Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient backpropagation algorithms. However, challenges remain in solving complex ODEs, including high-order and nonlinear cases, emphasizing the need for improved efficiency and effectiveness. Traditional methods have typically relied on established knowledge integration to improve problem-solving efficiency. In contrast, this study takes a different approach by introducing a new neural network architecture for constructing trial functions, known as ratio net. This architecture draws inspiration from rational fraction polynomial approximation functions, specifically the Pade approximant. Through empirical trials, it demonstrated that the proposed method exhibits higher efficiency compared to existing approaches, including polynomial-based and multilayer perceptron (MLP) neural network-based methods. The ratio net holds promise for advancing the efficiency and effectiveness of solving differential equations.
Given the remarkable achievements in image generation through diffusion models, the research community has shown increasing interest in extending these models to video generation. Recent diffusion models for video generation have predominantly utilized attention layers to extract temporal features. However, attention layers are limited by their memory consumption, which increases quadratically with the length of the sequence. This limitation presents significant challenges when attempting to generate longer video sequences using diffusion models. To overcome this challenge, we propose leveraging state-space models (SSMs). SSMs have recently gained attention as viable alternatives due to their linear memory consumption relative to sequence length. In the experiments, we first evaluate our SSM-based model with UCF101, a standard benchmark of video generation. In addition, to investigate the potential of SSMs for longer video generation, we perform an experiment using the MineRL Navigate dataset, varying the number of frames to 64 and 150. In these settings, our SSM-based model can considerably save memory consumption for longer sequences, while maintaining competitive FVD scores to the attention-based models. Our codes are available at //github.com/shim0114/SSM-Meets-Video-Diffusion-Models.
The field of emotion recognition of conversation (ERC) has been focusing on separating sentence feature encoding and context modeling, lacking exploration in generative paradigms based on unified designs. In this study, we propose a novel approach, \textbf{InstructERC}, to reformulate the ERC task from a discriminative framework to a generative framework based on Large Language Models (LLMs). InstructERC makes three significant contributions: (1) it introduces a simple yet effective retrieval template module, which helps the model explicitly integrate multi-granularity dialogue supervision information. (2) We introduce two additional emotion alignment tasks, namely speaker identification and emotion prediction tasks, to implicitly model the dialogue role relationships and future emotional tendencies in conversations. (3) Pioneeringly, we unify emotion labels across benchmarks through the feeling wheel to fit real application scenarios. InstructERC still perform impressively on this unified dataset. Our LLM-based plugin framework significantly outperforms all previous models and achieves comprehensive SOTA on three commonly used ERC datasets. Extensive analysis of parameter-efficient and data-scaling experiments provides empirical guidance for applying it in practical scenarios. Our code and aligned unified dataset (UIME) can be found in the Github link.\footnote{You can find the offical realization in the Github link: //github.com/LIN-SHANG/InstructERC}
Recent advances in instruction-tuned Large Vision-Language Models (LVLMs) have imbued the models with the ability to generate high-level, image-grounded explanations with ease. While such capability is largely attributed to the rich world knowledge contained within the Large Language Models (LLMs), our work reveals their shortcomings in fine-grained visual categorization (FGVC) across six different benchmark settings. Most recent state-of-the-art LVLMs like LLaVa-1.5, InstructBLIP and GPT-4V not only severely deteriorate in terms of classification performance, e.g., average drop of 65.58 in EM for Stanford Dogs for LLaVA-1.5, but also struggle to generate an accurate explanation with detailed attributes based on the concept that appears within an input image despite their capability to generate holistic image-level descriptions. In-depth analyses show that instruction-tuned LVLMs exhibit modality gap, showing discrepancy when given textual and visual inputs that correspond to the same concept, preventing the image modality from leveraging the rich parametric knowledge within the LLMs. In an effort to further the community's endeavor in this direction, we propose a multiple granularity attribute-centric evaluation benchmark, Finer, which aims to establish a ground to evaluate LVLMs' fine-grained visual comprehension ability and provide significantly improved explainability.
Graph neural networks (GNNs) have proven effective in capturing relationships among nodes in a graph. This study introduces a novel perspective by considering a graph as a simplicial complex, encompassing nodes, edges, triangles, and $k$-simplices, enabling the definition of graph-structured data on any $k$-simplices. Our contribution is the Hodge-Laplacian heterogeneous graph attention network (HL-HGAT), designed to learn heterogeneous signal representations across $k$-simplices. The HL-HGAT incorporates three key components: HL convolutional filters (HL-filters), simplicial projection (SP), and simplicial attention pooling (SAP) operators, applied to $k$-simplices. HL-filters leverage the unique topology of $k$-simplices encoded by the Hodge-Laplacian (HL) operator, operating within the spectral domain of the $k$-th HL operator. To address computation challenges, we introduce a polynomial approximation for HL-filters, exhibiting spatial localization properties. Additionally, we propose a pooling operator to coarsen $k$-simplices, combining features through simplicial attention mechanisms of self-attention and cross-attention via transformers and SP operators, capturing topological interconnections across multiple dimensions of simplices. The HL-HGAT is comprehensively evaluated across diverse graph applications, including NP-hard problems, graph multi-label and classification challenges, and graph regression tasks in logistics, computer vision, biology, chemistry, and neuroscience. The results demonstrate the model's efficacy and versatility in handling a wide range of graph-based scenarios.
