The paper introduces the directional linear separability measure (D‑LSM) to quantify how much linear separability is preserved or improved by injective affine maps in neural networks. It characterizes the geometry supporting D‑LSM, proves its invariance under injective affine embeddings, and derives conditions for gated activations (ReLU, GELU, SiLU) to preserve and recover samples. Experiments validate the theoretical bounds, demonstrate affine‑tube constructions that achieve guaranteed recovery, and apply the method to Vision Transformer representations to obtain early post‑activation separability certificates.
By Yi Wei, Xuan Qi, Suorong Yang, Furao Shen
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.
By Peng Wang, Xiao Li, Can Yaras, Zhihui Zhu, Laura Balzano, Wei Hu, Qing Qu
arXiv:2608.30028v1 Announce Type: new
Abstract: This paper introduces a family of multiclass linear Perceptron classifiers with a multiplicative margin mechanism (MMPerc), as an alternative to standa...
By Dmitri Rachkovskij, Evgeny Osipov, Olexander Volkov, Daswin De Silva, Denis Kleyko
arXiv:2602. 24264v2 Announce Type: replace-cross Abstract: Compositional generalization, the ability to recognize familiar parts in novel contexts, is a defining property of intelligent systems.
By Arnas Uselis, Andrea Dittadi, Seong Joon Oh
arXiv:2606. 16028v1 Announce Type: new Abstract: Modern deep learning architectures are increasingly multi-task and multi-modal, using a pretrained foundation model combined with task-specific, fine-tuned models.
By Thomas Dittrich, Oliver Potocki, Philipp Grohs
arXiv:2607. 18930v1 Announce Type: cross Abstract: The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error.
By Anuragine S A, Prem Jagadeesan
arXiv:2608.23182v1 Announce Type: cross
Abstract: We present a comparative study of label-free metrics for assessing the quality of representations in deep neural networks to understand their reliabi...
By Daniel Richards Arputharaj, Daniel J\"onsson, Gabriel Eilertsen
arXiv:2606. 01746v1 Announce Type: cross Abstract: Modern neural networks are highly susceptible to adversarial perturbations.
By Kai Wang
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.
By Shaojie Li, Yunbei Xu
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
By Julia Nakhleh, Robert D. Nowak
NObSP (Nonlinear Oblique Subspace Projections) is a framework that decomposes neural network predictions into explicit per‑feature contribution functions and an interaction residual, leveraging the linear final layer and oblique projections to avoid double counting when feature subspaces overlap. It connects to functional ANOVA and the Kolmogorov‑Arnold representation theorem, and introduces an efficient partial regression algorithm for out‑of‑sample evaluation. For convolutional networks, NObSP‑CAM generates class activation maps without backward passes after a single calibration, and experiments on tabular and vision datasets show faithfulness comparable to established attribution methods, with high function reproduction scores and improved class purity on TinyImageNet.
By Alexander Caicedo, V\'ictor De La Hoz, Santiago Alf\'erez
arXiv:2606. 29951v1 Announce Type: new Abstract: Interpretable Mesomorphic Neural Networks (IMNs) offer a promising framework that combines the predictive power of deep neural networks with the interpretability of linear models.
By Hugo L. Hammer, Vajira Thambawita, Kristoffer Herland Hellton, P{\aa}l Halvorsen