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In this work, the uncertainty associated with the finite element discretization error is modeled following the Bayesian paradigm. First, a continuous formulation is derived, where a Gaussian process prior over the solution space is updated based on observations from a finite element discretization. To avoid the computation of intractable integrals, a second, finer, discretization is introduced that is assumed sufficiently dense to represent the true solution field. A prior distribution is assumed over the fine discretization, which is then updated based on observations from the coarse discretization. This yields a posterior distribution with a mean that serves as an estimate of the solution, and a covariance that models the uncertainty associated with this estimate. Two particular choices of prior are investigated: a prior defined implicitly by assigning a white noise distribution to the right-hand side term, and a prior whose covariance function is equal to the Green's function of the partial differential equation. The former yields a posterior distribution with a mean close to the reference solution, but a covariance that contains little information regarding the finite element discretization error. The latter, on the other hand, yields posterior distribution with a mean equal to the coarse finite element solution, and a covariance with a close connection to the discretization error. For both choices of prior a contradiction arises, since the discretization error depends on the right-hand side term, but the posterior covariance does not. We demonstrate how, by rescaling the eigenvalues of the posterior covariance, this independence can be avoided.

Emotion recognition in conversation (ERC) is a crucial task in natural language processing and affective computing. This paper proposes MultiDAG+CL, a novel approach for Multimodal Emotion Recognition in Conversation (ERC) that employs Directed Acyclic Graph (DAG) to integrate textual, acoustic, and visual features within a unified framework. The model is enhanced by Curriculum Learning (CL) to address challenges related to emotional shifts and data imbalance. Curriculum learning facilitates the learning process by gradually presenting training samples in a meaningful order, thereby improving the model's performance in handling emotional variations and data imbalance. Experimental results on the IEMOCAP and MELD datasets demonstrate that the MultiDAG+CL models outperform baseline models. We release the code for MultiDAG+CL and experiments: //github.com/vanntc711/MultiDAG-CL

This paper optimizes the Convolutional Neural Network (CNN) algorithm using high-performance computing (HPC) technologies. It uses multi-core processors, GPUs, and parallel computing frameworks like OpenMPI and CUDA to speed up CNN model training. The approach improves performance and training time and is superior to alternative strategies. The study demonstrates how HPC technologies can refine the CNN method, resulting in faster and more accurate training of large-scale CNN models.

Deep Graph Neural Networks struggle with oversmoothing. This paper introduces a novel, physics-inspired GNN model designed to mitigate this issue. Our approach integrates with existing GNN architectures, introducing an entropy-aware message passing term. This term performs gradient ascent on the entropy during node aggregation, thereby preserving a certain degree of entropy in the embeddings. We conduct a comparative analysis of our model against state-of-the-art GNNs across various common datasets.

This paper proposes the User Viewing Flow Modeling (SINGLE) method for the article recommendation task, which models the user constant preference and instant interest from user-clicked articles. Specifically, we first employ a user constant viewing flow modeling method to summarize the user's general interest to recommend articles. In this case, we utilize Large Language Models (LLMs) to capture constant user preferences from previously clicked articles, such as skills and positions. Then we design the user instant viewing flow modeling method to build interactions between user-clicked article history and candidate articles. It attentively reads the representations of user-clicked articles and aims to learn the user's different interest views to match the candidate article. Our experimental results on the Alibaba Technology Association (ATA) website show the advantage of SINGLE, achieving a 2.4% improvement over previous baseline models in the online A/B test. Our further analyses illustrate that SINGLE has the ability to build a more tailored recommendation system by mimicking different article viewing behaviors of users and recommending more appropriate and diverse articles to match user interests.

This paper introduces Hierarchical Diffusion Policy (HDP), a hierarchical agent for multi-task robotic manipulation. HDP factorises a manipulation policy into a hierarchical structure: a high-level task-planning agent which predicts a distant next-best end-effector pose (NBP), and a low-level goal-conditioned diffusion policy which generates optimal motion trajectories. The factorised policy representation allows HDP to tackle both long-horizon task planning while generating fine-grained low-level actions. To generate context-aware motion trajectories while satisfying robot kinematics constraints, we present a novel kinematics-aware goal-conditioned control agent, Robot Kinematics Diffuser (RK-Diffuser). Specifically, RK-Diffuser learns to generate both the end-effector pose and joint position trajectories, and distill the accurate but kinematics-unaware end-effector pose diffuser to the kinematics-aware but less accurate joint position diffuser via differentiable kinematics. Empirically, we show that HDP achieves a significantly higher success rate than the state-of-the-art methods in both simulation and real-world.

