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Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein distances, have recently been developed to address this need. These methods reduce the computational burden of optimal transport by slicing hyperspheres into one-dimensional projections, i.e., lines or circles. Concurrently, linear optimal transport has been proposed to embed distributions into \( L^2 \) spaces, where the \( L^2 \) distance approximates the optimal transport distance, thereby simplifying comparisons across multiple distributions. In this work, we introduce the Linear Spherical Sliced Optimal Transport (LSSOT) framework, which utilizes slicing to embed spherical distributions into \( L^2 \) spaces while preserving their intrinsic geometry, offering a computationally efficient metric for spherical probability measures. We establish the metricity of LSSOT and demonstrate its superior computational efficiency in applications such as cortical surface registration, 3D point cloud interpolation via gradient flow, and shape embedding. Our results demonstrate the significant computational benefits and high accuracy of LSSOT in these applications.

Ensuring adherence to traffic sign regulations is essential for both human and autonomous vehicle navigation. While current benchmark datasets concentrate on lane perception or basic traffic sign recognition, they often overlook the intricate task of integrating these regulations into lane operations. Addressing this gap, we introduce MapDR, a novel dataset designed for the extraction of Driving Rules from traffic signs and their association with vectorized, locally perceived HD Maps. MapDR features over 10,000 annotated video clips that capture the intricate correlation between traffic sign regulations and lanes. We define two pivotal sub-tasks: 1) Rule Extraction from Traffic Sign, which accurately deciphers regulatory instructions, and 2) Rule-Lane Correspondence Reasoning, which aligns these rules with their respective lanes. Built upon this benchmark, we provide a multimodal solution that offers a strong baseline for advancing autonomous driving technologies. It fills a critical gap in the integration of traffic sign rules, contributing to the development of reliable autonomous navigation systems., Comment: 27 pages, 13 figures

The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between probability measures. To reduce the computational complexity of OT solvers, methods like entropic regularization and sliced optimal transport have been proposed. The sliced OT framework improves efficiency by comparing one-dimensional projections (slices) of high-dimensional distributions. However, despite their computational efficiency, sliced-Wasserstein approaches lack a transportation plan between the input measures, limiting their use in scenarios requiring explicit coupling. In this paper, we address two key questions: Can a transportation plan be constructed between two probability measures using the sliced transport framework? If so, can this plan be used to define a metric between the measures? We propose a "lifting" operation to extend one-dimensional optimal transport plans back to the original space of the measures. By computing the expectation of these lifted plans, we derive a new transportation plan, termed expected sliced transport (EST) plans. We prove that using the EST plan to weight the sum of the individual Euclidean costs for moving from one point to another results in a valid metric between the input discrete probability measures. We demonstrate the connection between our approach and the recently proposed min-SWGG, along with illustrative numerical examples that support our theoretical findings.

High-Definition Maps (HD maps) are essential for the precise navigation and decision-making of autonomous vehicles, yet their creation and upkeep present significant cost and timeliness challenges. The online construction of HD maps using on-board sensors has emerged as a promising solution; however, these methods can be impeded by incomplete data due to occlusions and inclement weather. This paper proposes the PriorDrive framework to addresses these limitations by harnessing the power of prior maps, significantly enhancing the robustness and accuracy of online HD map construction. Our approach integrates a variety of prior maps, such as OpenStreetMap's Standard Definition Maps (SD maps), outdated HD maps from vendors, and locally constructed maps from historical vehicle data. To effectively encode this prior information into online mapping models, we introduce a Hybrid Prior Representation (HPQuery) that standardizes the representation of diverse map elements. At the core of PriorDrive is the Unified Vector Encoder (UVE), which employs a dual encoding mechanism to process vector data. The intra-vector encoder captures fine-grained local features, while the inter-vector encoder integrates global context. Furthermore, we propose a segment-level and point-level pre-training strategy that enables the UVE to learn the prior distribution of vector data, thereby improving the encoder's generalizability and performance. Through extensive testing on the nuScenes dataset, we demonstrate that PriorDrive is highly compatible with various online mapping models and substantially improves map prediction capabilities. The integration of prior maps through the PriorDrive framework offers a robust solution to the challenges of single-perception data, paving the way for more reliable autonomous vehicle navigation.

