Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the limited availability of known altermagnetic materials hinders the study of such properties. Hence, discovering more types of altermagnetic materials with different properties is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next generation of information technologies, e.g. storage devices and high-sensitivity sensors. Since each altermagnetic material has a unique crystal structure, we propose an automated discovery approach empowered by an artificial intelligence (AI) search engine that employs a pre-trained graph neural network to learn the intrinsic features of the material crystal structure, followed by fine-tuning a classifier with limited positive samples to predict the altermagnetism probability of a given material candidate. Finally, we successfully discovered 50 new altermagnetic materials that cover metals, semiconductors and insulators, confirmed by first-principles electronic structure calculations. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g. the anomalous Hall effect, anomalous Kerr effect and topological property. It is worth noting that we discovered four i-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeted properties.

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well as convolutional layers, contain most of the variational parameters that are trained and stored. Compressing a deep neural network to reduce its number of variational parameters but not its prediction power is an important but challenging problem toward the establishment of an optimized scheme in training efficiently these parameters and in lowering the risk of overfitting. Here we show that this problem can be effectively solved by representing linear transformations with matrix product operators (MPOs), which is a tensor network originally proposed in physics to characterize the short-range entanglement in one-dimensional quantum states. We have tested this approach in five typical neural networks, including FC2, LeNet-5, VGG, ResNet, and DenseNet on two widely used data sets, namely, MNIST and CIFAR-10, and found that this MPO representation indeed sets up a faithful and efficient mapping between input and output signals, which can keep or even improve the prediction accuracy with a dramatically reduced number of parameters. Our method greatly simplifies the representations in deep learnin, and opens a possible route toward establishing a framework of modern neural networks which might be simpler and cheaper, but more efficient.

The deep neural network (DNN) based speech enhancement approaches have achieved promising performance. However, the number of parameters involved in these methods is usually enormous for the real applications of speech enhancement on the device with the limited resources. This seriously restricts the applications. To deal with this issue, model compression techniques are being widely studied. In this paper, we propose a model compression method based on matrix product operators (MPO) to substantially reduce the number of parameters in DNN models for speech enhancement. In this method, the weight matrices in the linear transformations of neural network model are replaced by the MPO decomposition format before training. In experiment, this process is applied to the causal neural network models, such as the feedforward multilayer perceptron (MLP) and long short-term memory (LSTM) models. Both MLP and LSTM models with/without compression are then utilized to estimate the ideal ratio mask for monaural speech enhancement. The experimental results show that our proposed MPO-based method outperforms the widely-used pruning method for speech enhancement under various compression rates, and further improvement can be achieved with respect to low compression rates. Our proposal provides an effective model compression method for speech enhancement, especially in cloud-free application.

Developing inverse design methods for functional materials with specific properties is critical to advancing fields like renewable energy, catalysis, energy storage, and carbon capture. Generative models based on diffusion principles can directly produce new materials that meet performance constraints, thereby significantly accelerating the material design process. However, existing methods for generating and predicting crystal structures often remain limited by low success rates. In this work, we propose a novel inverse material design generative framework called InvDesFlow-AL, which is based on active learning strategies. This framework can iteratively optimize the material generation process to gradually guide it towards desired performance characteristics. In terms of crystal structure prediction, the InvDesFlow-AL model achieves an RMSE of 0.0423 Å, representing an 32.96% improvement in performance compared to existing generative models. Additionally, InvDesFlow-AL has been successfully validated in the design of low-formation-energy and low-E_hull materials. It can systematically generate materials with progressively lower formation energies while continuously expanding the exploration across diverse chemical spaces. Notably, through DFT structural relaxation validation, we identified 1,598,551 materials with E_hull < 50 meV, indicating their thermodynamic stability and atomic forces below 1e-4 eV/Å. These results fully demonstrate the effectiveness of the proposed active learning-driven generative model in accelerating material discovery and inverse design. To further prove the effectiveness of this method, we took the search for BCS superconductors under ambient pressure as an example explored by InvDesFlow-AL. As a result, we successfully identified Li₂AuH₆ as a conventional BCS superconductor with an ultra-high transition temperature of 140 K, and also discovered several other superconducting materials that surpass the theoretical McMillan limit and have transition temperatures within the liquid nitrogen temperature range. This discovery provides strong empirical support for the application of inverse design in materials science.

Symbolic regression has a crucial role in modern scientific research owing to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and generalizable mathematical formulas, in an infinite search space, while intending to fit the training data. Existing algorithms have faced a critical bottleneck of accuracy and efficiency over a decade when handling problems of complexity, which essentially hinders the pace of applying symbolic regression for scientific exploration across interdisciplinary domains. Here, to this end, we introduce parallel symbolic enumeration (PSE) to efficiently distill generic mathematical expressions from limited data. Experiments show that PSE achieves higher accuracy and faster computation compared with the state-of-the-art baseline algorithms across over 200 synthetic and experimental problem sets (for example, improving the recovery accuracy by up to 99% and reducing runtime by an order of magnitude). PSE represents an advance in accurate and efficient data-driven discovery of symbolic, interpretable models (for example, underlying physical laws), and improves the scalability of symbolic learning.