Neural operators, which emerge as implicit solution operators of hidden governing equations, have recently become popular tools for learning responses of complex real-world physical systems. Nevertheless, the majority of neural operator applications has thus far been data-driven, which neglects the intrinsic preservation of fundamental physical laws in data. In this paper, we introduce a novel integral neural operator architecture, to learn physical models with fundamental conservation laws automatically guaranteed. In particular, by replacing the frame-dependent position information with its invariant counterpart in the kernel space, the proposed neural operator is by design translation- and rotation-invariant, and consequently abides by the conservation laws of linear and angular momentums. As applications, we demonstrate the expressivity and efficacy of our model in learning complex material behaviors from both synthetic and experimental datasets, and show that, by automatically satisfying these essential physical laws, our learned neural operator is not only generalizable in handling translated and rotated datasets, but also achieves state-of-the-art accuracy and efficiency as compared to baseline neural operator models.
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Sequential recommenders have made great strides in capturing a user's preferences. Nevertheless, the cold-start recommendation remains a fundamental challenge in which only a few user-item interactions are available for personalization. Gradient-based meta-learning approaches have recently emerged in the sequential recommendation field due to their fast adaptation and easy-to-integrate abilities. The meta-learning algorithms formulate the cold-start recommendation as a few-shot learning problem, where each user is represented as a task to be adapted. However, while meta-learning algorithms generally assume that task-wise samples are evenly distributed over classes or values, user-item interactions are not that way in real-world applications (e.g., watching favorite videos multiple times, leaving only good ratings and no bad ones). As a result, in the real-world, imbalanced user feedback that accounts for most task training data may dominate the user adaptation and prevent meta-learning algorithms from learning meaningful meta-knowledge for personalized recommendations. To alleviate this limitation, we propose a novel sequential recommendation framework based on gradient-based meta-learning that captures the imbalance of each user's rating distribution and accordingly computes adaptive loss for user-specific learning. It is the first work to tackle the impact of imbalanced ratings in cold-start sequential recommendation scenarios. We design adaptive weighted loss and improve the existing meta-learning algorithms for state-of-the-art sequential recommendation methods. Extensive experiments conducted on real-world datasets demonstrate the effectiveness of our framework.
To navigate complex environments, robots must increasingly use high-dimensional visual feedback (e.g. images) for control. However, relying on high-dimensional image data to make control decisions raises important questions; particularly, how might we prove the safety of a visual-feedback controller? Control barrier functions (CBFs) are powerful tools for certifying the safety of feedback controllers in the state-feedback setting, but CBFs have traditionally been poorly-suited to visual feedback control due to the need to predict future observations in order to evaluate the barrier function. In this work, we solve this issue by leveraging recent advances in neural radiance fields (NeRFs), which learn implicit representations of 3D scenes and can render images from previously-unseen camera perspectives, to provide single-step visual foresight for a CBF-based controller. This novel combination is able to filter out unsafe actions and intervene to preserve safety. We demonstrate the effect of our controller in real-time simulation experiments where it successfully prevents the robot from taking dangerous actions.
The automation of factories and manufacturing processes has been accelerating over the past few years, boosted by the Industry 4.0 paradigm, including diverse scenarios with mobile, flexible agents. Efficient coordination between mobile robots requires reliable wireless transmission in highly dynamic environments, often with strict timing requirements. Goal-oriented communication is a possible solution for this problem: communication decisions should be optimized for the target control task, providing the information that is most relevant to decide which action to take. From the control perspective, networked control design takes the communication impairments into account in its optmization of physical actions. In this work, we propose a joint design that combines goal-oriented communication and networked control into a single optimization model, an extension of a multiagent POMDP which we call Cyber-Physical POMDP (CP-POMDP). The model is flexible enough to represent several swarm and cooperative scenarios, and we illustrate its potential with two simple reference scenarios with a single agent and a set of supporting sensors. Joint training of the communication and control systems can significantly improve the overall performance, particularly if communication is severely constrained, and can even lead to implicit coordination of communication actions.
