Temporal knowledge graph completion (TKGC) aims to fill in missing facts within a given temporal knowledge graph at a specific time. Existing methods, operating in real or complex spaces, have demonstrated promising performance in this task. This paper advances beyond conventional approaches by introducing more expressive quaternion representations for TKGC within hypercomplex space. Unlike existing quaternion-based methods, our study focuses on capturing time-sensitive relations rather than time-aware entities. Specifically, we model time-sensitive relations through time-aware rotation and periodic time translation, effectively capturing complex temporal variability. Furthermore, we theoretically demonstrate our method's capability to model symmetric, asymmetric, inverse, compositional, and evolutionary relation patterns. Comprehensive experiments on public datasets validate that our proposed approach achieves state-of-the-art performance in the field of TKGC.
In dueling bandits, the learner receives preference feedback between arms, and the regret of an arm is defined in terms of its suboptimality to a winner arm. The more challenging and practically motivated non-stationary variant of dueling bandits, where preferences change over time, has been the focus of several recent works (Saha and Gupta, 2022; Buening and Saha, 2023; Suk and Agarwal, 2023). The goal is to design algorithms without foreknowledge of the amount of change. The bulk of known results here studies the Condorcet winner setting, where an arm preferred over any other exists at all times. Yet, such a winner may not exist and, to contrast, the Borda version of this problem (which is always well-defined) has received little attention. In this work, we establish the first optimal and adaptive Borda dynamic regret upper bound, which highlights fundamental differences in the learnability of severe non-stationarity between Condorcet vs. Borda regret objectives in dueling bandits. Surprisingly, our techniques for non-stationary Borda dueling bandits also yield improved rates within the Condorcet winner setting, and reveal new preference models where tighter notions of non-stationarity are adaptively learnable. This is accomplished through a novel generalized Borda score framework which unites the Borda and Condorcet problems, thus allowing reduction of Condorcet regret to a Borda-like task. Such a generalization was not previously known and is likely to be of independent interest.
The evolution and growing automation of collaborative robots introduce more complexity and unpredictability to systems, highlighting the crucial need for robot's adaptability and flexibility to address the increasing complexities of their environment. In typical industrial production scenarios, robots are often required to be re-programmed when facing a more demanding task or even a few changes in workspace conditions. To increase productivity, efficiency and reduce human effort in the design process, this paper explores the potential of using digital twin combined with Reinforcement Learning (RL) to enable robots to generate self-improving collision-free trajectories in real time. The digital twin, acting as a virtual counterpart of the physical system, serves as a 'forward run' for monitoring, controlling, and optimizing the physical system in a safe and cost-effective manner. The physical system sends data to synchronize the digital system through the video feeds from cameras, which allows the virtual robot to update its observation and policy based on real scenarios. The bidirectional communication between digital and physical systems provides a promising platform for hardware-in-the-loop RL training through trial and error until the robot successfully adapts to its new environment. The proposed online training framework is demonstrated on the Unfactory Xarm5 collaborative robot, where the robot end-effector aims to reach the target position while avoiding obstacles. The experiment suggest that proposed framework is capable of performing policy online training, and that there remains significant room for improvement.
The field of general time series analysis has recently begun to explore unified modeling, where a common architectural backbone can be retrained on a specific task for a specific dataset. In this work, we approach unification from a complementary vantage point: unification across tasks and domains. To this end, we explore the impact of discrete, learnt, time series data representations that enable generalist, cross-domain training. Our method, TOTEM, or TOkenized Time Series EMbeddings, proposes a simple tokenizer architecture that embeds time series data from varying domains using a discrete vectorized representation learned in a self-supervised manner. TOTEM works across multiple tasks and domains with minimal to no tuning. We study the efficacy of TOTEM with an extensive evaluation on 17 real world time series datasets across 3 tasks. We evaluate both the specialist (i.e., training a model on each domain) and generalist (i.e., training a single model on many domains) settings, and show that TOTEM matches or outperforms previous best methods on several popular benchmarks. The code can be found at: https://github.com/SaberaTalukder/TOTEM.
