Simultaneous localization and mapping (SLAM) plays a fundamental role in extended reality (XR) applications. As the standards for immersion in XR continue to increase, the demands for SLAM benchmarking have become more stringent. Trajectory accuracy is the key metric, and marker-based optical motion capture (MoCap) systems are widely used to generate ground truth (GT) because of their drift-free and relatively accurate measurements. However, the precision of MoCap-based GT is limited by two factors: the spatiotemporal calibration with the device under test (DUT) and the inherent jitter in the MoCap measurements. These limitations hinder accurate SLAM benchmarking, particularly for key metrics like rotation error and inter-frame jitter, which are critical for immersive XR experiences. This paper presents a novel continuous-time maximum likelihood estimator to address these challenges. The proposed method integrates auxiliary inertial measurement unit (IMU) data to compensate for MoCap jitter. Additionally, a variable time synchronization method and a pose residual based on screw congruence constraints are proposed, enabling precise spatiotemporal calibration across multiple sensors and the DUT. Experimental results demonstrate that our approach outperforms existing methods, achieving the precision necessary for comprehensive benchmarking of state-of-the-art SLAM algorithms in XR applications. Furthermore, we thoroughly validate the practicality of our method by benchmarking several leading XR devices and open-source SLAM algorithms. The code is publicly available at https://github.com/ylab-xrpg/xr-hpgt.

Kolmogorov-Arnold Networks (KANs) have garnered significant attention for their promise of improved parameter efficiency and explainability compared to traditional Deep Neural Networks (DNNs). KANs' key innovation lies in the use of learnable non-linear activation functions, which are parametrized as splines. Splines are expressed as a linear combination of basis functions (B-splines). B-splines prove particularly challenging to accelerate due to their recursive definition. Systolic Array (SA)based architectures have shown great promise as DNN accelerators thanks to their energy efficiency and low latency. However, their suitability and efficiency in accelerating KANs have never been assessed. Thus, in this work, we explore the use of SA architecture to accelerate the KAN inference. We show that, while SAs can be used to accelerate part of the KAN inference, their utilization can be reduced to 30%. Hence, we propose KAN-SAs, a novel SA-based accelerator that leverages intrinsic properties of B-splines to enable efficient KAN inference. By including a nonrecursive B-spline implementation and leveraging the intrinsic KAN sparsity, KAN-SAs enhances conventional SAs, enabling efficient KAN inference, in addition to conventional DNNs. KAN-SAs achieves up to 100% SA utilization and up to 50% clock cycles reduction compared to conventional SAs of equivalent area, as shown by hardware synthesis results on a 28nm FD-SOI technology. We also evaluate different configurations of the accelerator on various KAN applications, confirming the improved efficiency of KAN inference provided by KAN-SAs.

This paper proposes KAN/H, a variant of Kolmogorov-Arnold Network (KAN) that uses a Haar-variant basis system having both global and local bases instead of B-spline. The resulting algorithm is applied to function approximation problems and MNIST. We show that it does not require most of the problem-specific hyper-parameter tunings.

In order to provide more information and explanation about our training data and evaluation benchmark, we introduce our synthetic samples with respect to the length and density of point trajectory.

This paper presents a method for planning a trajectory in workspace coordinates using a spatially fixed tool center point (TCP), while taking into account the processing path on a part. This approach is beneficial if it is easier to move the part rather than moving the tool. Whether a mathematical description that defines the shape to be processed or single points from a design program are used, the robot path is finally represented using B-splines. The use of splines enables the path to be continuous with a desired degree, which finally leads to a smooth robot trajectory. While calculating the robot trajectory through prescribed orientation, additionally a given velocity at the TCP has to be considered. The procedure was validated on a real system using an industrial robot moving an arbitrary defined part.

Kolmogorov-Arnold Networks or KANs have shown the ability to outperform classical Deep Neural Networks, while using far fewer trainable parameters for regression problems on scientific domains. Even more powerful has been their interpretability due to their structure being composed of univariate B-Spline functions. This enables us to derive closed-form equations from trained KANs for a wide range of problems. This paper introduces a quantum-inspired variant of the KAN based on Quantum Data Re-uploading (DR) models. The Quantum-Inspired Re-uploading KAN or QuIRK model replaces B-Splines with single-qubit DR models as the univariate function approximator, allowing them to match or outperform traditional KANs while using even fewer parameters. This is especially apparent in the case of periodic functions. Additionally, since the model utilizes only single-qubit circuits, it remains classically tractable to simulate with straightforward GPU acceleration. Finally, we also demonstrate that QuIRK retains the interpretability advantages and the ability to produce closed-form solutions.

In order to provide more information and explanation about our training data and evaluation benchmark, we introduce our synthetic samples with respect to the length and density of point trajectory.

Kolmogorov-Arnold Networks (KANs) offer a structured and interpretable framework for multivariate function approximation by composing univariate transformations through additive or multiplicative aggregation. This paper establishes theoretical convergence guarantees for KANs when the univariate components are represented by B-splines. We prove that both additive and hybrid additive-multiplicative KANs attain the minimax-optimal convergence rate $O(n^{-2r/(2r+1)})$ for functions in Sobolev spaces of smoothness $r$. We further derive guidelines for selecting the optimal number of knots in the B-splines. The theory is supported by simulation studies that confirm the predicted convergence rates. These results provide a theoretical foundation for using KANs in nonparametric regression and highlight their potential as a structured alternative to existing methods.

Activation functions in neural networks are typically selected from a set of empirically validated, commonly used static functions such as ReLU, tanh, or sigmoid. However, by optimizing the shapes of a network's activation functions, we can train models that are more parameter-efficient and accurate by assigning more optimal activations to the neurons. In this paper, I present and compare 9 training methodologies to explore dual-optimization dynamics in neural networks with parameterized linear B-spline activation functions. The experiments realize up to 94% lower end model error rates in FNNs and 51% lower rates in CNNs compared to traditional ReLU-based models. These gains come at the cost of additional development and training complexity as well as end model latency.

Reinforcement learning (RL) has shown promise in a large number of robotic control tasks. Nevertheless, its deployment on unmanned aerial vehicles (UAVs) remains challenging, mainly because of reliance on accurate dynamic models and platform-specific sensing, which hinders cross-platform transfer. This paper presents the CORB-Planner (Corridor-as-Observations for RL B-spline planner), a real-time, RL-based trajectory planning framework for high-speed autonomous UAV flight across heterogeneous platforms. The key idea is to combine B-spline trajectory generation with the RL policy producing successive control points with a compact safe flight corridor (SFC) representation obtained via heuristic search. The SFC abstracts obstacle information in a low-dimensional form, mitigating overfitting to platform-specific details and reducing sensitivity to model inaccuracies. To narrow the sim-to-real gap, we adopt an easy-to-hard progressive training pipeline in simulation. A value-based soft decomposed-critic Q (SDCQ) algorithm is used to learn effective policies within approximately ten minutes of training. Benchmarks in simulation and real-world tests demonstrate real-time planning on lightweight onboard hardware and support maximum flight speeds up to 8.2m/s in dense, cluttered environments without external positioning. Compatibility with various UAV configurations (quadrotors, hexarotors) and modest onboard compute underlines the generality and robustness of CORB-Planner for practical deployment.