Long-term Action Quality Assessment (AQA) evaluates the execution of activities in videos. However, the length presents challenges in fine-grained interpretability, with current AQA methods typically producing a single score by averaging clip features, lacking detailed semantic meanings of individual clips. Long-term videos pose additional difficulty due to the complexity and diversity of actions, exacerbating interpretability challenges. While query-based transformer networks offer promising long-term modeling capabilities, their interpretability in AQA remains unsatisfactory due to a phenomenon we term Temporal Skipping, where the model skips self-attention layers to prevent output degradation. To address this, we propose an attention loss function and a query initialization method to enhance performance and interpretability. Additionally, we introduce a weight-score regression module designed to approximate the scoring patterns observed in human judgments and replace conventional single-score regression, improving the rationality of interpretability. Our approach achieves state-of-the-art results on three real-world, long-term AQA benchmarks. Our code is available at: https://github.com/dx199771/Interpretability-AQA, Comment: Accepted to British Machine Vision Conference (BMVC) 2024

The Boulby UnderGround Screening (BUGS) facility, located at the Boulby Underground Laboratory, has significantly advanced its material screening capabilities by installing two XIA UltraLo-1800 alpha particle detectors. This study presents a comprehensive evaluation of one of these detectors, operated 1,100 meters underground at the Boulby Underground Laboratory, which provides significant shielding from cosmic radiation and maintains a low ambient radon activity of 2.30 $\pm$ 0.03 Bq/m$^3$. Our evaluation focuses on energy reconstruction accuracy, background radiation rates, and operational stability. The XIA UltraLo-1800 detector demonstrates remarkable stability in energy reconstruction, with less than 0.1 MeV variation over four years. Moreover, the implementation of a graphite-filled PTFE liner in the sample tray resulted in a significant reduction in background radiation levels compared to measurements with the original stainless steel tray, achieving an average activity of 0.15 $\pm$ 0.01 $\alpha$/cm$^2$/khr. Copper sample assays, performed before and after radon exposure, demonstrated the detector's ability to accurately identify and quantify $^{210}$Po contamination. By implementing the robust cleanliness procedures and protocols described in this article, we observed a reduction in $^{210}$Po activity from 0.504 $\pm$ 0.022 mBq to 0.336 $\pm$ 0.013 mBq, highlighting the crucial role of refined cleaning methods in minimizing background for sensitive experiments. Additionally, observations of elevated background activity levels post-high-activity sample measurements illustrate the need for careful management of assay conditions and environment to maintain low background levels. These results highlight the potential of the XIA UltraLo-1800 in enhancing the precision of material assays essential for reducing background interference in rare event experiments.

In this paper, we introduce a novel benchmark, dubbed VastTrack, towards facilitating the development of more general visual tracking via encompassing abundant classes and videos. VastTrack possesses several attractive properties: (1) Vast Object Category. In particular, it covers target objects from 2,115 classes, largely surpassing object categories of existing popular benchmarks (e.g., GOT-10k with 563 classes and LaSOT with 70 categories). With such vast object classes, we expect to learn more general object tracking. (2) Larger scale. Compared with current benchmarks, VastTrack offers 50,610 sequences with 4.2 million frames, which makes it to date the largest benchmark regarding the number of videos, and thus could benefit training even more powerful visual trackers in the deep learning era. (3) Rich Annotation. Besides conventional bounding box annotations, VastTrack also provides linguistic descriptions for the videos. The rich annotations of VastTrack enables development of both the vision-only and the vision-language tracking. To ensure precise annotation, all videos are manually labeled with multiple rounds of careful inspection and refinement. To understand performance of existing trackers and to provide baselines for future comparison, we extensively assess 25 representative trackers. The results, not surprisingly, show significant drops compared to those on current datasets due to lack of abundant categories and videos from diverse scenarios for training, and more efforts are required to improve general tracking. Our VastTrack and all the evaluation results will be made publicly available https://github.com/HengLan/VastTrack., Comment: Tech. report

The Gromov-Wasserstein (GW) distance has gained increasing interest in the machine learning community in recent years, as it allows for the comparison of measures in different metric spaces. To overcome the limitations imposed by the equal mass requirements of the classical GW problem, researchers have begun exploring its application in unbalanced settings. However, Unbalanced GW (UGW) can only be regarded as a discrepancy rather than a rigorous metric/distance between two metric measure spaces (mm-spaces). In this paper, we propose a particular case of the UGW problem, termed Partial Gromov-Wasserstein (PGW). We establish that PGW is a well-defined metric between mm-spaces and discuss its theoretical properties, including the existence of a minimizer for the PGW problem and the relationship between PGW and GW, among others. We then propose two variants of the Frank-Wolfe algorithm for solving the PGW problem and show that they are mathematically and computationally equivalent. Moreover, based on our PGW metric, we introduce the analogous concept of barycenters for mm-spaces. Finally, we validate the effectiveness of our PGW metric and related solvers in applications such as shape matching, shape retrieval, and shape interpolation, comparing them against existing baselines.

