The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the Lipschitz constant. Typically, this involves solving a large matrix verification problem, the computational cost of which grows significantly for both deeper and wider networks. In this paper, we provide a compositional approach to estimate Lipschitz constants for deep feed-forward neural networks. We first obtain an exact decomposition of the large matrix verification problem into smaller sub-problems. Then, leveraging the underlying cascade structure of the network, we develop two algorithms. The first algorithm explores the geometric features of the problem and enables us to provide Lipschitz estimates that are comparable to existing methods by solving small semidefinite programs (SDPs) that are only as large as the size of each layer. The second algorithm relaxes these sub-problems and provides a closed-form solution to each sub-problem for extremely fast estimation, altogether eliminating the need to solve SDPs. The two algorithms represent different levels of trade-offs between efficiency and accuracy. Finally, we demonstrate that our approach provides a steep reduction in computation time (as much as several thousand times faster, depending on the algorithm for deeper networks) while yielding Lipschitz bounds that are very close to or even better than those achieved by state-of-the-art approaches in a broad range of experiments. In summary, our approach considerably advances the scalability and efficiency of certifying neural network robustness, making it particularly attractive for online learning tasks.

As deep learning technology research continues to progress, artificial intelligence technology is gradually empowering various fields. To achieve a more natural human-computer interaction experience, how to accurately recognize emotional state of speech interactions has become a new research hotspot. Sequence modeling methods based on deep learning techniques have promoted the development of emotion recognition, but the mainstream methods still suffer from insufficient multimodal information interaction, difficulty in learning emotion-related features, and low recognition accuracy. In this paper, we propose a transformer-based deep-scale fusion network (TDFNet) for multimodal emotion recognition, solving the aforementioned problems. The multimodal embedding (ME) module in TDFNet uses pretrained models to alleviate the data scarcity problem by providing a priori knowledge of multimodal information to the model with the help of a large amount of unlabeled data. In addition, a mutual transformer (MT) module is introduced to learn multimodal emotional commonality and speaker-related emotional features to improve contextual emotional semantic understanding. In addition, we design a novel emotion feature learning method named the deep-scale transformer (DST), which further improves emotion recognition by aligning multimodal features and learning multiscale emotion features through GRUs with shared weights. To comparatively evaluate the performance of TDFNet, experiments are conducted with the IEMOCAP corpus under three reasonable data splitting strategies. The experimental results show that TDFNet achieves 82.08% WA and 82.57% UA in RA data splitting, which leads to 1.78% WA and 1.17% UA improvements over the previous state-of-the-art method, respectively. Benefiting from the attentively aligned mutual correlations and fine-grained emotion-related features, TDFNet successfully achieves significant improvements in multimodal emotion recognition.

Aspect-based sentiment analysis aims to identify the sentiment polarity of a certain aspect in the context sentence. It only use the syntax dependency tree to construct graph convolution in previous sentiment analysis methods. But one aspect of sentiment sometimes only be determined by a few words, and relying entirely on the syntax tree may distract the model's attention. Also, due to the limitations of the corpus, the model is only able to learn limited knowledge. To address the above limitations, we propose a sentiment classification model based on aspect-dependent heterogeneous graph convolutional network (named ADHGCN). The model prunes the dependency tree, and then it can reduce the influence of featherweight information on the results. In addition, the model fuses multiple feature relationships between words by constructing a heterogeneous graph, and applies graph convolutional network (GCN) to seek meaningful representations for each node. It makes the model further integrate a variety of information on the original basis, and then it is no longer purely dependent on one relation. At the same time, this paper will introduce a common-sense knowledge base to participate in the construction of heterogeneous graphs, so that the model can learn knowledge beyond the corpus, thereby improving the accuracy of sentiment classification. Through experiments, we have demonstrated that our network performs better than others on five public datasets.

Remote sensing image scene classification has attracted much attention due to its wide application. In this letter, a new end-to-end attentive context network under the guidance of human visual system has been proposed. The network can focus on some critical regions of the image selectively and then extract high-level feature information so as to generalize the whole image. The contributions of this letter are as follows: 1) a novel attention structure which expresses the attention of image by stacking attention modules is designed and 2) the context information of the image is used to make a holistic analysis of the attention mechanism on the basis of the top–down feedforward structure. Experiments performed on several datasets demonstrate that the proposed framework can obtain outstanding performance compared with the state-of-the-art approaches.