Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer can accurately approximate PDE solutions by utilizing multi-head attention mechanisms to capture temporal dependencies. PINNsFormer transforms point-wise inputs into pseudo sequences and replaces point-wise PINNs loss with a sequential loss. Additionally, it incorporates a novel activation function, Wavelet, which anticipates Fourier decomposition through deep neural networks. Empirical results demonstrate that PINNsFormer achieves superior generalization ability and accuracy across various scenarios, including PINNs failure modes and high-dimensional PDEs. Moreover, PINNsFormer offers flexibility in integrating existing learning schemes for PINNs, further enhancing its performance.
With the breakthrough of AlphaGo, deep reinforcement learning becomes a recognized technique for solving sequential decision-making problems. Despite its reputation, data inefficiency caused by its trial and error learning mechanism makes deep reinforcement learning hard to be practical in a wide range of areas. Plenty of methods have been developed for sample efficient deep reinforcement learning, such as environment modeling, experience transfer, and distributed modifications, amongst which, distributed deep reinforcement learning has shown its potential in various applications, such as human-computer gaming, and intelligent transportation. In this paper, we conclude the state of this exciting field, by comparing the classical distributed deep reinforcement learning methods, and studying important components to achieve efficient distributed learning, covering single player single agent distributed deep reinforcement learning to the most complex multiple players multiple agents distributed deep reinforcement learning. Furthermore, we review recently released toolboxes that help to realize distributed deep reinforcement learning without many modifications of their non-distributed versions. By analyzing their strengths and weaknesses, a multi-player multi-agent distributed deep reinforcement learning toolbox is developed and released, which is further validated on Wargame, a complex environment, showing usability of the proposed toolbox for multiple players and multiple agents distributed deep reinforcement learning under complex games. Finally, we try to point out challenges and future trends, hoping this brief review can provide a guide or a spark for researchers who are interested in distributed deep reinforcement learning.
Causal Machine Learning (CausalML) is an umbrella term for machine learning methods that formalize the data-generation process as a structural causal model (SCM). This allows one to reason about the effects of changes to this process (i.e., interventions) and what would have happened in hindsight (i.e., counterfactuals). We categorize work in \causalml into five groups according to the problems they tackle: (1) causal supervised learning, (2) causal generative modeling, (3) causal explanations, (4) causal fairness, (5) causal reinforcement learning. For each category, we systematically compare its methods and point out open problems. Further, we review modality-specific applications in computer vision, natural language processing, and graph representation learning. Finally, we provide an overview of causal benchmarks and a critical discussion of the state of this nascent field, including recommendations for future work.
Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids (in Lagrangian descriptions). Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities. It is a potential alternative approach to understanding complex fluid mechanics, such as turbulence, that are difficult to model using traditional methods of mathematical physics.
Classic machine learning methods are built on the $i.i.d.$ assumption that training and testing data are independent and identically distributed. However, in real scenarios, the $i.i.d.$ assumption can hardly be satisfied, rendering the sharp drop of classic machine learning algorithms' performances under distributional shifts, which indicates the significance of investigating the Out-of-Distribution generalization problem. Out-of-Distribution (OOD) generalization problem addresses the challenging setting where the testing distribution is unknown and different from the training. This paper serves as the first effort to systematically and comprehensively discuss the OOD generalization problem, from the definition, methodology, evaluation to the implications and future directions. Firstly, we provide the formal definition of the OOD generalization problem. Secondly, existing methods are categorized into three parts based on their positions in the whole learning pipeline, namely unsupervised representation learning, supervised model learning and optimization, and typical methods for each category are discussed in detail. We then demonstrate the theoretical connections of different categories, and introduce the commonly used datasets and evaluation metrics. Finally, we summarize the whole literature and raise some future directions for OOD generalization problem. The summary of OOD generalization methods reviewed in this survey can be found at //out-of-distribution-generalization.com.
Semi-supervised learning on class-imbalanced data, although a realistic problem, has been under studied. While existing semi-supervised learning (SSL) methods are known to perform poorly on minority classes, we find that they still generate high precision pseudo-labels on minority classes. By exploiting this property, in this work, we propose Class-Rebalancing Self-Training (CReST), a simple yet effective framework to improve existing SSL methods on class-imbalanced data. CReST iteratively retrains a baseline SSL model with a labeled set expanded by adding pseudo-labeled samples from an unlabeled set, where pseudo-labeled samples from minority classes are selected more frequently according to an estimated class distribution. We also propose a progressive distribution alignment to adaptively adjust the rebalancing strength dubbed CReST+. We show that CReST and CReST+ improve state-of-the-art SSL algorithms on various class-imbalanced datasets and consistently outperform other popular rebalancing methods.
