Computer-assisted global regularity across nonlinear families of three-dimensional periodic Navier-Stokes flows
本文通过结合有限参考轨迹与通用误差界限,开发了一种计算机辅助框架,以证明三维周期性Navier-Stokes流连续族的全局正则性。
本文通过结合有限参考轨迹与通用误差界限,开发了一种计算机辅助框架,以证明三维周期性Navier-Stokes流连续族的全局正则性。
本文探讨了量子安全加密机制,针对可能的量子计算威胁,分析了现有应用迁移至量子安全方案的方法及面临的挑战。
论文提出响应重正化方法,解决深度平衡模型中由于雅可比矩阵接近奇异导致的梯度不稳定问题,从而提高优化可靠性。
This work addresses the challenges of statistical inconsistency, high communication overhead, and privacy concerns in traditional principal component analysis (PCA) when applied to high-dimensional distributed data. The authors propose a novel distributed PCA framework that incorporates wavelet-based sparsification, leveraging wavelet transforms to obtain sparse representations of variables. By integrating this sparsification with a distributed optimization algorithm, the method efficiently estimates the global shared subspace without requiring raw data aggregation. The approach preserves statistical consistency while substantially reducing communication costs. Experimental results demonstrate that, for dimensions \(d \geq 152\), the proposed method consistently outperforms existing approaches in both estimation accuracy and the number of transmitted coefficients.
Existing implicit neural layers struggle to disentangle the distinct contributions of input stimuli, local propagation, global context, and solver dynamics to the learned representations. This work proposes SILVA, a unified fixed-point architecture that explicitly decouples stimulus injection, local and global interactions, damping, and readout mechanisms. Through domain-adaptive designs of node, neighborhood, and global summarization modules, SILVA is tailored for diverse tasks spanning images, molecular graphs, citation networks, and long-range graph problems. As the first method to structurally decompose multi-source interactions within implicit layers, SILVA renders internal dynamics trainable, ablatable, and visualizable. Experiments reveal that graph tasks predominantly rely on local interactions, MNIST exhibits limited recursive gains under high capacity, and long-range node classification significantly benefits from explicitly modeled global interactions.
本文通过结合有限参考轨迹与通用误差界限,开发了一种计算机辅助框架,以证明三维周期性Navier-Stokes流连续族的全局正则性。
本文探讨了量子安全加密机制,针对可能的量子计算威胁,分析了现有应用迁移至量子安全方案的方法及面临的挑战。
论文提出响应重正化方法,解决深度平衡模型中由于雅可比矩阵接近奇异导致的梯度不稳定问题,从而提高优化可靠性。
This work addresses the challenges of statistical inconsistency, high communication overhead, and privacy concerns in traditional principal component analysis (PCA) when applied to high-dimensional distributed data. The authors propose a novel distributed PCA framework that incorporates wavelet-based sparsification, leveraging wavelet transforms to obtain sparse representations of variables. By integrating this sparsification with a distributed optimization algorithm, the method efficiently estimates the global shared subspace without requiring raw data aggregation. The approach preserves statistical consistency while substantially reducing communication costs. Experimental results demonstrate that, for dimensions \(d \geq 152\), the proposed method consistently outperforms existing approaches in both estimation accuracy and the number of transmitted coefficients.
Existing implicit neural layers struggle to disentangle the distinct contributions of input stimuli, local propagation, global context, and solver dynamics to the learned representations. This work proposes SILVA, a unified fixed-point architecture that explicitly decouples stimulus injection, local and global interactions, damping, and readout mechanisms. Through domain-adaptive designs of node, neighborhood, and global summarization modules, SILVA is tailored for diverse tasks spanning images, molecular graphs, citation networks, and long-range graph problems. As the first method to structurally decompose multi-source interactions within implicit layers, SILVA renders internal dynamics trainable, ablatable, and visualizable. Experiments reveal that graph tasks predominantly rely on local interactions, MNIST exhibits limited recursive gains under high capacity, and long-range node classification significantly benefits from explicitly modeled global interactions.