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Symmetric Nonnegative Matrix Factorization (SymNMF) is a technique in data analysis and machine learning that approximates a symmetric matrix with a product of a nonnegative, low-rank matrix and its transpose. To design faster and more scalable algorithms for SymNMF we develop two randomized algorithms for its computation. The first algorithm uses randomized matrix sketching to compute an initial low-rank input matrix and proceeds to use this input to rapidly compute a SymNMF. The second algorithm uses randomized leverage score sampling to approximately solve constrained least squares problems. Many successful methods for SymNMF rely on (approximately) solving sequences of constrained least squares problems. We prove theoretically that leverage score sampling can approximately solve nonnegative least squares problems to a chosen accuracy with high probability. Finally we demonstrate that both methods work well in practice by applying them to graph clustering tasks on large real world data sets. These experiments show that our methods approximately maintain solution quality and achieve significant speed ups for both large dense and large sparse problems.

Solving Partial Differential Equations (PDEs) is the core of many fields of science and engineering. While classical approaches are often prohibitively slow, machine learning models often fail to incorporate complete system information. Over the past few years, transformers have had a significant impact on the field of Artificial Intelligence and have seen increased usage in PDE applications. However, despite their success, transformers currently lack integration with physics and reasoning. This study aims to address this issue by introducing PITT: Physics Informed Token Transformer. The purpose of PITT is to incorporate the knowledge of physics by embedding partial differential equations (PDEs) into the learning process. PITT uses an equation tokenization method to learn an analytically-driven numerical update operator. By tokenizing PDEs and embedding partial derivatives, the transformer models become aware of the underlying knowledge behind physical processes. To demonstrate this, PITT is tested on challenging 1D and 2D PDE neural operator prediction tasks. The results show that PITT outperforms popular neural operator models and has the ability to extract physically relevant information from governing equations.

Simultaneous Localization and Mapping (SLAM) presents a formidable challenge in robotics, involving the dynamic construction of a map while concurrently determining the precise location of the robotic agent within an unfamiliar environment. This intricate task is further compounded by the inherent "chicken-and-egg" dilemma, where accurate mapping relies on a dependable estimation of the robot's location, and vice versa. Moreover, the computational intensity of SLAM adds an additional layer of complexity, making it a crucial yet demanding topic in the field. In our research, we address the challenges of SLAM by adopting the Particle Filter SLAM method. Our approach leverages encoded data and fiber optic gyro (FOG) information to enable precise estimation of vehicle motion, while lidar technology contributes to environmental perception by providing detailed insights into surrounding obstacles. The integration of these data streams culminates in the establishment of a Particle Filter SLAM framework, representing a key endeavor in this paper to effectively navigate and overcome the complexities associated with simultaneous localization and mapping in robotic systems.

With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.

When learning tasks over time, artificial neural networks suffer from a problem known as Catastrophic Forgetting (CF). This happens when the weights of a network are overwritten during the training of a new task causing forgetting of old information. To address this issue, we propose MetA Reusable Knowledge or MARK, a new method that fosters weight reusability instead of overwriting when learning a new task. Specifically, MARK keeps a set of shared weights among tasks. We envision these shared weights as a common Knowledge Base (KB) that is not only used to learn new tasks, but also enriched with new knowledge as the model learns new tasks. Key components behind MARK are two-fold. On the one hand, a metalearning approach provides the key mechanism to incrementally enrich the KB with new knowledge and to foster weight reusability among tasks. On the other hand, a set of trainable masks provides the key mechanism to selectively choose from the KB relevant weights to solve each task. By using MARK, we achieve state of the art results in several popular benchmarks, surpassing the best performing methods in terms of average accuracy by over 10% on the 20-Split-MiniImageNet dataset, while achieving almost zero forgetfulness using 55% of the number of parameters. Furthermore, an ablation study provides evidence that, indeed, MARK is learning reusable knowledge that is selectively used by each task.

Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

As a field of AI, Machine Reasoning (MR) uses largely symbolic means to formalize and emulate abstract reasoning. Studies in early MR have notably started inquiries into Explainable AI (XAI) -- arguably one of the biggest concerns today for the AI community. Work on explainable MR as well as on MR approaches to explainability in other areas of AI has continued ever since. It is especially potent in modern MR branches, such as argumentation, constraint and logic programming, planning. We hereby aim to provide a selective overview of MR explainability techniques and studies in hopes that insights from this long track of research will complement well the current XAI landscape. This document reports our work in-progress on MR explainability.

Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.

We introduce an effective model to overcome the problem of mode collapse when training Generative Adversarial Networks (GAN). Firstly, we propose a new generator objective that finds it better to tackle mode collapse. And, we apply an independent Autoencoders (AE) to constrain the generator and consider its reconstructed samples as "real" samples to slow down the convergence of discriminator that enables to reduce the gradient vanishing problem and stabilize the model. Secondly, from mappings between latent and data spaces provided by AE, we further regularize AE by the relative distance between the latent and data samples to explicitly prevent the generator falling into mode collapse setting. This idea comes when we find a new way to visualize the mode collapse on MNIST dataset. To the best of our knowledge, our method is the first to propose and apply successfully the relative distance of latent and data samples for stabilizing GAN. Thirdly, our proposed model, namely Generative Adversarial Autoencoder Networks (GAAN), is stable and has suffered from neither gradient vanishing nor mode collapse issues, as empirically demonstrated on synthetic, MNIST, MNIST-1K, CelebA and CIFAR-10 datasets. Experimental results show that our method can approximate well multi-modal distribution and achieve better results than state-of-the-art methods on these benchmark datasets. Our model implementation is published here: //github.com/tntrung/gaan