While many multi-armed bandit algorithms assume that rewards for all arms are constant across rounds, this assumption does not hold in many real-world scenarios. This paper considers the setting of recovering bandits (Pike-Burke & Grunewalder, 2019), where the reward depends on the number of rounds elapsed since the last time an arm was pulled. We propose a new reinforcement learning (RL) algorithm tailored to this setting, named the State-Separate SARSA (SS-SARSA) algorithm, which treats rounds as states. The SS-SARSA algorithm achieves efficient learning by reducing the number of state combinations required for Q-learning/SARSA, which often suffers from combinatorial issues for large-scale RL problems. Additionally, it makes minimal assumptions about the reward structure and offers lower computational complexity. Furthermore, we prove asymptotic convergence to an optimal policy under mild assumptions. Simulation studies demonstrate the superior performance of our algorithm across various settings.
Motivated by the abundance of functional data such as time series and images, there has been a growing interest in integrating such data into neural networks and learning maps from function spaces to R (i.e., functionals). In this paper, we study the approximation of functionals on reproducing kernel Hilbert spaces (RKHS's) using neural networks. We establish the universality of the approximation of functionals on the RKHS's. Specifically, we derive explicit error bounds for those induced by inverse multiquadric, Gaussian, and Sobolev kernels. Moreover, we apply our findings to functional regression, proving that neural networks can accurately approximate the regression maps in generalized functional linear models. Existing works on functional learning require integration-type basis function expansions with a set of pre-specified basis functions. By leveraging the interpolating orthogonal projections in RKHS's, our proposed network is much simpler in that we use point evaluations to replace basis function expansions.
In standard Reinforcement Learning settings, agents typically assume immediate feedback about the effects of their actions after taking them. However, in practice, this assumption may not hold true due to physical constraints and can significantly impact the performance of RL algorithms. In this paper, we focus on addressing observation delays in partially observable environments. We propose leveraging world models, which have shown success in integrating past observations and learning dynamics, to handle observation delays. By reducing delayed POMDPs to delayed MDPs with world models, our methods can effectively handle partial observability, where existing approaches achieve sub-optimal performance or even degrade quickly as observability decreases. Experiments suggest that one of our methods can outperform a naive model-based approach by up to %30. Moreover, we evaluate our methods on visual input based delayed environment, for the first time showcasing delay-aware reinforcement learning on visual observations.
Mesh is a fundamental representation of 3D assets in various industrial applications, and is widely supported by professional softwares. However, due to its irregular structure, mesh creation and manipulation is often time-consuming and labor-intensive. In this paper, we propose a highly controllable generative model, GetMesh, for mesh generation and manipulation across different categories. By taking a varying number of points as the latent representation, and re-organizing them as triplane representation, GetMesh generates meshes with rich and sharp details, outperforming both single-category and multi-category counterparts. Moreover, it also enables fine-grained control over the generation process that previous mesh generative models cannot achieve, where changing global/local mesh topologies, adding/removing mesh parts, and combining mesh parts across categories can be intuitively, efficiently, and robustly accomplished by adjusting the number, positions or features of latent points. Project page is https://getmesh.github.io.
From the perspective of control theory, convolutional layers (of neural networks) are 2-D (or N-D) linear time-invariant dynamical systems. The usual representation of convolutional layers by the convolution kernel corresponds to the representation of a dynamical system by its impulse response. However, many analysis tools from control theory, e.g., involving linear matrix inequalities, require a state space representation. For this reason, we explicitly provide a state space representation of the Roesser type for 2-D convolutional layers with $c_\mathrm{in}r_1 + c_\mathrm{out}r_2$ states, where $c_\mathrm{in}$/$c_\mathrm{out}$ is the number of input/output channels of the layer and $r_1$/$r_2$ characterizes the width/length of the convolution kernel. This representation is shown to be minimal for $c_\mathrm{in} = c_\mathrm{out}$. We further construct state space representations for dilated, strided, and N-D convolutions.
Automated feature extraction from MRI brain scans and diagnosis of Alzheimer's disease are ongoing challenges. With advances in 3D imaging technology, 3D data acquisition is becoming more viable and efficient than its 2D counterpart. Rather than using feature-based vectors, in this paper, for the first time, we suggest a pipeline to extract novel covariance-based descriptors from the cortical surface using the Ricci energy optimization. The covariance descriptors are components of the nonlinear manifold of symmetric positive-definite matrices, thus we focus on using the Gaussian radial basis function to apply manifold-based classification to the 3D shape problem. Applying this novel signature to the analysis of abnormal cortical brain morphometry allows for diagnosing Alzheimer's disease. Experimental studies performed on about two hundred 3D MRI brain models, gathered from Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate the effectiveness of our descriptors in achieving remarkable classification accuracy.