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Object detection and multiple object tracking (MOT) are essential components of self-driving systems. Accurate detection and uncertainty quantification are both critical for onboard modules, such as perception, prediction, and planning, to improve the safety and robustness of autonomous vehicles. Collaborative object detection (COD) has been proposed to improve detection accuracy and reduce uncertainty by leveraging the viewpoints of multiple agents. However, little attention has been paid to how to leverage the uncertainty quantification from COD to enhance MOT performance. In this paper, as the first attempt to address this challenge, we design an uncertainty propagation framework called MOT-CUP. Our framework first quantifies the uncertainty of COD through direct modeling and conformal prediction, and propagates this uncertainty information into the motion prediction and association steps. MOT-CUP is designed to work with different collaborative object detectors and baseline MOT algorithms. We evaluate MOT-CUP on V2X-Sim, a comprehensive collaborative perception dataset, and demonstrate a 2% improvement in accuracy and a 2.67X reduction in uncertainty compared to the baselines, e.g. SORT and ByteTrack. In scenarios characterized by high occlusion levels, our MOT-CUP demonstrates a noteworthy $4.01\%$ improvement in accuracy. MOT-CUP demonstrates the importance of uncertainty quantification in both COD and MOT, and provides the first attempt to improve the accuracy and reduce the uncertainty in MOT based on COD through uncertainty propagation. Our code is public on //coperception.github.io/MOT-CUP/.

3D neural implicit representations play a significant component in many robotic applications. However, reconstructing neural radiance fields (NeRF) from realistic event data remains a challenge due to the sparsities and the lack of information when only event streams are available. In this paper, we utilize motion, geometry, and density priors behind event data to impose strong physical constraints to augment NeRF training. The proposed novel pipeline can directly benefit from those priors to reconstruct 3D scenes without additional inputs. Moreover, we present a novel density-guided patch-based sampling strategy for robust and efficient learning, which not only accelerates training procedures but also conduces to expressions of local geometries. More importantly, we establish the first large dataset for event-based 3D reconstruction, which contains 101 objects with various materials and geometries, along with the groundtruth of images and depth maps for all camera viewpoints, which significantly facilitates other research in the related fields. The code and dataset will be publicly available at //github.com/Mercerai/PAEv3d.

Despite advances in generative methods, accurately modeling the distribution of graphs remains a challenging task primarily because of the absence of predefined or inherent unique graph representation. Two main strategies have emerged to tackle this issue: 1) restricting the number of possible representations by sorting the nodes, or 2) using permutation-invariant/equivariant functions, specifically Graph Neural Networks (GNNs). In this paper, we introduce a new framework named Discrete Graph Auto-Encoder (DGAE), which leverages the strengths of both strategies and mitigate their respective limitations. In essence, we propose a strategy in 2 steps. We first use a permutation-equivariant auto-encoder to convert graphs into sets of discrete latent node representations, each node being represented by a sequence of quantized vectors. In the second step, we sort the sets of discrete latent representations and learn their distribution with a specifically designed auto-regressive model based on the Transformer architecture. Through multiple experimental evaluations, we demonstrate the competitive performances of our model in comparison to the existing state-of-the-art across various datasets. Various ablation studies support the interest of our method.

For turbulent problems of industrial scale, computational cost may become prohibitive due to the stability constraints associated with explicit time discretization of the underlying conservation laws. On the other hand, implicit methods allow for larger time-step sizes but require exorbitant computational resources. Implicit-explicit (IMEX) formulations combine both temporal approaches, using an explicit method in nonstiff portions of the domain and implicit in stiff portions. While these methods can be shown to be orders of magnitude faster than typical explicit discretizations, they are still limited by their implicit discretization in terms of cost. Hybridization reduces the scaling of these systems to an effective lower dimension, which allows the system to be solved at significant speedup factors compared to standard implicit methods. This work proposes an IMEX scheme that combines hybridized and standard flux reconstriction (FR) methods to tackle geometry-induced stiffness. By using the so-called transmission conditions, an overall conservative formulation can be obtained after combining both explicit FR and hybridized implicit FR methods. We verify and apply our approach to a series of numerical examples, including a multi-element airfoil at Reynolds number 1.7 million. Results demonstrate speedup factors of four against standard IMEX formulations and at least 15 against standard explicit formulations for the same problem.

