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.
arXiv:2507. 14177v2 Announce Type: replace-cross Abstract: This paper aims to understand the training solution, which is obtained by the back-propagation algorithm, of two-layer neural networks whose hidden layer is composed of the units with smooth activation functions, including the usual sigmoid type most commonly used before the advent of ReLUs.
Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs. We present a global operator theory of the \emph{F-adjoint} framework, which reformulates the layerwise backward recursion of an $L$-depth feedforward network into a single linear system $(I-\cB)\Xs=\bG$, where $\bG$ is a source vector.
arXiv:2602. 19799v2 Announce Type: replace-cross Abstract: Despite recent algorithmic advances, we still lack principled ways to leverage the well-documented rescaling symmetries in ReLU neural network parameters.
arXiv:2604. 14037v2 Announce Type: replace Abstract: Parameter space is not function space for neural network architectures.
arXiv:2508. 03867v2 Announce Type: replace-cross Abstract: We introduce a class of algebraic varieties naturally associated with ReLU neural networks, arising from the piecewise linear structure of their outputs across activation regions in input space, and the piecewise multilinear structure in parameter space.
arXiv:2607. 11289v1 Announce Type: cross Abstract: Backpropagation is the computational engine of deep learning, yet its mathematical structure is typically treated as a procedural traversal of computational graphs.
arXiv:2607. 16720v1 Announce Type: new Abstract: Understanding deep neural networks remains a central challenge in machine learning.
arXiv:2606. 09744v1 Announce Type: new Abstract: We study feed-forward ReLU networks with fixed readout and quadratic loss.
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:2608. 02624v1 Announce Type: cross Abstract: Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling.
arXiv:2601. 16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks.
arXiv:2607. 23397v1 Announce Type: new Abstract: Hierarchical neural networks are widely used in artificial intelligence, yet their mathematical properties remain incompletely understood.