Exploration-exploitation is a powerful and practical tool in multi-agent learning (MAL), however, its effects are far from understood. To make progress in this direction, we study a smooth analogue of Q-learning. We start by showing that our learning model has strong theoretical justification as an optimal model for studying exploration-exploitation. Specifically, we prove that smooth Q-learning has bounded regret in arbitrary games for a cost model that explicitly captures the balance between game and exploration costs and that it always converges to the set of quantal-response equilibria (QRE), the standard solution concept for games under bounded rationality, in weighted potential games with heterogeneous learning agents. In our main task, we then turn to measure the effect of exploration in collective system performance. We characterize the geometry of the QRE surface in low-dimensional MAL systems and link our findings with catastrophe (bifurcation) theory. In particular, as the exploration hyperparameter evolves over-time, the system undergoes phase transitions where the number and stability of equilibria can change radically given an infinitesimal change to the exploration parameter. Based on this, we provide a formal theoretical treatment of how tuning the exploration parameter can provably lead to equilibrium selection with both positive as well as negative (and potentially unbounded) effects to system performance.
Graph representation learning resurges as a trending research subject owing to the widespread use of deep learning for Euclidean data, which inspire various creative designs of neural networks in the non-Euclidean domain, particularly graphs. With the success of these graph neural networks (GNN) in the static setting, we approach further practical scenarios where the graph dynamically evolves. Existing approaches typically resort to node embeddings and use a recurrent neural network (RNN, broadly speaking) to regulate the embeddings and learn the temporal dynamics. These methods require the knowledge of a node in the full time span (including both training and testing) and are less applicable to the frequent change of the node set. In some extreme scenarios, the node sets at different time steps may completely differ. To resolve this challenge, we propose EvolveGCN, which adapts the graph convolutional network (GCN) model along the temporal dimension without resorting to node embeddings. The proposed approach captures the dynamism of the graph sequence through using an RNN to evolve the GCN parameters. Two architectures are considered for the parameter evolution. We evaluate the proposed approach on tasks including link prediction, edge classification, and node classification. The experimental results indicate a generally higher performance of EvolveGCN compared with related approaches. The code is available at \url{//github.com/IBM/EvolveGCN}.
Graph-based semi-supervised learning (SSL) is an important learning problem where the goal is to assign labels to initially unlabeled nodes in a graph. Graph Convolutional Networks (GCNs) have recently been shown to be effective for graph-based SSL problems. GCNs inherently assume existence of pairwise relationships in the graph-structured data. However, in many real-world problems, relationships go beyond pairwise connections and hence are more complex. Hypergraphs provide a natural modeling tool to capture such complex relationships. In this work, we explore the use of GCNs for hypergraph-based SSL. In particular, we propose HyperGCN, an SSL method which uses a layer-wise propagation rule for convolutional neural networks operating directly on hypergraphs. To the best of our knowledge, this is the first principled adaptation of GCNs to hypergraphs. HyperGCN is able to encode both the hypergraph structure and hypernode features in an effective manner. Through detailed experimentation, we demonstrate HyperGCN's effectiveness at hypergraph-based SSL.
This paper describes a general framework for learning Higher-Order Network Embeddings (HONE) from graph data based on network motifs. The HONE framework is highly expressive and flexible with many interchangeable components. The experimental results demonstrate the effectiveness of learning higher-order network representations. In all cases, HONE outperforms recent embedding methods that are unable to capture higher-order structures with a mean relative gain in AUC of $19\%$ (and up to $75\%$ gain) across a wide variety of networks and embedding methods.
Convolutional Neural Networks (CNNs) have gained significant traction in the field of machine learning, particularly due to their high accuracy in visual recognition. Recent works have pushed the performance of GPU implementations of CNNs to significantly improve their classification and training times. With these improvements, many frameworks have become available for implementing CNNs on both CPUs and GPUs, with no support for FPGA implementations. In this work we present a modified version of the popular CNN framework Caffe, with FPGA support. This allows for classification using CNN models and specialized FPGA implementations with the flexibility of reprogramming the device when necessary, seamless memory transactions between host and device, simple-to-use test benches, and the ability to create pipelined layer implementations. To validate the framework, we use the Xilinx SDAccel environment to implement an FPGA-based Winograd convolution engine and show that the FPGA layer can be used alongside other layers running on a host processor to run several popular CNNs (AlexNet, GoogleNet, VGG A, Overfeat). The results show that our framework achieves 50 GFLOPS across 3x3 convolutions in the benchmarks. This is achieved within a practical framework, which will aid in future development of FPGA-based CNNs.