arXiv:2608. 02624v1 Announce Type: cross Abstract: Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling.
arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
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:2607. 20586v1 Announce Type: new Abstract: We study vector-valued affine refinement operators of the form [ (W\gamma)(t)=\sum_{j\in\mathbb{Z}} A_j\gamma(Mt-j)+B(t), ] with finitely supported matrix mask and compactly supported continuous piecewise linear input and forcing data.
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:2606. 30935v1 Announce Type: cross Abstract: While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints.
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.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
arXiv:2607. 21651v1 Announce Type: new Abstract: We prove that the maximum of $n$ real numbers is exactly representable by a ReLU network with two hidden layers for every $n\le 10$.
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
arXiv:2606. 26705v1 Announce Type: cross Abstract: Feedforward neural network (NN) expressivity is typically studied by emulating optimal basis-expansion schemes.
arXiv:2607. 04597v1 Announce Type: new Abstract: In this paper, we study the universal approximation property of residual neural networks, and obtain some new results.
arXiv:2602. 06737v2 Announce Type: replace Abstract: We present a generalized framework for the range verification of neural networks featuring non-linear activation functions.