Comparing spherical probability distributions is of great interest in various fields, including geology, medical domains, computer vision, and deep representation learning. The utility of optimal transport-based distances, such as the Wasserstein distance, for comparing probability measures has spurred active research in developing computationally efficient variations of these distances for spherical probability measures. This paper introduces a high-speed and highly parallelizable distance for comparing spherical measures using the stereographic projection and the generalized Radon transform, which we refer to as the Stereographic Spherical Sliced Wasserstein (S3W) distance. We carefully address the distance distortion caused by the stereographic projection and provide an extensive theoretical analysis of our proposed metric and its rotationally invariant variation. Finally, we evaluate the performance of the proposed metrics and compare them with recent baselines in terms of both speed and accuracy through a wide range of numerical studies, including gradient flows and self-supervised learning. Our code is available at https://github.com/mint-vu/s3wd., Comment: Published at ICML 2024 (Spotlight). Project page: https://abi-kothapalli.github.io/s3w/

The COVID-19 infodemic, characterized by the rapid spread of misinformation and unverified claims related to the pandemic, presents a significant challenge. This paper presents a comparative analysis of the COVID-19 infodemic in the English and Chinese languages, utilizing textual data extracted from social media platforms. To ensure a balanced representation, two infodemic datasets were created by augmenting previously collected social media textual data. Through word frequency analysis, the thirty-five most frequently occurring infodemic words are identified, shedding light on prevalent discussions surrounding the infodemic. Moreover, topic clustering analysis uncovers thematic structures and provides a deeper understanding of primary topics within each language context. Additionally, sentiment analysis enables comprehension of the emotional tone associated with COVID-19 information on social media platforms in English and Chinese. This research contributes to a better understanding of the COVID-19 infodemic phenomenon and can guide the development of strategies to combat misinformation during public health crises across different languages.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

Modeling and synthesizing low-light raw noise is a fundamental problem for computational photography and image processing applications. Although most recent works have adopted physics-based models to synthesize noise, the signal-independent noise in low-light conditions is far more complicated and varies dramatically across camera sensors, which is beyond the description of these models. To address this issue, we introduce a new perspective to synthesize the signal-independent noise by a generative model. Specifically, we synthesize the signal-dependent and signal-independent noise in a physics- and learning-based manner, respectively. In this way, our method can be considered as a general model, that is, it can simultaneously learn different noise characteristics for different ISO levels and generalize to various sensors. Subsequently, we present an effective multi-scale discriminator termed Fourier transformer discriminator (FTD) to distinguish the noise distribution accurately. Additionally, we collect a new low-light raw denoising (LRD) dataset for training and benchmarking. Qualitative validation shows that the noise generated by our proposed noise model can be highly similar to the real noise in terms of distribution. Furthermore, extensive denoising experiments demonstrate that our method performs favorably against state-of-the-art methods on different sensors., Comment: 11 pages, 7 figures. Accepted by ICCV 2023

Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a growing interest in defining transport-based distances that allow for comparing signed measures and, more generally, multi-channeled signals. Transport $\mathrm{L}^{p}$ distances are notable extensions of the optimal transport framework to signed and possibly multi-channeled signals. In this paper, we introduce partial transport $\mathrm{L}^{p}$ distances as a new family of metrics for comparing generic signals, benefiting from the robustness of partial transport distances. We provide theoretical background such as the existence of optimal plans and the behavior of the distance in various limits. Furthermore, we introduce the sliced variation of these distances, which allows for rapid comparison of generic signals. Finally, we demonstrate the application of the proposed distances in signal class separability and nearest neighbor classification.

