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Object-based maps are relevant for scene understanding since they integrate geometric and semantic information of the environment, allowing autonomous robots to robustly localize and interact with on objects. In this paper, we address the task of constructing a metric-semantic map for the purpose of long-term object-based localization. We exploit 3D object detections from monocular RGB frames for both, the object-based map construction, and for globally localizing in the constructed map. To tailor the approach to a target environment, we propose an efficient way of generating 3D annotations to finetune the 3D object detection model. We evaluate our map construction in an office building, and test our long-term localization approach on challenging sequences recorded in the same environment over nine months. The experiments suggest that our approach is suitable for constructing metric-semantic maps, and that our localization approach is robust to long-term changes. Both, the mapping algorithm and the localization pipeline can run online on an onboard computer. We will release an open-source C++/ROS implementation of our approach.

Mobile robots have become more and more popular in large-scale and crowded environments, such as airports, shopping malls, etc. However, due to sparse landmarks and crowd noise, localization in this environment is a great challenge. Furthermore, it is unreliable for the robot to navigate safely in crowds while considering human comfort. Thus, how to navigate safely with localization precision in that environment is a critical problem. To solve this problem, we proposed a curiosity-based framework that can find an effective path with the consideration of human comfort and crowds, localization uncertainty, and the cost-to-go to the target. Three parts are involved in the proposed framework: the distance assessment module, the Curiosity for Positive Content (CPC), namely information-rich areas, and the Curiosity for Negative Content (CNC), namely crowded areas. CPC is introduced when the real-time localization uncertainty evaluation is not satisfied. This factor is predicted through the propagation of uncertainty along the candidate trajectory to provoke the robot to approach localization-referenced landmarks. The Human Comfort and Crowd Density Map (HCCDM) based on the Gaussian Mixture Model (GMM) is established to calculate CNC, which drives the robot to bypass the crowd and consider human comfort. The evaluation is conducted in a series of large-scale and crowded environments. The results show that our method can find a feasible path that can consider the localization uncertainty while simultaneously avoiding the crowded area.

Localization in a pre-built map is a basic technique for robot autonomous navigation. Existing mapping and localization methods commonly work well in small-scale environments. As a map grows larger, however, more memory is required and localization becomes inefficient. To solve these problems, map sparsification becomes a practical necessity to acquire a subset of the original map for localization. Previous map sparsification methods add a quadratic term in mixed-integer programming to enforce a uniform distribution of selected landmarks, which requires high memory capacity and heavy computation. In this paper, we formulate map sparsification in an efficient linear form and select uniformly distributed landmarks based on 2D discretized grids. Furthermore, to reduce the influence of different spatial distributions between the mapping and query sequences, which is not considered in previous methods, we also introduce a space constraint term based on 3D discretized grids. The exhaustive experiments in different datasets demonstrate the superiority of the proposed methods in both efficiency and localization performance. The relevant codes will be released at //github.com/fishmarch/SLAM_Map_Compression.

Real engineering and scientific applications often involve one or more qualitative inputs. Standard Gaussian processes (GPs), however, cannot directly accommodate qualitative inputs. The recently introduced latent variable Gaussian process (LVGP) overcomes this issue by first mapping each qualitative factor to underlying latent variables (LVs), and then uses any standard GP covariance function over these LVs. The LVs are estimated similarly to the other GP hyperparameters through maximum likelihood estimation, and then plugged into the prediction expressions. However, this plug-in approach will not account for uncertainty in estimation of the LVs, which can be significant especially with limited training data. In this work, we develop a fully Bayesian approach for the LVGP model and for visualizing the effects of the qualitative inputs via their LVs. We also develop approximations for scaling up LVGPs and fully Bayesian inference for the LVGP hyperparameters. We conduct numerical studies comparing plug-in inference against fully Bayesian inference over a few engineering models and material design applications. In contrast to previous studies on standard GP modeling that have largely concluded that a fully Bayesian treatment offers limited improvements, our results show that for LVGP modeling it offers significant improvements in prediction accuracy and uncertainty quantification over the plug-in approach.

Generalised hyperbolic (GH) processes are a class of stochastic processes that are used to model the dynamics of a wide range of complex systems that exhibit heavy-tailed behavior, including systems in finance, economics, biology, and physics. In this paper, we present novel simulation methods based on subordination with a generalised inverse Gaussian (GIG) process and using a generalised shot-noise representation that involves random thinning of infinite series of decreasing jump sizes. Compared with our previous work on GIG processes, we provide tighter bounds for the construction of rejection sampling ratios, leading to improved acceptance probabilities in simulation. Furthermore, we derive methods for the adaptive determination of the number of points required in the associated random series using concentration inequalities. Residual small jumps are then approximated using an appropriately scaled Brownian motion term with drift. Finally the rejection sampling steps are made significantly more computationally efficient through the use of squeezing functions based on lower and upper bounds on the L\'evy density. Experimental results are presented illustrating the strong performance under various parameter settings and comparing the marginal distribution of the GH paths with exact simulations of GH random variates. The new simulation methodology is made available to researchers through the publication of a Python code repository.

