We propose a framework to combine strong non-linear expressiveness with strict SO(3)-equivariance in prediction of the electronic-structure Hamiltonian, by exploring the mathematical relationships between SO(3)-invariant and SO(3)-equivariant quantities and their representations. The proposed framework, called TraceGrad, first constructs theoretical SO(3)-invariant trace quantities derived from the Hamiltonian targets, and use these invariant quantities as supervisory labels to guide the learning of high-quality SO(3)-invariant features. Given that SO(3)-invariance is preserved under non-linear operations, the learning of invariant features can extensively utilize non-linear mappings, thereby fully capturing the non-linear patterns inherent in physical systems. Building on this, we propose a gradient-based mechanism to induce SO(3)-equivariant encodings of various degrees from the learned SO(3)-invariant features. This mechanism can incorporate powerful non-linear expressive capabilities into SO(3)-equivariant features with correspondence of physical dimensions to the regression targets, while theoretically preserving equivariant properties, establishing a strong foundation for predicting electronic-structure Hamiltonian. Experimental results on eight challenging benchmark databases demonstrate that our method achieves state-of-the-art performance in Hamiltonian prediction.

Cloud removal is a critical step to improve the usability of cloud-contaminated remote sensing images. Deep learning methods based on convolutional neural networks (CNNs) and transformer architectures are widely used for cloud removal tasks. However, the localization of convolutional operations limits the capture of global features, and Transformer is prone to forget local spatial details when processing high-resolution images, which affects the further improvement of cloud removal accuracy. This study proposes a novel cloud removal model, Mamba-CR, based on the state-space model. In this model, the Convolution State-Space Group (CSSG) is designed to extract and reconstruct shallow spatial features of remote sensing images to alleviate the sequential dependence of Mamba on the data input of image processing sequences; the Transformer Structured State-Space Group (TSSG) is designed to enhance the model’s ability to sense global context and capture long-range spatial dependencies. Compared with other SOTA cloud removal methods on three publicly available datasets, Mamba-CR achieves a definite performance advantage while keeping the computational effort low.

With the wide application of network technology, the Internet of Things (IoT) systems are facing the increasingly serious situation of network threats; the network threat situation assessment becomes an important approach to solve these problems. Aiming at the traditional methods based on data category tag that has high modeling cost and low efficiency in the network threat situation assessment, this paper proposes a network threat situation assessment model based on unsupervised learning for IoT. Firstly, we combine the encoder of variational autoencoder (VAE) and the discriminator of generative adversarial networks (GAN) to form the V-G network. Then, we obtain the reconstruction error of each layer network by training the network collection layer of the V-G network with normal network traffic. Besides, we conduct the reconstruction error learning by the 3-layer variational autoencoder of the output layer and calculate the abnormal threshold of the training. Moreover, we carry out the group threat testing with the test dataset containing abnormal network traffic and calculate the threat probability of each test group. Finally, we obtain the threat situation value (TSV) according to the threat probability and the threat impact. The simulation results show that, compared with the other methods, this proposed method can evaluate the overall situation of network security threat more intuitively and has a stronger characterization ability for network threats.