Hyperbolic neural networks have emerged as a powerful tool for modeling hierarchical data structures prevalent in real-world datasets. Notably, residual connections, which facilitate the direct flow of information across layers, have been instrumental in the success of deep neural networks. However, current methods for constructing hyperbolic residual networks suffer from limitations such as increased model complexity, numerical instability, and errors due to multiple mappings to and from the tangent space. To address these limitations, we introduce LResNet, a novel Lorentzian residual neural network based on the weighted Lorentzian centroid in the Lorentz model of hyperbolic geometry. Our method enables the efficient integration of residual connections in Lorentz hyperbolic neural networks while preserving their hierarchical representation capabilities. We demonstrate that our method can theoretically derive previous methods while offering improved stability, efficiency, and effectiveness. Extensive experiments on both graph and vision tasks showcase the superior performance and robustness of our method compared to state-of-the-art Euclidean and hyperbolic alternatives. Our findings highlight the potential of LResNet for building more expressive neural networks in hyperbolic embedding space as a generally applicable method to multiple architectures, including CNNs, GNNs, and graph Transformers.

We propose a minimal power white box adversarial attack for Deep Learning based Automatic Modulation Classification (AMC). The proposed attack uses the Golden Ratio Search (GRS) method to find powerful attacks with minimal power. We evaluate the efficacy of the proposed method by comparing it with existing adversarial attack approaches. Additionally, we test the robustness of the proposed attack against various state-of-the-art architectures, including defense mechanisms such as adversarial training, binarization, and ensemble methods. Experimental results demonstrate that the proposed attack is powerful, requires minimal power, and can be generated in less time, significantly challenging the resilience of current AMC methods.