We consider decentralized optimization problems in which a number of agents collaborate to minimize the average of their local functions by exchanging over an underlying communication graph. Specifically, we place ourselves in an asynchronous model where only a random portion of nodes perform computation at each iteration, while the information exchange can be conducted between all the nodes and in an asymmetric fashion. For this setting, we propose an algorithm that combines gradient tracking with a network-level variance reduction (in contrast to variance reduction within each node). This enables each node to track the average of the gradients of the objective functions. Our theoretical analysis shows that the algorithm converges linearly, when the local objective functions are strongly convex, under mild connectivity conditions on the expected mixing matrices. In particular, our result does not require the mixing matrices to be doubly stochastic. In the experiments, we investigate a broadcast mechanism that transmits information from computing nodes to their neighbors, and confirm the linear convergence of our method on both synthetic and real-world datasets.

Out-of-distribution (OOD) detection methods assume that they have test ground truths, i.e., whether individual test samples are in-distribution (IND) or OOD. However, in the real world, we do not always have such ground truths, and thus do not know which sample is correctly detected and cannot compute the metric like AUROC to evaluate the performance of different OOD detection methods. In this paper, we are the first to introduce the unsupervised evaluation problem in OOD detection, which aims to evaluate OOD detection methods in real-world changing environments without OOD labels. We propose three methods to compute Gscore as an unsupervised indicator of OOD detection performance. We further introduce a new benchmark Gbench, which has 200 real-world OOD datasets of various label spaces to train and evaluate our method. Through experiments, we find a strong quantitative correlation betwwen Gscore and the OOD detection performance. Extensive experiments demonstrate that our Gscore achieves state-of-the-art performance. Gscore also generalizes well with different IND/OOD datasets, OOD detection methods, backbones and dataset sizes. We further provide interesting analyses of the effects of backbones and IND/OOD datasets on OOD detection performance. The data and code will be available.

Formally verifying software properties is a highly desirable but labor-intensive task. Recent work has developed methods to automate formal verification using proof assistants, such as Coq and Isabelle/HOL, e.g., by training a model to predict one proof step at a time, and using that model to search through the space of possible proofs. This paper introduces a new method to automate formal verification: We use large language models, trained on natural language text and code and fine-tuned on proofs, to generate whole proofs for theorems at once, rather than one step at a time. We combine this proof generation model with a fine-tuned repair model to repair generated proofs, further increasing proving power. As its main contributions, this paper demonstrates for the first time that: (1) Whole-proof generation using transformers is possible and is as effective as search-based techniques without requiring costly search. (2) Giving the learned model additional context, such as a prior failed proof attempt and the ensuing error message, results in proof repair and further improves automated proof generation. (3) We establish a new state of the art for fully automated proof synthesis. We reify our method in a prototype, Baldur, and evaluate it on a benchmark of 6,336 Isabelle/HOL theorems and their proofs. In addition to empirically showing the effectiveness of whole-proof generation, repair, and added context, we show that Baldur improves on the state-of-the-art tool, Thor, by automatically generating proofs for an additional 8.7% of the theorems. Together, Baldur and Thor can prove 65.7% of the theorems fully automatically. This paper paves the way for new research into using large language models for automating formal verification.

Monitoring plants and fruits at high resolution play a key role in the future of agriculture. Accurate 3D information can pave the way to a diverse number of robotic applications in agriculture ranging from autonomous harvesting to precise yield estimation. Obtaining such 3D information is non-trivial as agricultural environments are often repetitive and cluttered, and one has to account for the partial observability of fruit and plants. In this paper, we address the problem of jointly estimating complete 3D shapes of fruit and their pose in a 3D multi-resolution map built by a mobile robot. To this end, we propose an online multi-resolution panoptic mapping system where regions of interest are represented with a higher resolution. We exploit data to learn a general fruit shape representation that we use at inference time together with an occlusion-aware differentiable rendering pipeline to complete partial fruit observations and estimate the 7 DoF pose of each fruit in the map. The experiments presented in this paper, evaluated both in the controlled environment and in a commercial greenhouse, show that our novel algorithm yields higher completion and pose estimation accuracy than existing methods, with an improvement of 41% in completion accuracy and 52% in pose estimation accuracy while keeping a low inference time of 0.6s in average.

Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.