Learning from set-structured data, such as point clouds, has gained significant attention from the machine learning community. Geometric deep learning provides a blueprint for designing effective set neural networks that preserve the permutation symmetry of set-structured data. Of our interest are permutation invariant networks, which are composed of a permutation equivariant backbone, permutation invariant global pooling, and regression/classification head. While existing literature has focused on improving equivariant backbones, the impact of the pooling layer is often overlooked. In this paper, we examine the interplay between permutation equivariant backbones and permutation invariant global pooling on three benchmark point cloud classification datasets. Our findings reveal that: 1) complex pooling methods, such as transport-based or attention-based poolings, can significantly boost the performance of simple backbones, but the benefits diminish for more complex backbones, 2) even complex backbones can benefit from pooling layers in low data scenarios, 3) surprisingly, the choice of pooling layers can have a more significant impact on the model's performance than adjusting the width and depth of the backbone, and 4) pairwise combination of pooling layers can significantly improve the performance of a fixed backbone. Our comprehensive study provides insights for practitioners to design better permutation invariant set neural networks. Our code is available at https://github.com/mint-vu/backbone_vs_pooling., Comment: Published in the GRaM workshop at ICML 2024

Lifelong learning agents aim to learn multiple tasks sequentially over a lifetime. This involves the ability to exploit previous knowledge when learning new tasks and to avoid forgetting. Modulating masks, a specific type of parameter isolation approach, have recently shown promise in both supervised and reinforcement learning. While lifelong learning algorithms have been investigated mainly within a single-agent approach, a question remains on how multiple agents can share lifelong learning knowledge with each other. We show that the parameter isolation mechanism used by modulating masks is particularly suitable for exchanging knowledge among agents in a distributed and decentralized system of lifelong learners. The key idea is that the isolation of specific task knowledge to specific masks allows agents to transfer only specific knowledge on-demand, resulting in robust and effective distributed lifelong learning. We assume fully distributed and asynchronous scenarios with dynamic agent numbers and connectivity. An on-demand communication protocol ensures agents query their peers for specific masks to be transferred and integrated into their policies when facing each task. Experiments indicate that on-demand mask communication is an effective way to implement distributed lifelong reinforcement learning and provides a lifelong learning benefit with respect to distributed RL baselines such as DD-PPO, IMPALA, and PPO+EWC. The system is particularly robust to connection drops and demonstrates rapid learning due to knowledge exchange., Comment: 25 pages, 14 figures, 9 tables, to be published in the Second Conference on Lifelong Learning Agents (CoLLAs 2023), code can be found at https://github.com/DMIU-ShELL/deeprl-shell

Planar object tracking is a critical computer vision problem and has drawn increasing interest owing to its key roles in robotics, augmented reality, etc. Despite rapid progress, its further development, especially in the deep learning era, is largely hindered due to the lack of large-scale challenging benchmarks. Addressing this, we introduce PlanarTrack, a large-scale challenging planar tracking benchmark. Specifically, PlanarTrack consists of 1,000 videos with more than 490K images. All these videos are collected in complex unconstrained scenarios from the wild, which makes PlanarTrack, compared with existing benchmarks, more challenging but realistic for real-world applications. To ensure the high-quality annotation, each frame in PlanarTrack is manually labeled using four corners with multiple-round careful inspection and refinement. To our best knowledge, PlanarTrack, to date, is the largest and most challenging dataset dedicated to planar object tracking. In order to analyze the proposed PlanarTrack, we evaluate 10 planar trackers and conduct comprehensive comparisons and in-depth analysis. Our results, not surprisingly, demonstrate that current top-performing planar trackers degenerate significantly on the challenging PlanarTrack and more efforts are needed to improve planar tracking in the future. In addition, we further derive a variant named PlanarTrack$_{\mathbf{BB}}$ for generic object tracking from PlanarTrack. Our evaluation of 10 excellent generic trackers on PlanarTrack$_{\mathrm{BB}}$ manifests that, surprisingly, PlanarTrack$_{\mathrm{BB}}$ is even more challenging than several popular generic tracking benchmarks and more attention should be paid to handle such planar objects, though they are rigid. All benchmarks and evaluations will be released at the project webpage., Comment: Tech. Report

