Zheng Ma

Keke Wu, Xiong-bin Yan, Shi Jin et al.

In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transport problem. We observe that the vanilla physics-informed DeepONets with modified MLP may exhibit instability in maintaining the desired limiting macroscopic behavior. Therefore, this necessitates the utilization of an asymptotic-preserving loss function. Drawing inspiration from the heat kernel in the diffusion equation, we propose a new architecture called Convolutional Deep Operator Networks, which employ multiple local convolution operations instead of a global heat kernel, along with pooling and activation operations in each filter layer. Our APCON methods possess a parameter count that is independent of the grid size and are capable of capturing the diffusive behavior of the linear transport problem. Finally, we validate the effectiveness of our methods through several numerical examples.

Ruize Ma, Yilei Jiang, Shilin Zhang et al.

Multimodal Automated Program Repair (MAPR) extends traditional program repair by requiring models to jointly reason over source code, textual issue descriptions, and visual artifacts such as GUI screenshots. While recent LLM-based repair systems have shown promising results, existing approaches face several limitations: rigid workflow pipelines restrict exploration during debugging, visual reasoning is often performed over full-page screenshots without localized grounding, and failed repair attempts are rarely transformed into reusable knowledge. To address these challenges, we propose FailureMem, a multimodal repair framework that integrates three key mechanisms: a hybrid workflow-agent architecture that balances structured localization with flexible reasoning, active perception tools that enable region-level visual grounding, and a Failure Memory Bank that converts past repair attempts into reusable guidance. Experiments on SWE-bench Multimodal demonstrate FailureMem improves the resolved rate over GUIRepair by 3.7%.

Bo Hu, Han Yuan, Vlad Pandelea et al.

The rapid advancement of large language models (LLMs) has sparked widespread adoption across diverse applications, making robust evaluation frameworks crucial for assessing their performance. While conventional evaluation metrics remain applicable for shorter texts, their efficacy diminishes when evaluating the quality of long-form answers. This limitation is particularly critical in real-world scenarios involving extended questions, extensive context, and long-form answers, such as financial analysis or regulatory compliance. In this paper, we use a practical financial use case to illustrate applications that handle "long question-context-answer triplets". We construct a real-world financial dataset comprising long triplets and demonstrate the inadequacies of traditional metrics. To address this, we propose an effective Extract, Match, and Score (EMS) evaluation approach tailored to the complexities of long-form LLMs' outputs, providing practitioners with a reliable methodology for assessing LLMs' performance in complex real-world scenarios.

Shiyu Tang, Peijun Tang, Yanxiang Gong et al.

Previous feature alignment methods in Unsupervised domain adaptation(UDA) mostly only align global features without considering the mismatch between class-wise features. In this work, we propose a new coarse-to-fine feature alignment method using contrastive learning called CFContra. It draws class-wise features closer than coarse feature alignment or class-wise feature alignment only, therefore improves the model's performance to a great extent. We build it upon one of the most effective methods of UDA called entropy minimization to further improve performance. In particular, to prevent excessive memory occupation when applying contrastive loss in semantic segmentation, we devise a new way to build and update the memory bank. In this way, we make the algorithm more efficient and viable with limited memory. Extensive experiments show the effectiveness of our method and model trained on the GTA5 to Cityscapes dataset has boost mIOU by 3.5 compared to the MinEnt algorithm. Our code will be publicly available.

Zheng Ma, Junyu Xuan, Yu Guang Wang et al.

Graph neural networks (GNNs) extends the functionality of traditional neural networks to graph-structured data. Similar to CNNs, an optimized design of graph convolution and pooling is key to success. Borrowing ideas from physics, we propose a path integral based graph neural networks (PAN) for classification and regression tasks on graphs. Specifically, we consider a convolution operation that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. It generalizes the graph Laplacian to a new transition matrix we call maximal entropy transition (MET) matrix derived from a path integral formalism. Importantly, the diagonal entries of the MET matrix are directly related to the subgraph centrality, thus providing a natural and adaptive pooling mechanism. PAN provides a versatile framework that can be tailored for different graph data with varying sizes and structures. We can view most existing GNN architectures as special cases of PAN. Experimental results show that PAN achieves state-of-the-art performance on various graph classification/regression tasks, including a new benchmark dataset from statistical mechanics we propose to boost applications of GNN in physical sciences.

Hao Ge, Xiaoguang Tu, Yanxiang Gong et al.

The interpretability of Convolutional Neural Networks (CNNs) is an important topic in the field of computer vision. In recent years, works in this field generally adopt a mature model to reveal the internal mechanism of CNNs, helping to understand CNNs thoroughly. In this paper, we argue the working mechanism of CNNs can be revealed through a totally different interpretation, by comparing the communication systems and CNNs. This paper successfully obtained the corresponding relationship between the modules of the two, and verified the rationality of the corresponding relationship with experiments. Finally, through the analysis of some cutting-edge research on neural networks, we find the inherent relation between these two tasks can be of help in explaining these researches reasonably, as well as helping us discover the correct research direction of neural networks.

Hao Ge, Xiaoguang Tu, Mei Xie et al.

In recent years, deep learning has shown impressive performance on many tasks. However, recent researches showed that deep learning systems are vulnerable to small, specially crafted perturbations that are imperceptible to humans. Images with such perturbations are the so called adversarial examples, which have proven to be an indisputable threat to the DNN based applications. The lack of better understanding of the DNNs has prevented the development of efficient defenses against adversarial examples. In this paper, we propose a two-stream architecture to protect CNN from attacking by adversarial examples. Our model draws on the idea of "two-stream" which commonly used in the security field, and successfully defends different kinds of attack methods by the differences of "high-resolution" and "low-resolution" networks in feature extraction. We provide a reasonable interpretation on why our two-stream architecture is difficult to defeat, and show experimentally that our method is hard to defeat with state-of-the-art attacks. We demonstrate that our two-stream architecture is robust to adversarial examples built by currently known attacking algorithms.

