Estimating the global Lipschitz constant of neural networks is crucial for understanding and improving their robustness and generalization capabilities. However, precise calculations are NP-hard, and current semidefinite programming (SDP) methods face challenges such as high memory usage and slow processing speeds. In this paper, we propose HiQ-Lip, a hybrid quantum-classical hierarchical method that leverages Coherent Ising Machines (CIMs) to estimate the global Lipschitz constant. We tackle the estimation by converting it into a Quadratic Unconstrained Binary Optimization (QUBO) problem and implement a multilevel graph coarsening and refinement strategy to adapt to the constraints of contemporary quantum hardware. Our experimental evaluations on fully connected neural networks demonstrate that HiQ-Lip not only provides estimates comparable to state-of-the-art methods but also significantly accelerates the computation process. In specific tests involving two-layer neural networks with 256 hidden neurons, HiQ-Lip doubles the solving speed and offers more accurate upper bounds than the existing best method, LiPopt. These findings highlight the promising utility of small-scale quantum devices in advancing the estimation of neural network robustness.

Images captured in low-light environments have problems of insufficient brightness and low contrast, which will affect subsequent image processing tasks. Although most current enhancement methods can obtain high-contrast images, they still suffer from noise amplification and color distortion. To address these issues, this paper proposes a low-light image enhancement network based on multi-scale feature complementation (LIEN-MFC), which is a U-shaped encoder-decoder network supervised by multiple images of different scales. In the encoder, four feature extraction branches are constructed to extract features of low-light images at different scales. In the decoder, to ensure the integrity of the learned features at each scale, a feature supplementary fusion module (FSFM) is proposed to complement and integrate features from different branches of the encoder and decoder. In addition, a feature restoration module (FRM) and an image reconstruction module (IRM) are built in each branch to reconstruct the restored features and output enhanced images. To better train the network, a joint loss function is defined, in which a discriminative loss term is designed to ensure that the enhanced results better meet the visual properties of the human eye. Extensive experiments on benchmark datasets show that the proposed method outperforms some state-of-the-art methods subjectively and objectively.