The paper introduces a unified matrix‑spectral framework that treats deep neural networks as data‑dependent products of linear operators, enabling the analysis of stability and interpretability through spectral quantities. It defines a Global Matrix Stability Index that aggregates spectral information from Jacobians, parameter gradients, Neural Tangent Kernel operators, and loss Hessians into a single stability scale, and shows that spectral entropy provides a more realistic measure of sensitivity than worst‑case bounds. Experiments on MNIST, CIFAR‑10, and CIFAR‑100 demonstrate that modest spectral regularization can significantly improve attribution stability without large changes to global spectral summaries.
By Ronald Katende
arXiv:2606. 16883v1 Announce Type: cross Abstract: Generalization is a critical property of data-driven models, particularly deep learning models deployed in safety-critical applications.
By Abdul-Rauf Nuhu, Parham M. Kebria, Vahid Hemmati, Mahmoud N. Mahmoud, Edward Tunstel, Abdollah Homaifar
The paper introduces two multi-stage neural operator learning frameworks—Deep Collocation Neural Operator (DCNO) and Deep Galerkin Neural Operator (DGNO)—for efficiently computing convolution integrals. DCNO is a supervised method that iteratively refines operator approximations by learning residuals from data pairs, while DGNO is an unsupervised approach that uses the weak form of a PDE residual when the operator can be represented by a PDE. Both frameworks build basis operators across multiple training stages, yielding markedly higher accuracy than one-shot learning and achieving near machine‑precision results for convolution problems, with significant efficiency gains for repeated queries or parametric variations.
By Zhiping Mao, Zhenye Wen, Yong Zhang, Xiaofei Zhao
arXiv:2502. 17055v5 Announce Type: replace Abstract: Training instability in modern deep learning systems is frequently triggered by rare but extreme gradient-norm spikes, which can induce oversized parameter updates, corrupt optimizer state, and lead to slow recovery or divergence.
By Tianjin Huang, Zhangyang Wang, Haotian Hu, Zhenyu Zhang, Gaojie Jin, Xiang Li, Li Shen, Jiaxing Shang, Tianlong Chen, Ke Li, Lu Liu, Qingsong Wen, Shiwei Liu
The paper introduces StablePDENet, a physics-informed adversarial training framework that regularizes the residual sensitivity of neural operators to improve stability against input perturbations. The method formulates operator learning as a min–max optimization, where a physics-based projected‑gradient adversary generates perturbations and the outer objective combines the attacked physics loss with a normalized residual‑sensitivity penalty. Experiments on benchmark problems show that StablePDENet outperforms PI‑DeepONet and its adversarial variant in accuracy under adversarial attacks while maintaining competitive performance on clean data, and it also enhances generalization and highlights the distinction between model sensitivity and intrinsic operator ill‑conditioning.
By Chutian Huang, Chang Ma, Kaibo Wang, Yang Xiang
arXiv:2603. 23878v3 Announce Type: replace-cross Abstract: The parameterized CROWN analysis, a.
By Henry LeCates, Haoze Wu
The paper introduces the Quantization Analysis Tool, a system built on the ONNX framework that streamlines quantization workflows for deep learning models. It offers layer‑wise sensitivity analysis, visualizations of weight and activation distributions, and guidance for selecting precision levels to balance model size, latency, and accuracy. Experiments on various neural network architectures show that the tool improves quantized accuracy and overall deployment efficiency.
By Dwith Chenna, Kanishka Macherla
The paper introduces Conflict‑Aware Evidential Deep Learning (C‑EDL), a lightweight post‑hoc method that improves uncertainty quantification for deep learning models. C‑EDL applies diverse, task‑preserving transformations to each input and uses representational disagreement to adjust predictions, thereby reducing overconfident errors on adversarial and out‑of‑distribution data. Experiments demonstrate that C‑EDL outperforms existing Evidential Deep Learning variants and baselines, achieving up to 55 % reduction in coverage for OOD data and 90 % for adversarial data across multiple datasets and attack types.
By Charmaine Barker, Daniel Bethell, Simos Gerasimou
arXiv:2606. 04317v1 Announce Type: cross Abstract: Deep neural networks are increasingly deployed across heterogeneous and partially untrusted environments, where models are distributed through cloud storage, CI/CD pipelines, containerized services, and edge execution platforms.
By Bin Duan, Zeyu Bai, Guowei Yang
arXiv:2510. 18989v2 Announce Type: replace Abstract: Neural operators are commonly utilized as fast surrogates for numerical solvers in PDE problems, mapping input functions to solution functions.
By Yifei Sun
arXiv:2506.17874v3 Announce Type: replace-cross
Abstract: In many real-world applications, ensuring the robustness and stability of deep neural networks (DNNs) is crucial, particularly for image clas...
By Jiaming Hu, Yeping Jin, Debarghya Mukherjee, Ioannis Ch. Paschalidis
arXiv:2606. 30930v1 Announce Type: cross Abstract: Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory.
By Konstantinos Emmanouilidis, Lachlan MacDonald, Salma Tarmoun, Rene Vidal