Despite its potential benefits, applying DST to GANs presents challenges due to the adversarial nature of the training process.

Sharpness-aware minimization (SAM) is a recently proposed method that minimizes the sharpness of the training loss of a neural network.

Machine learning applications require fast and reliable per-sample uncertainty estimation. A common approach is to use predictive distributions from Bayesian or approximation methods and additively decompose uncertainty into aleatoric (i.e., data-related) and epistemic (i.e., model-related) components. However, additive decomposition has recently been questioned, with evidence that it breaks down when using finite-ensemble sampling and/or mismatched predictive distributions. This paper introduces Variance-Gated Ensembles (VGE), an intuitive, differentiable framework that injects epistemic sensitivity via a signal-to-noise gate computed from ensemble statistics. VGE provides: (i) a Variance-Gated Margin Uncertainty (VGMU) score that couples decision margins with ensemble predictive variance; and (ii) a Variance-Gated Normalization (VGN) layer that generalizes the variance-gated uncertainty mechanism to training via per-class, learnable normalization of ensemble member probabilities. We derive closed-form vector-Jacobian products enabling end-to-end training through ensemble sample mean and variance. VGE matches or exceeds state-of-the-art information-theoretic baselines while remaining computationally efficient. As a result, VGE provides a practical and scalable approach to epistemic-aware uncertainty estimation in ensemble models. An open-source implementation is available at: https://github.com/nextdevai/vge.

We introduce Variational Joint Embedding (VJE), a framework that synthesizes joint embedding and variational inference to enable self-supervised learning of probabilistic representations in a reconstruction-free, non-contrastive setting. Compared to energy-based predictive objectives that optimize pointwise discrepancies, VJE maximizes a symmetric conditional evidence lower bound (ELBO) for a latent-variable model defined directly on encoder embeddings. We instantiate the conditional likelihood with a heavy-tailed Student-$t$ model using a polar decomposition that explicitly decouples directional and radial factors to prevent norm-induced instabilities during training. VJE employs an amortized inference network to parameterize a diagonal Gaussian variational posterior whose feature-wise variances are shared with the likelihood scale to capture anisotropic uncertainty without auxiliary projection heads. Across ImageNet-1K, CIFAR-10/100, and STL-10, VJE achieves performance comparable to standard non-contrastive baselines under linear and k-NN evaluation. We further validate these probabilistic semantics through one-class CIFAR-10 anomaly detection, where likelihood-based scoring under the proposed model outperforms comparable self-supervised baselines.

Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations and behavior under distributional shift remain poorly understood. In this work, we provide a principled statistical interpretation by proving that EDL training corresponds to amortized variational inference in a hierarchical Bayesian model with a tempered pseudo-likelihood. This perspective reveals a major drawback: standard EDL conflates epistemic and aleatoric uncertainty, leading to systematic overconfidence on out-of-distribution (OOD) inputs. To address this, we introduce Density-Informed Pseudo-count EDL (DIP-EDL), a new parametrization that decouples class prediction from the magnitude of uncertainty by separately estimating the conditional label distribution and the marginal covariate density. This separation preserves evidence in high-density regions while shrinking predictions toward a uniform prior for OOD data. Theoretically, we prove that DIP-EDL achieves asymptotic concentration. Empirically, we show that our method enhances interpretability and improves robustness and uncertainty calibration under distributional shift.

Diffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion models remains largely unexplored. In this work we investigate whether it provides tangible benefits for generative modelling. We find that while ensembling the scores generally improves the score-matching loss and model likelihood, it fails to consistently enhance perceptual quality metrics such as FID on image datasets. We confirm this observation across a breadth of aggregation rules using Deep Ensembles, Monte Carlo Dropout, on CIF AR-10 and FFHQ. We attempt to explain this discrepancy by investigating possible explanations, such as the link between score estimation and image quality. We also look into tabular data through random forests, and find that one aggregation strategy outperforms the others. Finally, we provide theoretical insights into the summing of score models, which shed light not only on ensembling but also on several model composition techniques (e.g.

Data attribution methods identify which training examples are responsible for a model's predictions, but their sensitivity to distributional perturbations undermines practical reliability. We present a unified framework for certified robust attribution that extends from convex models to deep networks. For convex settings, we derive Wasserstein-Robust Influence Functions (W-RIF) with provable coverage guarantees. For deep networks, we demonstrate that Euclidean certification is rendered vacuous by spectral amplification -- a mechanism where the inherent ill-conditioning of deep representations inflates Lipschitz bounds by over $10{,}000\times$. This explains why standard TRAK scores, while accurate point estimates, are geometrically fragile: naive Euclidean robustness analysis yields 0\% certification. Our key contribution is the Natural Wasserstein metric, which measures perturbations in the geometry induced by the model's own feature covariance. This eliminates spectral amplification, reducing worst-case sensitivity by $76\times$ and stabilizing attribution estimates. On CIFAR-10 with ResNet-18, Natural W-TRAK certifies 68.7\% of ranking pairs compared to 0\% for Euclidean baselines -- to our knowledge, the first non-vacuous certified bounds for neural network attribution. Furthermore, we prove that the Self-Influence term arising from our analysis equals the Lipschitz constant governing attribution stability, providing theoretical grounding for leverage-based anomaly detection. Empirically, Self-Influence achieves 0.970 AUROC for label noise detection, identifying 94.1\% of corrupted labels by examining just the top 20\% of training data.