Jicheng Li

Liqiang Dong, Jicheng Li, Xuenian Liu

In this paper, we first propose a new parameterized definition of comparison matrix of a given complex matrix, which generalizes the definition proposed by \cite {Axe1}. Based on this, we propose a new class of complex nonsymmetric algebraic Riccati equations (NAREs) which extends the class of nonsymmetric algebraic Riccati equations proposed by \cite {Axe1}. We also generalize the definition of the extremal solution of an NARE and show that the extremal solution of an NARE exists and is unique. Some classical algorithms can be applied to search for the extremal solution of an NARE, including Newton's method, some fixed-point iterative methods and doubling algorithms. Besides, we show that Newton's method is quadratically convergent and the fixed-point iterative method is linearly convergent. We also give some concrete strategies for choosing suitable parameters such that the doubling algorithms can be used to deliver the extremal solutions, and show that the two doubling algorithms with suitable parameters are quadratically convergent. Numerical experiments show that our strategies for parameters are effective.

Hao Shu, Jicheng Li, Yu Jin et al.

In recent years, the prediction of multidimensional time series data has become increasingly important due to its wide-ranging applications. Tensor-based prediction methods have gained attention for their ability to preserve the inherent structure of such data. However, existing approaches, such as tensor autoregression and tensor decomposition, often have consistently failed to provide clear assertions regarding the number of samples that can be exactly predicted. While matrix-based methods using nuclear norms address this limitation, their reliance on matrices limits accuracy and increases computational costs when handling multidimensional data. To overcome these challenges, we reformulate multidimensional time series prediction as a deterministic tensor completion problem and propose a novel theoretical framework. Specifically, we develop a deterministic tensor completion theory and introduce the Temporal Convolutional Tensor Nuclear Norm (TCTNN) model. By convolving the multidimensional time series along the temporal dimension and applying the tensor nuclear norm, our approach identifies the maximum forecast horizon for exact predictions. Additionally, TCTNN achieves superior performance in prediction accuracy and computational efficiency compared to existing methods across diverse real-world datasets, including climate temperature, network flow, and traffic ride data. Our implementation is publicly available at https://github.com/HaoShu2000/TCTNN.

Jicheng Li, Pengzhi Gao, Xuanfu Wu et al.

Diverse machine translation aims at generating various target language translations for a given source language sentence. Leveraging the linear relationship in the sentence latent space introduced by the mixup training, we propose a novel method, MixDiversity, to generate different translations for the input sentence by linearly interpolating it with different sentence pairs sampled from the training corpus when decoding. To further improve the faithfulness and diversity of the translations, we propose two simple but effective approaches to select diverse sentence pairs in the training corpus and adjust the interpolation weight for each pair correspondingly. Moreover, by controlling the interpolation weight, our method can achieve the trade-off between faithfulness and diversity without any additional training, which is required in most of the previous methods. Experiments on WMT'16 en-ro, WMT'14 en-de, and WMT'17 zh-en are conducted to show that our method substantially outperforms all previous diverse machine translation methods.

Jicheng Li, Yang Feng, Jiao Ou

Text style transfer aims to change the style of sentences while preserving the semantic meanings. Due to the lack of parallel data, the Denoising Auto-Encoder (DAE) is widely used in this task to model distributions of different sentence styles. However, because of the conflict between the target of the conventional denoising procedure and the target of style transfer task, the vanilla DAE can not produce satisfying enough results. To improve the transferability of the model, most of the existing works combine DAE with various complicated unsupervised networks, which makes the whole system become over-complex. In this work, we design a novel DAE model named Style-Enhanced DAE (SE-DAE), which is specifically designed for the text style transfer task. Compared with previous complicated style-transfer models, our model do not consist of any complicated unsupervised networks, but only relies on the high-quality pseudo-parallel data generated by a novel data refinement mechanism. Moreover, to alleviate the conflict between the targets of the conventional denoising procedure and the style transfer task, we propose another novel style denoising mechanism, which is more compatible with the target of the style transfer task. We validate the effectiveness of our model on two style benchmark datasets. Both automatic evaluation and human evaluation show that our proposed model is highly competitive compared with previous strong the state of the art (SOTA) approaches and greatly outperforms the vanilla DAE.