arXiv:2509. 11285v2 Announce Type: replace-cross Abstract: Class-Incremental Learning (CIL) in deep neural networks is conventionally framed as an iterative gradient-based optimization problem, incurring high computational cost, hyperparameter sensitivity, and risk of catastrophic forgetting.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv:2606. 06861v1 Announce Type: cross Abstract: Understanding nonlinear feature interactions is crucial in science and engineering, yet standard multilayer perceptrons (MLPs) often capture such interactions only implicitly, leading to entangled representations that can impair robustness and interpretability.
arXiv:2607. 12417v1 Announce Type: new Abstract: Although vast amounts of data, such as audio signal spectra, are naturally represented using complex numbers, conventional machine learning methods often simplify complex-domain problems by employing frameworks designed for real-valued variables.
arXiv:2412. 12036v2 Announce Type: replace Abstract: System identification, the process of deriving mathematical models of dynamical systems from observed input-output data, has undergone a paradigm shift with the advent of learning-based methods.
arXiv:2607. 08091v1 Announce Type: cross Abstract: The stationary distribution of reflected Brownian motion (RBM) plays an important role in the analysis of high-dimensional stochastic systems, yet closed-form solutions are known only for a few special cases.
arXiv:2603. 06861v2 Announce Type: replace Abstract: Activation functions are fundamental to deep neural networks, governing gradient flow, optimization stability, and representational capacity.
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...
arXiv:2606. 19888v1 Announce Type: cross Abstract: Modeling long-sequence medical time series data, such as electrocardiograms (ECG), poses significant challenges due to high sampling rates, multichannel signal complexity, inherent noise, and limited labeled data.
arXiv:2503. 10496v2 Announce Type: replace-cross Abstract: Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions.
The paper introduces SW-KAN, a Kolmogorov‑Arnold Network that replaces traditional B‑spline activations with Stieltjes‑Wigert q‑orthogonal polynomials defined on the semi‑infinite domain (0, ∞). It addresses the domain mismatch between unbounded inputs and bounded polynomial bases by applying a smooth exponential‑of‑tanh mapping, and uses a numerically stable three‑term recurrence to evaluate polynomial expansions efficiently. Experiments on image classification and continuous function approximation show that SW‑KAN achieves better accuracy‑efficiency trade‑offs than existing polynomial KANs, especially in resource‑constrained scenarios with limited data or feature dimensionality.
The paper introduces the Frequency Selective Neural Network (FSNN), a new foundation architecture for time‑series learning that embeds advanced signal‑processing mathematics into its neural topology. By using a fully differentiable Wiener‑like filter bank optimized with complex‑domain backpropagation, FSNN autonomously discovers and isolates the precise physical modes of a given task, thereby avoiding the spectral entanglement that plagues CNNs, RNNs, and Transformers. Extensive evaluations show that FSNN achieves state‑of‑the‑art predictive performance, attaining 77.0 % average accuracy on the 10 multivariate UEA datasets and leading all major metrics on the imbalanced PTB‑XL ECG benchmark, while converging directly on physically meaningful frequency bands such as the cardiac QRS complex.