Yu Guang Wang, Ming Li, Zheng Ma et al.

Deep Graph Neural Networks (GNNs) are useful models for graph classification and graph-based regression tasks. In these tasks, graph pooling is a critical ingredient by which GNNs adapt to input graphs of varying size and structure. We propose a new graph pooling operation based on compressive Haar transforms -- HaarPooling. HaarPooling implements a cascade of pooling operations; it is computed by following a sequence of clusterings of the input graph. A HaarPooling layer transforms a given input graph to an output graph with a smaller node number and the same feature dimension; the compressive Haar transform filters out fine detail information in the Haar wavelet domain. In this way, all the HaarPooling layers together synthesize the features of any given input graph into a feature vector of uniform size. Such transforms provide a sparse characterization of the data and preserve the structure information of the input graph. GNNs implemented with standard graph convolution layers and HaarPooling layers achieve state of the art performance on diverse graph classification and regression problems.

Ming Li, Zheng Ma, Yu Guang Wang et al.

Graph Neural Networks (GNNs) have become a topic of intense research recently due to their powerful capability in high-dimensional classification and regression tasks for graph-structured data. However, as GNNs typically define the graph convolution by the orthonormal basis for the graph Laplacian, they suffer from high computational cost when the graph size is large. This paper introduces Haar basis which is a sparse and localized orthonormal system for a coarse-grained chain on graph. The graph convolution under Haar basis, called Haar convolution, can be defined accordingly for GNNs. The sparsity and locality of the Haar basis allow Fast Haar Transforms (FHTs) on graph, by which a fast evaluation of Haar convolution between graph data and filters can be achieved. We conduct experiments on GNNs equipped with Haar convolution, which demonstrates state-of-the-art results on graph-based regression and node classification tasks.

Tao Luo, Zheng Ma, Zhi-Qin John Xu et al.

Along with fruitful applications of Deep Neural Networks (DNNs) to realistic problems, recently, some empirical studies of DNNs reported a universal phenomenon of Frequency Principle (F-Principle): a DNN tends to learn a target function from low to high frequencies during the training. The F-Principle has been very useful in providing both qualitative and quantitative understandings of DNNs. In this paper, we rigorously investigate the F-Principle for the training dynamics of a general DNN at three stages: initial stage, intermediate stage, and final stage. For each stage, a theorem is provided in terms of proper quantities characterizing the F-Principle. Our results are general in the sense that they work for multilayer networks with general activation functions, population densities of data, and a large class of loss functions. Our work lays a theoretical foundation of the F-Principle for a better understanding of the training process of DNNs.

Yaoyu Zhang, Zhi-Qin John Xu, Tao Luo et al.

It remains a puzzle that why deep neural networks (DNNs), with more parameters than samples, often generalize well. An attempt of understanding this puzzle is to discover implicit biases underlying the training process of DNNs, such as the Frequency Principle (F-Principle), i.e., DNNs often fit target functions from low to high frequencies. Inspired by the F-Principle, we propose an effective model of linear F-Principle (LFP) dynamics which accurately predicts the learning results of two-layer ReLU neural networks (NNs) of large widths. This LFP dynamics is rationalized by a linearized mean field residual dynamics of NNs. Importantly, the long-time limit solution of this LFP dynamics is equivalent to the solution of a constrained optimization problem explicitly minimizing an FP-norm, in which higher frequencies of feasible solutions are more heavily penalized. Using this optimization formulation, an a priori estimate of the generalization error bound is provided, revealing that a higher FP-norm of the target function increases the generalization error. Overall, by explicitizing the implicit bias of the F-Principle as an explicit penalty for two-layer NNs, our work makes a step towards a quantitative understanding of the learning and generalization of general DNNs.

Zheng Ma, Ming Li, Yuguang Wang

Convolution operations designed for graph-structured data usually utilize the graph Laplacian, which can be seen as message passing between the adjacent neighbors through a generic random walk. In this paper, we propose PAN, a new graph convolution framework that involves every path linking the message sender and receiver with learnable weights depending on the path length, which corresponds to the maximal entropy random walk. PAN generalizes the graph Laplacian to a new transition matrix we call \emph{maximal entropy transition} (MET) matrix derived from a path integral formalism. Most previous graph convolutional network architectures can be adapted to our framework, and many variations and derivatives based on the path integral idea can be developed. Experimental results show that the path integral based graph neural networks have great learnability and fast convergence rate, and achieve state-of-the-art performance on benchmark tasks.

Sirui Xie, Junning Huang, Lanxin Lei et al.

Reinforcement learning agents need exploratory behaviors to escape from local optima. These behaviors may include both immediate dithering perturbation and temporally consistent exploration. To achieve these, a stochastic policy model that is inherently consistent through a period of time is in desire, especially for tasks with either sparse rewards or long term information. In this work, we introduce a novel on-policy temporally consistent exploration strategy - Neural Adaptive Dropout Policy Exploration (NADPEx) - for deep reinforcement learning agents. Modeled as a global random variable for conditional distribution, dropout is incorporated to reinforcement learning policies, equipping them with inherent temporal consistency, even when the reward signals are sparse. Two factors, gradients' alignment with the objective and KL constraint in policy space, are discussed to guarantee NADPEx policy's stable improvement. Our experiments demonstrate that NADPEx solves tasks with sparse reward while naive exploration and parameter noise fail. It yields as well or even faster convergence in the standard mujoco benchmark for continuous control.