Learning activation functions has emerged as a promising direction in deep learning, allowing networks to adapt activation mechanisms to task-specific demands. In this work, we introduce a novel framework that employs the Gumbel-Softmax trick to enable discrete yet differentiable selection among a predefined set of activation functions during training. Our method dynamically learns the optimal activation function independently of the input, thereby enhancing both predictive accuracy and architectural flexibility. Experiments on synthetic datasets show that our model consistently […]

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arXiv:2601.02432v1 Announce Type: new Abstract: Speech-based machine learning systems are sensitive to noise, complicating reliable deployment in emotion recognition and voice pathology detection. We evaluate the robustness of a hybrid quantum machine learning model, quanvolutional neural networks (QNNs) against classical convolutional neural networks (CNNs) under four acoustic corruptions (Gaussian noise, pitch shift, temporal shift, and speed variation) in a clean-train/corrupted-test regime. Using AVFAD (voice pathology) and TESS (speech emotion), we compare three QNN models (Random, Basic, Strongly) to […]

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arXiv:2601.19595v1 Announce Type: cross Abstract: The deployment of Artificial Intelligence in high-risk domains, such as finance and healthcare, necessitates models that are both fair and transparent. While regulatory frameworks, including the EU’s AI Act, mandate bias mitigation, they are deliberately vague about the definition of bias. In line with existing research, we argue that true fairness requires addressing bias at the intersections of protected groups. We propose a unified framework that leverages Mixed-Integer Optimization (MIO) to train intersectionally […]

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Let 1 < a1 < a2 < · · · be integers with ( sum_{k=1}^infty a_k^{-1}<infty ), and set ( F(s)=1+sum_{k=1}^infty a_k^{-s}, qquad Re s>1. ) A question of Erdős and Ingham, recorded as Erdős Problem #967 in a compilation by T. F. Bloom (accessed 2025–12–01), asks whether one always has ( F(1+it)neq 0 ) for all real t. This paper does not resolve the problem; instead, it develops a modern dynamical-systems framework for its study. Using the […]

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arXiv:2601.19022v1 Announce Type: new Abstract: Forecasting rare events in multivariate time-series data is challenging due to severe class imbalance, long-range dependencies, and distributional uncertainty. We introduce EVEREST, a transformer-based architecture for probabilistic rare-event forecasting that delivers calibrated predictions and tail-aware risk estimation, with auxiliary interpretability via attention-based signal attribution. EVEREST integrates four components: (i) a learnable attention bottleneck for soft aggregation of temporal dynamics; (ii) an evidential head for estimating aleatoric and epistemic uncertainty via a Normal–Inverse–Gamma distribution; […]

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We introduce a new method – the group Dantzig selector – for high dimensional sparse regression with group structure, which has a convincing theory about why utilizing the group structure can be beneficial. Under a group restricted isometry condition, we obtain a significantly improved nonasymptotic $ell_2$-norm bound over the basis pursuit or the Dantzig selector which ignores the group structure. To gain more insight, we also introduce a surprisingly simple and intuitive “sparsity oracle condition” to obtain a […]

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When daily urgencies and immediate results take priority over long-term goals, when quick fixes are the default mode of execution instead of big-picture thinking or when you spend most of your time firefighting issues—putting out fires, responding to crises and reacting to challenges that surface unexpectedly—it may feel like you’re accomplishing a lot. Problems are being solved, challenges are being resolved and things are getting done. You’re highly engaged, super involved and extremely busy in trying to keep […]

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arXiv:2601.15464v1 Announce Type: new Abstract: Rank-metric codes, defined as sets of matrices over a finite field with the rank distance, have gained significant attention due to their applications in network coding and connections to diverse mathematical areas. Initially studied by Delsarte in 1978 and later rediscovered by Gabidulin, these codes have become a central topic in coding theory. This paper surveys the development and mathematical foundations, in particular, regarding bounds and constructions of rank-metric codes, emphasizing their extension […]

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