February 2026

arXiv:2512.23087v2 Announce Type: replace-cross Abstract: Reinforcement Learning (RL) for Large Language Models (LLMs) faces a fundamental tension: the numerical divergence between high-throughput inference engines and numerically precise training engines. Although these systems share the same parameters, they produce slightly different probability distributions, creating a training-inference mismatch. We prove that the bound on the log-probability divergence arising from this mismatch scales as $(1-p)$, where $p$ is the token probability. This scaling induces a highly asymmetric effect: the bound vanishes […]

Ver mais

arXiv:2511.08855v2 Announce Type: replace-cross Abstract: Detecting chemical modifications on RNA molecules remains a key challenge in epitranscriptomics. Traditional reverse transcription-based sequencing methods introduce enzyme- and sequence-dependent biases and fragment RNA molecules, confounding the accurate mapping of modifications across the transcriptome. Nanopore direct RNA sequencing offers a powerful alternative by preserving native RNA molecules, enabling the detection of modifications at single-molecule resolution. However, current computational tools can identify only a limited subset of modification types within well-characterized sequence contexts […]

Ver mais

arXiv:2511.08846v2 Announce Type: replace-cross Abstract: Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the topological descriptors – the Euler characteristic (EC) and persistent homology (PH). In particular, we establish a complete characterization of the expressive power of EC on general color-based filtrations. We also show that the PH descriptors of (virtual) graph […]

Ver mais

arXiv:2510.09796v2 Announce Type: replace-cross Abstract: The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as vanishing or exploding gradients, difficulties with non-smooth activations, and an inherently sequential structure that limits parallelisation. Lifted training methods offer an alternative by reformulating the nested optimisation problem into a higher-dimensional, constrained optimisation problem where the constraints are no longer enforced directly […]

Ver mais

arXiv:2510.02514v2 Announce Type: replace-cross Abstract: We introduce the Information-Estimation Metric (IEM), a novel form of distance function derived from an underlying continuous probability density over a domain of signals. The IEM is rooted in a fundamental relationship between information theory and estimation theory, which links the log-probability of a signal with the errors of an optimal denoiser, applied to noisy observations of the signal. In particular, the IEM between a pair of signals is obtained by comparing their […]

Ver mais

arXiv:2505.23506v4 Announce Type: replace-cross Abstract: Identifying and disentangling sources of predictive uncertainty is essential for trustworthy supervised learning. We argue that widely used second-order methods that disentangle aleatoric and epistemic uncertainty are fundamentally incomplete. First, we show that unaccounted bias contaminates uncertainty estimates by overestimating aleatoric (data-related) uncertainty and underestimating the epistemic (model-related) counterpart, leading to incorrect uncertainty quantification. Second, we demonstrate that existing methods capture only partial contributions to the variance-driven part of epistemic uncertainty; different approaches […]

Ver mais

arXiv:2505.13370v2 Announce Type: replace-cross Abstract: This paper addresses the growing concern of cascading extreme events, such as an extreme earthquake followed by a tsunami, by presenting a novel method for risk assessment focused on these domino effects. The proposed approach develops an extreme value theory framework within a Kolmogorov-Arnold network (KAN) to estimate the probability of one extreme event triggering another, conditionally on a feature vector. An extra layer is added to the KAN architecture to ensure that […]

Ver mais

arXiv:2504.15243v2 Announce Type: replace-cross Abstract: Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly convex. Existing methods often face limitations, including slow convergence rates or reliance on double-loop algorithmic designs. To overcome these challenges, we introduce a novel single-loop penalty-based stochastic algorithm. Following the classical exact penalty method, our approach employs a {bf hinge-based penalty}, which […]

Ver mais

arXiv:2503.06558v2 Announce Type: replace-cross Abstract: Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard […]

Ver mais

arXiv:2502.09740v2 Announce Type: replace-cross Abstract: This paper addresses the challenge of forecasting corporate distress, a problem marked by three key statistical hurdles: (i) right censoring, (ii) high-dimensional predictors, and (iii) mixed-frequency data. To overcome these complexities, we introduce a novel high-dimensional censored MIDAS (Mixed Data Sampling) logistic regression. Our approach handles censoring through inverse probability weighting and achieves accurate estimation with numerous mixed-frequency predictors by employing a sparse-group penalty. We establish finite-sample bounds for the estimation error, accounting […]

Ver mais