Spectral Graph Neural Networks (GNNs) have achieved tremendous success in graph learning. As an essential part of spectral GNNs, spectral graph convolution extracts crucial frequency information in graph data, leading to superior performance of spectral GNNs in downstream tasks. However, in this paper, we show that existing spectral GNNs remain critical drawbacks in performing the spectral graph convolution. Specifically, considering the spectral graph convolution as a construction operation towards target output, we prove that existing popular convolution paradigms cannot construct the target output with mild conditions on input graph signals, causing spectral GNNs to fall into suboptimal solutions. To address the issues, we rethink the spectral graph convolution from a more general two-dimensional (2-D) signal convolution perspective and propose a new convolution paradigm, named 2-D graph convolution. We prove that 2-D graph convolution unifies existing graph convolution paradigms, and is capable to construct arbitrary target output. Based on the proposed 2-D graph convolution, we further propose ChebNet2D, an efficient and effective GNN implementation of 2-D graph convolution through applying Chebyshev interpolation. Extensive experiments on benchmark datasets demonstrate both effectiveness and efficiency of the ChebNet2D.
Artificial General Intelligence (AGI), possessing the capacity to comprehend, learn, and execute tasks with human cognitive abilities, engenders significant anticipation and intrigue across scientific, commercial, and societal arenas. This fascination extends particularly to the Internet of Things (IoT), a landscape characterized by the interconnection of countless devices, sensors, and systems, collectively gathering and sharing data to enable intelligent decision-making and automation. This research embarks on an exploration of the opportunities and challenges towards achieving AGI in the context of the IoT. Specifically, it starts by outlining the fundamental principles of IoT and the critical role of Artificial Intelligence (AI) in IoT systems. Subsequently, it delves into AGI fundamentals, culminating in the formulation of a conceptual framework for AGI's seamless integration within IoT. The application spectrum for AGI-infused IoT is broad, encompassing domains ranging from smart grids, residential environments, manufacturing, and transportation to environmental monitoring, agriculture, healthcare, and education. However, adapting AGI to resource-constrained IoT settings necessitates dedicated research efforts. Furthermore, the paper addresses constraints imposed by limited computing resources, intricacies associated with large-scale IoT communication, as well as the critical concerns pertaining to security and privacy.