arXiv:2607. 19042v1 Announce Type: cross Abstract: Neural hypergraphs are a natural generalization of neural networks, the reference models in modern machine learning.
arXiv:2606. 20299v1 Announce Type: cross Abstract: Deep learning has managed to evade numerous intuitions from classical statistics to achieve unprecedented performance on a number of real-world tasks.
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:2606. 26873v1 Announce Type: cross Abstract: Graphs provide a natural language for relational data in chemistry, biology and optimisation.
The paper introduces a quantum tensor network learning framework that employs matrix product states (MPS) as a machine‑learning architecture, adding a global normalization condition to interpret the MPS as a quantum state. It compares two optimization strategies—gradient descent and a DMRG‑adapted method—to identify locally optimal tensors and evaluates their effectiveness.
arXiv:2505.11298v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive per...
arXiv:2502. 09928v2 Announce Type: replace-cross Abstract: Originating in quantum physics, tensor networks (TNs) have been widely adopted as exponential machines and parametric decomposers for recognition tasks.
arXiv:2606. 09880v1 Announce Type: new Abstract: Large-scale dynamic weighted directed networks (DWDNs) are widely used to model time-varying interactions among nodes.
The paper introduces Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training that turns hierarchical feature learning into an explicit iterative spectral procedure. In this framework, each layer independently selects directions with maximal low-degree correlation to the label, providing a tractable surrogate for deep learning and a kernel-space interpretation. Experiments on fully connected and convolutional networks show that Neural LoFi outperforms lazy random-feature baselines, recovers meaningful structured filters, and aligns with early gradient-descent feature discovery on real datasets.
arXiv:2506. 22271v3 Announce Type: replace Abstract: Neural networks often map low-dimensional embeddings to high-dimensional output spaces.
The paper introduces a pointwise generalization theory for fully connected deep neural networks, using a pointwise Riemannian Dimension derived from eigenvalues of learned feature representations across layers. This framework provides hypothesis-dependent, representation-aware generalization bounds that are significantly tighter than traditional size- or norm-based approaches, both theoretically and experimentally. The authors analytically identify structural properties that explain deep networks’ tractability and empirically show that the pointwise Riemannian Dimension captures feature compression, over‑parameterization effects, and optimizer bias.
arXiv:2607. 05017v1 Announce Type: cross Abstract: The performance of deep learning models crucially depends on the settings of hyperparameters like learning rate, initialization scale, and weight decay.