Explicit communication among humans is key to coordinating and learning. Social learning, which uses cues from experts, can greatly benefit from the usage of explicit communication to align heterogeneous policies, reduce sample complexity, and solve partially observable tasks. Emergent communication, a type of explicit communication, studies the creation of an artificial language to encode a high task-utility message directly from data. However, in most cases, emergent communication sends insufficiently compressed messages with little or null information, which also may not be understandable to a third-party listener. This paper proposes an unsupervised method based on the information bottleneck to capture both referential complexity and task-specific utility to adequately explore sparse social communication scenarios in multi-agent reinforcement learning (MARL). We show that our model is able to i) develop a natural-language-inspired lexicon of messages that is independently composed of a set of emergent concepts, which span the observations and intents with minimal bits, ii) develop communication to align the action policies of heterogeneous agents with dissimilar feature models, and iii) learn a communication policy from watching an expert's action policy, which we term `social shadowing'.
Many real-world offline reinforcement learning (RL) problems involve continuous-time environments with delays. Such environments are characterized by two distinctive features: firstly, the state x(t) is observed at irregular time intervals, and secondly, the current action a(t) only affects the future state x(t + g) with an unknown delay g > 0. A prime example of such an environment is satellite control where the communication link between earth and a satellite causes irregular observations and delays. Existing offline RL algorithms have achieved success in environments with irregularly observed states in time or known delays. However, environments involving both irregular observations in time and unknown delays remains an open and challenging problem. To this end, we propose Neural Laplace Control, a continuous-time model-based offline RL method that combines a Neural Laplace dynamics model with a model predictive control (MPC) planner--and is able to learn from an offline dataset sampled with irregular time intervals from an environment that has a inherent unknown constant delay. We show experimentally on continuous-time delayed environments it is able to achieve near expert policy performance.
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.
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related to the problem of numerical representation is the problem of quantization: in what manner should a set of continuous real-valued numbers be distributed over a fixed discrete set of numbers to minimize the number of bits required and also to maximize the accuracy of the attendant computations? This perennial problem of quantization is particularly relevant whenever memory and/or computational resources are severely restricted, and it has come to the forefront in recent years due to the remarkable performance of Neural Network models in computer vision, natural language processing, and related areas. Moving from floating-point representations to low-precision fixed integer values represented in four bits or less holds the potential to reduce the memory footprint and latency by a factor of 16x; and, in fact, reductions of 4x to 8x are often realized in practice in these applications. Thus, it is not surprising that quantization has emerged recently as an important and very active sub-area of research in the efficient implementation of computations associated with Neural Networks. In this article, we survey approaches to the problem of quantizing the numerical values in deep Neural Network computations, covering the advantages/disadvantages of current methods. With this survey and its organization, we hope to have presented a useful snapshot of the current research in quantization for Neural Networks and to have given an intelligent organization to ease the evaluation of future research in this area.
In many important graph data processing applications the acquired information includes both node features and observations of the graph topology. Graph neural networks (GNNs) are designed to exploit both sources of evidence but they do not optimally trade-off their utility and integrate them in a manner that is also universal. Here, universality refers to independence on homophily or heterophily graph assumptions. We address these issues by introducing a new Generalized PageRank (GPR) GNN architecture that adaptively learns the GPR weights so as to jointly optimize node feature and topological information extraction, regardless of the extent to which the node labels are homophilic or heterophilic. Learned GPR weights automatically adjust to the node label pattern, irrelevant on the type of initialization, and thereby guarantee excellent learning performance for label patterns that are usually hard to handle. Furthermore, they allow one to avoid feature over-smoothing, a process which renders feature information nondiscriminative, without requiring the network to be shallow. Our accompanying theoretical analysis of the GPR-GNN method is facilitated by novel synthetic benchmark datasets generated by the so-called contextual stochastic block model. We also compare the performance of our GNN architecture with that of several state-of-the-art GNNs on the problem of node-classification, using well-known benchmark homophilic and heterophilic datasets. The results demonstrate that GPR-GNN offers significant performance improvement compared to existing techniques on both synthetic and benchmark data.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.
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