Existing learned video compression models employ flow net or deformable convolutional networks (DCN) to estimate motion information. However, the limited receptive fields of flow net and DCN inherently direct their attentiveness towards the local contexts. Global contexts, such as large-scale motions and global correlations among frames are ignored, presenting a significant bottleneck for capturing accurate motions. To address this issue, we propose a joint local and global motion compensation module (LGMC) for leaned video coding. More specifically, we adopt flow net for local motion compensation. To capture global context, we employ the cross attention in feature domain for motion compensation. In addition, to avoid the quadratic complexity of vanilla cross attention, we divide the softmax operations in attention into two independent softmax operations, leading to linear complexity. To validate the effectiveness of our proposed LGMC, we integrate it with DCVC-TCM and obtain learned video compression with joint local and global motion compensation (LVC-LGMC). Extensive experiments demonstrate that our LVC-LGMC has significant rate-distortion performance improvements over baseline DCVC-TCM.
Skiplists have become prevalent in systems. The main advantages of skiplists are their simplicity and ease of implementation, and the ability to support operations in the same asymptotic complexities as their tree-based counterparts. In this survey, we explore skiplists and their many variants. We highlight many scenarios of how skiplists are useful and fit well in these usage scenarios. We study several extensions to skiplists to make them fit for more applications, e.g., their use in the multi-dimensional space, network overlaying algorithms, as well as serving as indexes in database systems. Besides, we also discuss systems that adopt the idea of skiplists and apply the probabilistic skip pattern into their designs.
We revisit the problem of spurious modes that are sometimes encountered in partial differential equations discretizations. It is generally suspected that one of the causes for spurious modes is due to how boundary conditions are treated, and we use this as the starting point of our investigations. By regarding boundary conditions as algebraic constraints on a differential equation, we point out that any differential equation with homogeneous boundary conditions also admits a typically infinite number of hidden or implicit boundary conditions. In most discretization schemes, these additional implicit boundary conditions are violated, and we argue that this is what leads to the emergence of spurious modes. These observations motivate two definitions of the quality of computed eigenvalues based on violations of derivatives of boundary conditions on the one hand, and on the Grassmann distance between subspaces associated with computed eigenspaces on the other. Both of these tests are based on a standardized treatment of boundary conditions and do not require a priori knowledge of eigenvalue locations. The effectiveness of these tests is demonstrated on several examples known to have spurious modes. In addition, these quality tests show that in most problems, about half the computed spectrum of a differential operator is of low quality. The tests also specifically identify the low accuracy modes, which can then be projected out as a type of model reduction scheme.
The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we develop an optimization solver based on the Levenberg-Marquardt algorithm that features an anisotropic, locally adaptive penalty method to enhance robustness and prevent cell degeneration in the computation of hypersonic, viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric that inhibits grid motion in directions with small element length scales, an element shape regularization that inhibits nonlinear deformations of the high-order elements, and a penalty regularization that penalizes degenerate elements. Additionally, we introduce a procedure for locally scaling the regularization operators in an adaptive, elementwise manner in order to maintain grid validity. We apply the proposed MDG-ICE formulation to two- and three-dimensional test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.
Graph neural networks (GNNs) have been demonstrated to be a powerful algorithmic model in broad application fields for their effectiveness in learning over graphs. To scale GNN training up for large-scale and ever-growing graphs, the most promising solution is distributed training which distributes the workload of training across multiple computing nodes. However, the workflows, computational patterns, communication patterns, and optimization techniques of distributed GNN training remain preliminarily understood. In this paper, we provide a comprehensive survey of distributed GNN training by investigating various optimization techniques used in distributed GNN training. First, distributed GNN training is classified into several categories according to their workflows. In addition, their computational patterns and communication patterns, as well as the optimization techniques proposed by recent work are introduced. Second, the software frameworks and hardware platforms of distributed GNN training are also introduced for a deeper understanding. Third, distributed GNN training is compared with distributed training of deep neural networks, emphasizing the uniqueness of distributed GNN training. Finally, interesting issues and opportunities in this field are discussed.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.