arXiv:2607. 06048v1 Announce Type: cross Abstract: We aim to identify scattering network architectures that maximize the separation capacity on data with low intrinsic dimension.
arXiv:2606. 30822v1 Announce Type: cross Abstract: In this paper, we attempt to enhance the theoretical understanding of convolutional neural networks (CNNs) as feature extractors in classification tasks by analyzing them through the lens of Cover's function-counting theory.
arXiv:2012. 01982v3 Announce Type: replace Abstract: This paper proposes a standard way to represent sparse tensors.
arXiv:2406. 08966v3 Announce Type: replace Abstract: The separation power of a machine learning model refers to its ability to distinguish between different inputs and is often used as a proxy for its expressivity.
arXiv:2510. 15814v2 Announce Type: replace-cross Abstract: Universality results for equivariant neural networks remain rare.
The paper develops a theory for relocating a finite number of compact sets in ℝ^n to arbitrary target domains using diffeomorphisms of ℝ^n. It proves that any such collection can be embedded differentiably into ℝ^{n+1} so that the images become linearly separable. The authors apply this result to show that compact datasets in ℝ^n can be made linearly separable by width‑n deep neural networks with Leaky‑ReLU, ELU, or SELU activations, and that mutually disjoint compact datasets can be separated in ℝ^{n+1} by a width‑(n+1) DNN.
arXiv:2607. 11938v1 Announce Type: cross Abstract: This book is about the mathematical foundations of data science.
arXiv:2607. 07035v1 Announce Type: cross Abstract: The architecture of deep feedforward neural networks is ubiquitous in deep learning, either as a whole system or as a subnetwork of other architectures, and thus its mechanism is a key ingredient of the black box of neural networks.
This work studies neural architectures for classifying symmetric positive-definite matrices, focusing on congruence-like layers, in which the input matrix is multiplied on the left and right by a (possibly rectangular) weight matrix $W$ and its transpose. Such layers lie at the core of the celebrated SPDNet and have also been employed independently for dimensionality reduction on positive-definite data.
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. 02490v1 Announce Type: new Abstract: This work studies neural architectures for classifying symmetric positive-definite matrices, focusing on congruence-like layers, in which the input matrix is multiplied on the left and right by a (possibly rectangular) weight matrix $W$ and its transpose.
The paper introduces a new concept called positive scattering to enhance identifiability of nonnegative tensor decompositions. By combining this scattering term with existing dimension-based conditions, the authors derive two sufficient criteria that guarantee minimality, nonnegative rank, and uniqueness for subsets of components. The key result is a positive splitting inequality that links dimension constraints with support-induced geometric rigidity, and the authors show that the scattering term’s mode costs are discrete, enabling an exact activation characterization via graph connectivity. This criterion can certify sparse nonnegative tensor decompositions that elude traditional Kruskal and Lovitz–Petrov conditions, even after reshaping, and reduces to familiar matrix results in the two-dimensional case.
arXiv:2606. 07728v1 Announce Type: new Abstract: It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space.