Heavy-tailed distributions are ubiquitous in real-world data, where rare but extreme events dominate risk and variability. However, standard Variational Autoencoders (VAEs) employ simple decoder distributions (e.g., Gaussian) that fail to capture heavy-tailed behavior, while existing heavy-tail-aware extensions remain restricted to predefined parametric families whose tail behavior is fixed a priori. We propose the Phase-Type Variational Autoencoder (PH-VAE), whose decoder distribution is a latent-conditioned Phase-Type (PH) distribution defined as the absorption time of a continuous-time Markov chain (CTMC). This formulation composes multiple exponential time scales, yielding a flexible and analytically tractable decoder that adapts its tail behavior directly from the observed data. Experiments on synthetic and real-world benchmarks demonstrate that PH-VAE accurately recovers diverse heavy-tailed distributions, significantly outperforming Gaussian, Student-t, and extreme-value-based VAE decoders in modeling tail behavior and extreme quantiles. In multivariate settings, PH-VAE captures realistic cross-dimensional tail dependence through its shared latent representation. To our knowledge, this is the first work to integrate Phase-Type distributions into deep generative modeling, bridging applied probability and representation learning.

Credal predictors are models that are aware of epistemic uncertainty and produce a convex set of probabilistic predictions. They offer a principled way to quantify predictive epistemic uncertainty (EU) and have been shown to improve model robustness in various settings. However, most state-of-the-art methods mainly define EU as disagreement caused by random training initializations, which mostly reflects sensitivity to optimization randomness rather than uncertainty from deeper sources. To address this, we define EU as disagreement among models trained with varying relaxations of the i.i.d. assumption between training and test data. Based on this idea, we propose CreDRO, which learns an ensemble of plausible models through distributionally robust optimization. As a result, CreDRO captures EU not only from training randomness but also from meaningful disagreement due to potential distribution shifts between training and test data. Empirical results show that CreDRO consistently outperforms existing credal methods on tasks such as out-of-distribution detection across multiple benchmarks and selective classification in medical applications.

Our most powerful artificial agents cannot be told exactly what to do, especially in complex planning environments. They almost exclusively rely on neural networks to perform their tasks, but neural networks cannot easily be told to obey certain rules or adhere to existing background knowledge. While such uncontrolled behaviour might be nothing more than a simple annoyance next time you ask an LLM to generate a schedule for reaching a deadline in two days and it starts to hallucinate that days have 48 hours instead of 24, it can be much more impactful when that same LLM is controlling an agent responsible for navigating a warehouse filled with TNT and it decides to go just a little too close to the storage compartments. Luckily, controlling neural networks has gained a lot of attention over the last years through the development of . Neurosymbolic AI, or NeSy for short, aims to combine the learning abilities of neural networks with the guarantees that symbolic methods based on automated mathematical reasoning offer.

However, the availability of such resources remains scarce and evaluation faces added complexity due to reproducibility issues in experimental protocols.

Out-of-Distribution (OoD) detection is vital for the reliability of Deep Neural Networks (DNNs).

Models (SDMs) predict species across space from spatially explicit features.

Specifically, LocCa employs two tasks, bounding box prediction and location-dependent captioning, conditioned on the image pixel input.