Zhe Xiong

Zhe Xiong, Qiaoqiao Ding, Xiaoqun Zhang

Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One powerful framework for such transformations is normalizing flow, which transforms an unknown distribution into a standard normal distribution using an invertible network. In this paper, we introduce a novel model called SyMOT-Flow that trains an invertible transformation by minimizing the symmetric maximum mean discrepancy between samples from two unknown distributions, and an optimal transport cost is incorporated as regularization to obtain a short-distance and interpretable transformation. The resulted transformation leads to more stable and accurate sample generation. Several theoretical results are established for the proposed model and its effectiveness is validated with low-dimensional illustrative examples as well as high-dimensional bi-modality medical image generation through the forward and reverse flows.

Zhe Xiong, Qiaoqiao Ding, Xiaoqun Zhang

Recently, medical image synthesis gains more and more popularity, along with the rapid development of generative models. Medical image synthesis aims to generate an unacquired image modality, often from other observed data modalities. Synthesized images can be used for clinical diagnostic assistance, data augmentation for model training and validation or image quality improving. In the meanwhile, the flow-based models are among the successful generative models for the ability of generating realistic and high-quality synthetic images. However, most flow-based models require to calculate flow ordinary different equation (ODE) evolution steps in synthesis process, for which the performances are significantly limited by heavy computation time due to a large number of time iterations. In this paper, we propose a novel flow-based model, namely bi-directional Discrete Process Matching (Bi-DPM) to accomplish the bi-modality image synthesis tasks. Different to other flow matching based models, we propose to utilize both forward and backward ODE flows and enhance the consistency on the intermediate images over a few discrete time steps, resulting in a synthesis process maintaining high-quality generations for both modalities under the guidance of paired data. Our experiments on three datasets of MRI T1/T2 and CT/MRI demonstrate that Bi-DPM outperforms other state-of-the-art flow-based methods for bi-modality image synthesis, delivering higher image quality with accurate anatomical regions.

Yuan Cheng, Yu Huang, Zhe Xiong et al.

Uncovering hidden graph structures underlying real-world data is a critical challenge with broad applications across scientific domains. Recently, transformer-based models leveraging the attention mechanism have demonstrated strong empirical success in capturing complex dependencies within graphs. However, the theoretical understanding of their training dynamics has been limited to tree-like graphs, where each node depends on a single parent. Extending provable guarantees to more general directed acyclic graphs (DAGs) -- which involve multiple parents per node -- remains challenging, primarily due to the difficulty in designing training objectives that enable different attention heads to separately learn multiple different parent relationships. In this work, we address this problem by introducing a novel information-theoretic metric: the kernel-guided mutual information (KG-MI), based on the $f$-divergence. Our objective combines KG-MI with a multi-head attention framework, where each head is associated with a distinct marginal transition kernel to model diverse parent-child dependencies effectively. We prove that, given sequences generated by a $K$-parent DAG, training a single-layer, multi-head transformer via gradient ascent converges to the global optimum in polynomial time. Furthermore, we characterize the attention score patterns at convergence. In addition, when particularizing the $f$-divergence to the KL divergence, the learned attention scores accurately reflect the ground-truth adjacency matrix, thereby provably recovering the underlying graph structure. Experimental results validate our theoretical findings.

Yuchen Guo, Nicholas Hanoian, Zhexiao Lin et al.

We propose a novel model for a topic-aware chatbot by combining the traditional Recurrent Neural Network (RNN) encoder-decoder model with a topic attention layer based on Nonnegative Matrix Factorization (NMF). After learning topic vectors from an auxiliary text corpus via NMF, the decoder is trained so that it is more likely to sample response words from the most correlated topic vectors. One of the main advantages in our architecture is that the user can easily switch the NMF-learned topic vectors so that the chatbot obtains desired topic-awareness. We demonstrate our model by training on a single conversational data set which is then augmented with topic matrices learned from different auxiliary data sets. We show that our topic-aware chatbot not only outperforms the non-topic counterpart, but also that each topic-aware model qualitatively and contextually gives the most relevant answer depending on the topic of question.