arXiv:2608. 07043v1 Announce Type: cross Abstract: Developing nonlinear models that are both expressive and computationally efficient remains a challenge in machine learning and nonlinear system identification.
arXiv:2606. 09880v1 Announce Type: new Abstract: Large-scale dynamic weighted directed networks (DWDNs) are widely used to model time-varying interactions among nodes.
arXiv:2608. 17135v1 Announce Type: cross Abstract: Tensor networks are powerful formats for compressing large-scale data.
arXiv:2609.09434v1 Announce Type: cross Abstract: In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems. However, in high-dimensional setting...
arXiv:2607. 00329v1 Announce Type: cross Abstract: Recursive Feature Machines (RFMs) are a class of kernel machines that utilize the Average Gradient Outer Product (AGOP) as a mechanism for feature learning.
arXiv:2606. 00130v2 Announce Type: replace-cross Abstract: Large deep neural networks are costly to store and deploy because inference must move and evaluate many parameters.
The paper presents a formal analysis of the quotient geometry of tree tensor networks (TTNs) and introduces efficient first- and second-order optimization algorithms that leverage this geometry. It also develops a backpropagation method for training TTNs in a kernel learning context. Numerical experiments on a digit classification task demonstrate a tradeoff between two horizontal distributions: one provides clearer geometric insights, while the other yields more efficient algorithms.
arXiv:2607. 15916v1 Announce Type: new Abstract: Central to machine learning and signal processing is the ability to perform universal function approximation and learn complex input-output relationships from limited numbers of observations.
The paper discusses tensorizing neural networks by reshaping dense weight matrices into higher-order tensors and approximating them with low-rank tensor network decompositions. This approach offers promising model compression and introduces bond indices that create new latent spaces, potentially enhancing interpretability. Despite encouraging empirical results, tensorized neural networks remain underused, and the authors call for more research to address practical scaling and adoption challenges.
arXiv:2505. 17740v2 Announce Type: replace Abstract: Making accurate predictions of chaotic time series is a complex challenge.
arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.
arXiv:2311. 02960v5 Announce Type: replace Abstract: Over the past decade, deep learning has proven to be a highly effective tool for learning meaningful features from raw data.
The paper surveys continuous‑time (CT) machine learning, a framework for modeling temporal dynamics as continuous processes, especially useful when data are sampled irregularly or over long horizons. It introduces a unified taxonomy that groups major CT methods by their underlying mathematical formulations and shows how different architectural choices—such as vector‑field parameterization, stochasticity, memory mechanisms, and discretization—relate these families. The survey compares training algorithms, optimization strategies, failure modes, computational complexity, and benchmarks, reviews supporting software ecosystems, and outlines open challenges and future research directions.