We consider the problem of finding an $\epsilon$-stationary point of a nonconvex function with a Lipschitz continuous Hessian and propose a quadratic regularized Newton method incorporating a new class of regularizers constructed from the current and previous gradients. The method leverages a recently developed linear conjugate gradient approach with a negative curvature monitor to solve the regularized Newton equation. Notably, our algorithm is adaptive, requiring no prior knowledge of the Lipschitz constant of the Hessian, and achieves a global complexity of $O(\epsilon^{-\frac{3}{2}}) + \tilde O(1)$ in terms of the second-order oracle calls, and $\tilde O(\epsilon^{-\frac{7}{4}})$ for Hessian-vector products, respectively. Moreover, when the iterates converge to a point where the Hessian is positive definite, the method exhibits quadratic local convergence. Preliminary numerical results illustrate the competitiveness of our algorithm.

In public roads, autonomous vehicles (AVs) face the challenge of frequent interactions with human-driven vehicles (HDVs), which render uncertain driving behavior due to varying social characteristics among humans. To effectively assess the risks prevailing in the vicinity of AVs in social interactive traffic scenarios and achieve safe autonomous driving, this article proposes a social-suitable and safety-sensitive trajectory planning (S4TP) framework. Specifically, S4TP integrates the Social-Aware Trajectory Prediction (SATP) and Social-Aware Driving Risk Field (SADRF) modules. SATP utilizes Transformers to effectively encode the driving scene and incorporates an AV's planned trajectory during the prediction decoding process. SADRF assesses the expected surrounding risk degrees during AVs-HDVs interactions, each with different social characteristics, visualized as two-dimensional heat maps centered on the AV. SADRF models the driving intentions of the surrounding HDVs and predicts trajectories based on the representation of vehicular interactions. S4TP employs an optimization-based approach for motion planning, utilizing the predicted HDVs'trajectories as input. With the integration of SADRF, S4TP executes real-time online optimization of the planned trajectory of AV within lowrisk regions, thus improving the safety and the interpretability of the planned trajectory. We have conducted comprehensive tests of the proposed method using the SMARTS simulator. Experimental results in complex social scenarios, such as unprotected left turn intersections, merging, cruising, and overtaking, validate the superiority of our proposed S4TP in terms of safety and rationality. S4TP achieves a pass rate of 100% across all scenarios, surpassing the current state-of-the-art methods Fanta of 98.25% and Predictive-Decision of 94.75%.

Place recognition is an important task for robots and autonomous cars to localize themselves and close loops in pre-built maps. While single-modal sensor-based methods have shown satisfactory performance, cross-modal place recognition that retrieving images from a point-cloud database remains a challenging problem. Current cross-modal methods transform images into 3D points using depth estimation for modality conversion, which are usually computationally intensive and need expensive labeled data for depth supervision. In this work, we introduce a fast and lightweight framework to encode images and point clouds into place-distinctive descriptors. We propose an effective Field of View (FoV) transformation module to convert point clouds into an analogous modality as images. This module eliminates the necessity for depth estimation and helps subsequent modules achieve real-time performance. We further design a non-negative factorization-based encoder to extract mutually consistent semantic features between point clouds and images. This encoder yields more distinctive global descriptors for retrieval. Experimental results on the KITTI dataset show that our proposed methods achieve state-of-the-art performance while running in real time. Additional evaluation on the HAOMO dataset covering a 17 km trajectory further shows the practical generalization capabilities. We have released the implementation of our methods as open source at: https://github.com/haomo-ai/ModaLink.git.

We design a series of serial and parallel proximal point (gradient) ADMMs for the fully connected residual networks (FCResNets) training problem by introducing auxiliary variables. Convergence of the proximal point version is proven based on a Kurdyka-Lojasiewicz (KL) property analysis framework, and we can ensure a locally R-linear or sublinear convergence rate depending on the different ranges of the Kurdyka-Lojasiewicz (KL) exponent, in which a necessary auxiliary function is constructed to realize our goal. Moreover, the advantages of the parallel implementation in terms of lower time complexity and less (per-node) memory consumption are analyzed theoretically. To the best of our knowledge, this is the first work analyzing the convergence, convergence rate, time complexity and (per-node) runtime memory requirement of the ADMM applied in the FCResNets training problem theoretically. Experiments are reported to show the high speed, better performance, robustness and potential in the deep network training tasks. Finally, we present the advantage and potential of our parallel training in large-scale problems.

Place recognition is an important capability for autonomously navigating vehicles operating in complex environments and under changing conditions. It is a key component for tasks such as loop closing in SLAM or global localization. In this paper, we address the problem of place recognition based on 3D LiDAR scans recorded by an autonomous vehicle. We propose a novel lightweight neural network exploiting the range image representation of LiDAR sensors to achieve fast execution with less than 2 ms per frame. We design a yaw-angle-invariant architecture exploiting a transformer network, which boosts the place recognition performance of our method. We evaluate our approach on the KITTI and Ford Campus datasets. The experimental results show that our method can effectively detect loop closures compared to the state-of-the-art methods and generalizes well across different environments. To evaluate long-term place recognition performance, we provide a novel dataset containing LiDAR sequences recorded by a mobile robot in repetitive places at different times. The implementation of our method and dataset are released here: https://github.com/haomo-ai/OverlapTransformer

Training deep neural networks (DNNs) is an important and challenging optimization problem in machine learning due to its non-convexity and non-separable structure. The alternating minimization (AM) approaches split the composition structure of DNNs and have drawn great interest in the deep learning and optimization communities. In this paper, we propose a unified framework for analyzing the convergence rate of AM-type network training methods. Our analysis is based on the non-monotone $j$-step sufficient decrease conditions and the Kurdyka-Lojasiewicz (KL) property, which relaxes the requirement of designing descent algorithms. We show the detailed local convergence rate if the KL exponent $\theta$ varies in $[0,1)$. Moreover, the local R-linear convergence is discussed under a stronger $j$-step sufficient decrease condition.

High-definition (HD) semantic map generation of the environment is an essential component of autonomous driving. Existing methods have achieved good performance in this task by fusing different sensor modalities, such as LiDAR and camera. However, current works are based on raw data or network feature-level fusion and only consider short-range HD map generation, limiting their deployment to realistic autonomous driving applications. In this paper, we focus on the task of building the HD maps in both short ranges, i.e., within 30 m, and also predicting long-range HD maps up to 90 m, which is required by downstream path planning and control tasks to improve the smoothness and safety of autonomous driving. To this end, we propose a novel network named SuperFusion, exploiting the fusion of LiDAR and camera data at multiple levels. We use LiDAR depth to improve image depth estimation and use image features to guide long-range LiDAR feature prediction. We benchmark our SuperFusion on the nuScenes dataset and a self-recorded dataset and show that it outperforms the state-of-the-art baseline methods with large margins on all intervals. Additionally, we apply the generated HD map to a downstream path planning task, demonstrating that the long-range HD maps predicted by our method can lead to better path planning for autonomous vehicles. Our code and self-recorded dataset will be available at https://github.com/haomo-ai/SuperFusion.