The Friendship Paradox is a simple and powerful statement about node degrees in a graph (Feld 1991). However, it only applies to undirected graphs with no edge weights, and the only node characteristic it concerns is degree. Since many social networks are more complex than that, it is useful to generalize this phenomenon, if possible, and a number of papers have proposed different generalizations. Here, we unify these generalizations in a common framework, retaining the focus on undirected graphs and allowing for weighted edges and for numeric node attributes other than degree to be considered, since this extension allows for a clean characterization and links to the original concepts most naturally. While the original Friendship Paradox and the Weighted Friendship Paradox hold for all graphs, considering non-degree attributes actually makes the extensions fail around 50% of the time, given random attribute assignment. We provide simple correlation-based rules to see whether an attribute-based version of the paradox holds. In addition to theory, our simulation and data results show how all the concepts can be applied to synthetic and real networks. Where applicable, we draw connections to prior work to make this an accessible and comprehensive paper that lets one understand the math behind the Friendship Paradox and its basic extensions.
Advances in artificial intelligence (AI) are fueling a new paradigm of discoveries in natural sciences. Today, AI has started to advance natural sciences by improving, accelerating, and enabling our understanding of natural phenomena at a wide range of spatial and temporal scales, giving rise to a new area of research known as AI for science (AI4Science). Being an emerging research paradigm, AI4Science is unique in that it is an enormous and highly interdisciplinary area. Thus, a unified and technical treatment of this field is needed yet challenging. This work aims to provide a technically thorough account of a subarea of AI4Science; namely, AI for quantum, atomistic, and continuum systems. These areas aim at understanding the physical world from the subatomic (wavefunctions and electron density), atomic (molecules, proteins, materials, and interactions), to macro (fluids, climate, and subsurface) scales and form an important subarea of AI4Science. A unique advantage of focusing on these areas is that they largely share a common set of challenges, thereby allowing a unified and foundational treatment. A key common challenge is how to capture physics first principles, especially symmetries, in natural systems by deep learning methods. We provide an in-depth yet intuitive account of techniques to achieve equivariance to symmetry transformations. We also discuss other common technical challenges, including explainability, out-of-distribution generalization, knowledge transfer with foundation and large language models, and uncertainty quantification. To facilitate learning and education, we provide categorized lists of resources that we found to be useful. We strive to be thorough and unified and hope this initial effort may trigger more community interests and efforts to further advance AI4Science.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
Masked autoencoders are scalable vision learners, as the title of MAE \cite{he2022masked}, which suggests that self-supervised learning (SSL) in vision might undertake a similar trajectory as in NLP. Specifically, generative pretext tasks with the masked prediction (e.g., BERT) have become a de facto standard SSL practice in NLP. By contrast, early attempts at generative methods in vision have been buried by their discriminative counterparts (like contrastive learning); however, the success of mask image modeling has revived the masking autoencoder (often termed denoising autoencoder in the past). As a milestone to bridge the gap with BERT in NLP, masked autoencoder has attracted unprecedented attention for SSL in vision and beyond. This work conducts a comprehensive survey of masked autoencoders to shed insight on a promising direction of SSL. As the first to review SSL with masked autoencoders, this work focuses on its application in vision by discussing its historical developments, recent progress, and implications for diverse applications.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
The new era of technology has brought us to the point where it is convenient for people to share their opinions over an abundance of platforms. These platforms have a provision for the users to express themselves in multiple forms of representations, including text, images, videos, and audio. This, however, makes it difficult for users to obtain all the key information about a topic, making the task of automatic multi-modal summarization (MMS) essential. In this paper, we present a comprehensive survey of the existing research in the area of MMS.