Existing knowledge graph (KG) embedding models have primarily focused on static KGs. However, real-world KGs do not remain static, but rather evolve and grow in tandem with the development of KG applications. Consequently, new facts and previously unseen entities and relations continually emerge, necessitating an embedding model that can quickly learn and transfer new knowledge through growth. Motivated by this, we delve into an expanding field of KG embedding in this paper, i.e., lifelong KG embedding. We consider knowledge transfer and retention of the learning on growing snapshots of a KG without having to learn embeddings from scratch. The proposed model includes a masked KG autoencoder for embedding learning and update, with an embedding transfer strategy to inject the learned knowledge into the new entity and relation embeddings, and an embedding regularization method to avoid catastrophic forgetting. To investigate the impacts of different aspects of KG growth, we construct four datasets to evaluate the performance of lifelong KG embedding. Experimental results show that the proposed model outperforms the state-of-the-art inductive and lifelong embedding baselines.

This paper shows that masked autoencoders (MAE) are scalable self-supervised learners for computer vision. Our MAE approach is simple: we mask random patches of the input image and reconstruct the missing pixels. It is based on two core designs. First, we develop an asymmetric encoder-decoder architecture, with an encoder that operates only on the visible subset of patches (without mask tokens), along with a lightweight decoder that reconstructs the original image from the latent representation and mask tokens. Second, we find that masking a high proportion of the input image, e.g., 75%, yields a nontrivial and meaningful self-supervisory task. Coupling these two designs enables us to train large models efficiently and effectively: we accelerate training (by 3x or more) and improve accuracy. Our scalable approach allows for learning high-capacity models that generalize well: e.g., a vanilla ViT-Huge model achieves the best accuracy (87.8%) among methods that use only ImageNet-1K data. Transfer performance in downstream tasks outperforms supervised pre-training and shows promising scaling behavior.

Graph neural networks (GNNs) is widely used to learn a powerful representation of graph-structured data. Recent work demonstrates that transferring knowledge from self-supervised tasks to downstream tasks could further improve graph representation. However, there is an inherent gap between self-supervised tasks and downstream tasks in terms of optimization objective and training data. Conventional pre-training methods may be not effective enough on knowledge transfer since they do not make any adaptation for downstream tasks. To solve such problems, we propose a new transfer learning paradigm on GNNs which could effectively leverage self-supervised tasks as auxiliary tasks to help the target task. Our methods would adaptively select and combine different auxiliary tasks with the target task in the fine-tuning stage. We design an adaptive auxiliary loss weighting model to learn the weights of auxiliary tasks by quantifying the consistency between auxiliary tasks and the target task. In addition, we learn the weighting model through meta-learning. Our methods can be applied to various transfer learning approaches, it performs well not only in multi-task learning but also in pre-training and fine-tuning. Comprehensive experiments on multiple downstream tasks demonstrate that the proposed methods can effectively combine auxiliary tasks with the target task and significantly improve the performance compared to state-of-the-art methods.

This paper presents a new approach for assembling graph neural networks based on framelet transforms. The latter provides a multi-scale representation for graph-structured data. With the framelet system, we can decompose the graph feature into low-pass and high-pass frequencies as extracted features for network training, which then defines a framelet-based graph convolution. The framelet decomposition naturally induces a graph pooling strategy by aggregating the graph feature into low-pass and high-pass spectra, which considers both the feature values and geometry of the graph data and conserves the total information. The graph neural networks with the proposed framelet convolution and pooling achieve state-of-the-art performance in many types of node and graph prediction tasks. Moreover, we propose shrinkage as a new activation for the framelet convolution, which thresholds the high-frequency information at different scales. Compared to ReLU, shrinkage in framelet convolution improves the graph neural network model in terms of denoising and signal compression: noises in both node and structure can be significantly reduced by accurately cutting off the high-pass coefficients from framelet decomposition, and the signal can be compressed to less than half its original size with the prediction performance well preserved.