Wentao Huang

Xing He, Lei Chu, Robert Qiu et al.

The Jacobian matrix is the core part of power flow analysis, which is the basis for power system planning and operations. This paper estimates the Jacobian matrix in high dimensional space. Firstly, theoretical analysis and model-based calculation of the Jacobian matrix are introduced to obtain the benchmark value. Then, the estimation algorithms based on least-squared errors and the deviation estimation based on the neural network are studied in detail, including the theories, equations, derivations, codes, advantages and disadvantages, and application scenes. The proposed algorithms are data-driven and sensitive to up-to-date topology parameters and state variables. The efforts are validate by comparing the results to benchmark values.

Wentao Huang, Yuesheng Xu, Haizhang Zhang

Deep neural networks, as a powerful system to represent high dimensional complex functions, play a key role in deep learning. Convergence of deep neural networks is a fundamental issue in building the mathematical foundation for deep learning. We investigated the convergence of deep ReLU networks and deep convolutional neural networks in two recent researches (arXiv:2107.12530, 2109.13542). Only the Rectified Linear Unit (ReLU) activation was studied therein, and the important pooling strategy was not considered. In this current work, we study the convergence of deep neural networks as the depth tends to infinity for two other important activation functions: the leaky ReLU and the sigmoid function. Pooling will also be studied. As a result, we prove that the sufficient condition established in arXiv:2107.12530, 2109.13542 is still sufficient for the leaky ReLU networks. For contractive activation functions such as the sigmoid function, we establish a weaker sufficient condition for uniform convergence of deep neural networks.

Wentao Huang, Haizhang Zhang

Various powerful deep neural network architectures have made great contribution to the exciting successes of deep learning in the past two decades. Among them, deep Residual Networks (ResNets) are of particular importance because they demonstrated great usefulness in computer vision by winning the first place in many deep learning competitions. Also, ResNets were the first class of neural networks in the development history of deep learning that are really deep. It is of mathematical interest and practical meaning to understand the convergence of deep ResNets. We aim at characterizing the convergence of deep ResNets as the depth tends to infinity in terms of the parameters of the networks. Toward this purpose, we first give a matrix-vector description of general deep neural networks with shortcut connections and formulate an explicit expression for the networks by using the notions of activation domains and activation matrices. The convergence is then reduced to the convergence of two series involving infinite products of non-square matrices. By studying the two series, we establish a sufficient condition for pointwise convergence of ResNets. Our result is able to give justification for the design of ResNets. We also conduct experiments on benchmark machine learning data to verify our results.

Weimin Lyu, Qingqiao Hu, Kehan Qi et al.

Whole-slide images (WSIs) in pathology can reach up to 10,000 x 10,000 pixels, posing significant challenges for multimodal large language model (MLLM) due to long context length and high computational demands. Previous methods typically focus on patch-level analysis or slide-level classification using CLIP-based models with multi-instance learning, but they lack the generative capabilities needed for visual question answering (VQA). More recent MLLM-based approaches address VQA by feeding thousands of patch tokens directly into the language model, which leads to excessive resource consumption. To address these limitations, we propose Token Compression Pathology LLaVA (TCP-LLaVA), the first MLLM architecture to perform WSI VQA via token compression. TCP-LLaVA introduces a set of trainable compression tokens that aggregate visual and textual information through a modality compression module, inspired by the [CLS] token mechanism in BERT. Only the compressed tokens are forwarded to the LLM for answer generation, significantly reducing input length and computational cost. Experiments on ten TCGA tumor subtypes show that TCP-LLaVA outperforms existing MLLM baselines in VQA accuracy while reducing training resource consumption by a substantial margin.