Graph Convolution Networks (GCNs) manifest great potential in recommendation. This is attributed to their capability on learning good user and item embeddings by exploiting the collaborative signals from the high-order neighbors. Like other GCN models, the GCN based recommendation models also suffer from the notorious over-smoothing problem - when stacking more layers, node embeddings become more similar and eventually indistinguishable, resulted in performance degradation. The recently proposed LightGCN and LR-GCN alleviate this problem to some extent, however, we argue that they overlook an important factor for the over-smoothing problem in recommendation, that is, high-order neighboring users with no common interests of a user can be also involved in the user's embedding learning in the graph convolution operation. As a result, the multi-layer graph convolution will make users with dissimilar interests have similar embeddings. In this paper, we propose a novel Interest-aware Message-Passing GCN (IMP-GCN) recommendation model, which performs high-order graph convolution inside subgraphs. The subgraph consists of users with similar interests and their interacted items. To form the subgraphs, we design an unsupervised subgraph generation module, which can effectively identify users with common interests by exploiting both user feature and graph structure. To this end, our model can avoid propagating negative information from high-order neighbors into embedding learning. Experimental results on three large-scale benchmark datasets show that our model can gain performance improvement by stacking more layers and outperform the state-of-the-art GCN-based recommendation models significantly.
Graph Neural Networks (GNNs) have recently been used for node and graph classification tasks with great success, but GNNs model dependencies among the attributes of nearby neighboring nodes rather than dependencies among observed node labels. In this work, we consider the task of inductive node classification using GNNs in supervised and semi-supervised settings, with the goal of incorporating label dependencies. Because current GNNs are not universal (i.e., most-expressive) graph representations, we propose a general collective learning approach to increase the representation power of any existing GNN. Our framework combines ideas from collective classification with self-supervised learning, and uses a Monte Carlo approach to sampling embeddings for inductive learning across graphs. We evaluate performance on five real-world network datasets and demonstrate consistent, significant improvement in node classification accuracy, for a variety of state-of-the-art GNNs.
Deep neural networks (DNNs) are successful in many computer vision tasks. However, the most accurate DNNs require millions of parameters and operations, making them energy, computation and memory intensive. This impedes the deployment of large DNNs in low-power devices with limited compute resources. Recent research improves DNN models by reducing the memory requirement, energy consumption, and number of operations without significantly decreasing the accuracy. This paper surveys the progress of low-power deep learning and computer vision, specifically in regards to inference, and discusses the methods for compacting and accelerating DNN models. The techniques can be divided into four major categories: (1) parameter quantization and pruning, (2) compressed convolutional filters and matrix factorization, (3) network architecture search, and (4) knowledge distillation. We analyze the accuracy, advantages, disadvantages, and potential solutions to the problems with the techniques in each category. We also discuss new evaluation metrics as a guideline for future research.
In Multi-Label Text Classification (MLTC), one sample can belong to more than one class. It is observed that most MLTC tasks, there are dependencies or correlations among labels. Existing methods tend to ignore the relationship among labels. In this paper, a graph attention network-based model is proposed to capture the attentive dependency structure among the labels. The graph attention network uses a feature matrix and a correlation matrix to capture and explore the crucial dependencies between the labels and generate classifiers for the task. The generated classifiers are applied to sentence feature vectors obtained from the text feature extraction network (BiLSTM) to enable end-to-end training. Attention allows the system to assign different weights to neighbor nodes per label, thus allowing it to learn the dependencies among labels implicitly. The results of the proposed model are validated on five real-world MLTC datasets. The proposed model achieves similar or better performance compared to the previous state-of-the-art models.
Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to increase the receptive field, we propose a novel deep Hierarchical Graph Convolutional Network (H-GCN) for semi-supervised node classification. H-GCN first repeatedly aggregates structurally similar nodes to hyper-nodes and then refines the coarsened graph to the original to restore the representation for each node. Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each node, hence more global information can be learned. Comprehensive experiments conducted on public datasets demonstrate the effectiveness of the proposed method over the state-of-art methods. Notably, our model gains substantial improvements when only a few labeled samples are provided.