolation schedule in predictive distribution space. FRInGe replaces input baselines with a maximum-entropy predictive reference and follows a Fisher-Rao geodesic on the probability simplex. The corresponding input-space trajectory is realized through the pullback Fisher metric and stabilized by KL and Euclidean trust regions; attributions are obtained by integrating input gradients along this trajectory. Across six ImageNet architectures, FRInGe most clearly improves calibration-oriented attribution metrics, especially MAS scores, while remaining competitive on perturbation AUC and infidelity.

Are We Using Autoencoders in a Wrong Way?

Autoencoders are certainly among the most studied and used Deep Learning models: the idea behind them is to train a model in order to reconstruct the same input data. The peculiarity of these models is to compress the information through a bottleneck, creating what is called Latent Space. Autoencoders are generally used for dimensionality reduction, anomaly detection and feature extraction. These models have been extensively studied and updated, given their high simplicity and power. Examples are (i) the Denoising Autoencoder, where the model is trained to reconstruct an image from a noisy one; (ii) Sparse Autoencoder, where the bottleneck is created by a regularization term in the loss function; (iii) Variational Autoencoder, where the latent space is used to generate new consistent data. In this article, we revisited the standard training for the undercomplete Autoencoder modifying the shape of the latent space without using any explicit regularization term in the loss function. We forced the model to reconstruct not the same observation in input, but another one sampled from the same class distribution. We also explored the behaviour of the latent space in the case of reconstruction of a random sample from the whole dataset.