We propose a trust-region stochastic sequential quadratic programming algorithm (TR-StoSQP) to solve nonlinear optimization problems with stochastic objectives and deterministic equality constraints. We consider a fully stochastic setting, where at each step a single sample is generated to estimate the objective gradient. The algorithm adaptively selects the trust-region radius and, compared to the existing line-search StoSQP schemes, allows us to utilize indefinite Hessian matrices (i.e., Hessians without modification) in SQP subproblems. As a trust-region method for constrained optimization, our algorithm must address an infeasibility issue -- the linearized equality constraints and trust-region constraints may lead to infeasible SQP subproblems. In this regard, we propose an adaptive relaxation technique to compute the trial step, consisting of a normal step and a tangential step. To control the lengths of these two steps while ensuring a scale-invariant property, we adaptively decompose the trust-region radius into two segments, based on the proportions of the rescaled feasibility and optimality residuals to the rescaled full KKT residual. The normal step has a closed form, while the tangential step is obtained by solving a trust-region subproblem, to which a solution ensuring the Cauchy reduction is sufficient for our study. We establish a global almost sure convergence guarantee for TR-StoSQP, and illustrate its empirical performance on both a subset of problems in the CUTEst test set and constrained logistic regression problems using data from the LIBSVM collection.

The paper studies the problem of constructing nonparametric simultaneous confidence bands with nonasymptotic and distribition-free guarantees. The target function is assumed to be band-limited and the approach is based on the theory of Paley-Wiener reproducing kernel Hilbert spaces. The starting point of the paper is a recently developed algorithm to which we propose three types of improvements. First, we relax the assumptions on the noises by replacing the symmetricity assumption with a weaker distributional invariance principle. Then, we propose a more efficient way to estimate the norm of the target function, and finally we enhance the construction of the confidence bands by tightening the constraints of the underlying convex optimization problems. The refinements are also illustrated through numerical experiments.

Many scientific and technological problems are related to optimization. Among them, black-box optimization in high-dimensional space is particularly challenging. Recent neural network-based black-box optimization studies have shown noteworthy achievements. However, their capability in high-dimensional search space is still limited. This study proposes a black-box optimization method based on the evolution strategy (ES) and the generative neural network (GNN) model. We designed the algorithm so that the ES and the GNN model work cooperatively. This hybrid model enables reliable training of surrogate networks; it optimizes multi-objective, high-dimensional, and stochastic black-box functions. Our method outperforms baseline optimization methods in this experiment, including ES, and Bayesian optimization.

Isocontouring is one of the most widely used visualization techniques. However, many popular contouring algorithms were created prior to the advent of ubiquitous parallel approaches, such as multi-core, shared memory computing systems. With increasing data sizes and computational loads, it is essential to reimagine such algorithms to leverage the increased computing capabilities available today. To this end we have redesigned the SurfaceNets algorithm, a powerful technique which is often employed to isocontour non-continuous, discrete, volumetric scalar fields such as segmentation label maps. Label maps are ubiquitous to medical computing and biological analysis, used in applications ranging from anatomical atlas creation to brain connectomics. This novel Parallel SurfaceNets algorithm has been redesigned using concepts from the high-performance Flying Edges continuous isocontouring algorrithm. It consists of two basic steps, surface extraction followed by constrained smoothing, parallelized over volume edges and employing a double-buffering smoothing approach to guarantee determinism. The algorithm can extract and smooth multiple segmented objects in a single execution, producing a polygonal (triangular/quadrilateral) mesh with points and polygons fully shared between neighboring objects. Performance is typically one to two orders of magnitude faster than the current sequential algorithms for discrete isosurface extraction on small core-count commodity CPU hardware. We demonstrate the effectiveness of the algorithm on five different datasets including human torso and brain atlases, mouse brain segmentation, and electron microscopy connectomics. The software is currently available under a permissive, open source license in the VTK visualization system.

Split conformal prediction has recently sparked great interest due to its ability to provide formally guaranteed uncertainty sets or intervals for predictions made by black-box neural models, ensuring a predefined probability of containing the actual ground truth. While the original formulation assumes data exchangeability, some extensions handle non-exchangeable data, which is often the case in many real-world scenarios. In parallel, some progress has been made in conformal methods that provide statistical guarantees for a broader range of objectives, such as bounding the best $F_1$-score or minimizing the false negative rate in expectation. In this paper, we leverage and extend these two lines of work by proposing non-exchangeable conformal risk control, which allows controlling the expected value of any monotone loss function when the data is not exchangeable. Our framework is flexible, makes very few assumptions, and allows weighting the data based on its relevance for a given test example; a careful choice of weights may result on tighter bounds, making our framework useful in the presence of change points, time series, or other forms of distribution drift. Experiments with both synthetic and real world data show the usefulness of our method.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.