arXiv:2608. 09707v1 Announce Type: cross Abstract: Embedding trained neural networks as surrogates within optimisation problems is an established practice in operations research.
By Yu Liu, Jan Kronqvist, Fabricio Oliveira
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.
By Changcun Huang
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.
By Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
The paper investigates vector‑valued binary affine refinement operators with finite matrix masks and compactly supported continuous piecewise‑linear data. It demonstrates that every finite refinement iterate can be exactly realized by a ReLU network of fixed width and depth linear in the number of iterations, using a universal reflection‑doubling mechanism that replaces two binary transition matrices with a single fixed block matrix and a swap involution. The construction allows exact branch selection via a continuous piecewise‑linear cone switch, propagates full vectorized profiles without decomposing inputs, and handles stage‑dependent forcing while reducing the doubled cascade to a single parity sector through genuine reflection equivariance.
By Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
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.
By Shijun Zhang, Zuowei Shen, Yuesheng Xu
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.
By Long Kiu Chung, Shreyas Kousik