Measuring similarities between different tasks is critical in a broad spectrum of machine learning problems, including transfer, multi-task, continual, and meta-learning. Most current approaches to measuring task similarities are architecture-dependent: 1) relying on pre-trained models, or 2) training networks on tasks and using forward transfer as a proxy for task similarity. In this paper, we leverage the optimal transport theory and define a novel task embedding for supervised classification that is model-agnostic, training-free, and capable of handling (partially) disjoint label sets. In short, given a dataset with ground-truth labels, we perform a label embedding through multi-dimensional scaling and concatenate dataset samples with their corresponding label embeddings. Then, we define the distance between two datasets as the 2-Wasserstein distance between their updated samples. Lastly, we leverage the 2-Wasserstein embedding framework to embed tasks into a vector space in which the Euclidean distance between the embedded points approximates the proposed 2-Wasserstein distance between tasks. We show that the proposed embedding leads to a significantly faster comparison of tasks compared to related approaches like the Optimal Transport Dataset Distance (OTDD). Furthermore, we demonstrate the effectiveness of our proposed embedding through various numerical experiments and show statistically significant correlations between our proposed distance and the forward and backward transfer between tasks.

Centrosymmetric antiferromagnetic semiconductors, although abundant in nature, seem less promising than ferromagnets and ferroelectrics for practical applications in semiconductor spintronics. As a matter of fact, the lack of spontaneous polarization and magnetization hinders the efficient utilization of electronic spin in these materials. Here, we propose a paradigm to harness electronic spin in centrosymmetric antiferromagnets via Zeeman spin splittings of electronic energy levels -- termed as spin Zeeman effect -- which is controlled by electric field.By symmetry analysis, we identify twenty-one centrosymmetric antiferromagnetic point groups that accommodate such a spin Zeeman effect. We further predict by first-principles that two antiferromagnetic semiconductors, Fe$_2$TeO$_6$ and SrFe$_2$S$_2$O, are excellent candidates showcasing Zeeman splittings as large as $\sim$55 and $\sim$30 meV, respectively, induced by an electric field of 6 MV/cm. Moreover, the electronic spin magnetization associated to the splitting energy levels can be switched by reversing the electric field. Our work thus sheds light on the electric-field control of electronic spin in antiferromagnets, which broadens the scope of application of centrosymmetric antiferromagnetic semiconductors.

Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring near-real-time optimization. The majority of existing approaches focus on learning data-driven optimizers that lead to fewer iterations in solving an optimization. In this paper, we take a different approach and propose to replace the iterative solvers altogether with a trainable parametric set function, that outputs the optimal arguments/parameters of an optimization problem in a single feed forward. We denote our method as Learning to Optimize the Optimization Process (LOOP). We show the feasibility of learning such parametric (set) functions to solve various classic optimization problems including linear/nonlinear regression, principal component analysis, transport-based coreset, and quadratic programming in supply management applications. In addition, we propose two alternative approaches for learning such parametric functions, with and without a solver in the LOOP. Finally, through various numerical experiments, we show that the trained solvers could be orders of magnitude faster than the classic iterative solvers while providing near optimal solutions.

Extracting roads from high-resolution remote sensing images (HRSIs) is vital in a wide variety of applications, such as autonomous driving, path planning, and road navigation. Due to the long and thin shape as well as the shades induced by vegetation and buildings, small-sized roads are more difficult to discern. In order to improve the reliability and accuracy of small-sized road extraction when roads of multiple sizes coexist in an HRSI, an enhanced deep neural network model termed Dual-Decoder-U-Net (DDU-Net) is proposed in this paper. Motivated by the U-Net model, a small decoder is added to form a dual-decoder structure for more detailed features. In addition, we introduce the dilated convolution attention module (DCAM) between the encoder and decoders to increase the receptive field as well as to distill multi-scale features through cascading dilated convolution and global average pooling. The convolutional block attention module (CBAM) is also embedded in the parallel dilated convolution and pooling branches to capture more attention-aware features. Extensive experiments are conducted on the Massachusetts Roads dataset with experimental results showing that the proposed model outperforms the state-of-the-art DenseUNet, DeepLabv3+ and D-LinkNet by 6.5%, 3.3%, and 2.1% in the mean Intersection over Union (mIoU), and by 4%, 4.8%, and 3.1% in the F1 score, respectively. Both ablation and heatmap analyses are presented to validate the effectiveness of the proposed model.

Learning from set-structured data is an essential problem with many applications in machine learning and computer vision. This paper focuses on non-parametric and data-independent learning from set-structured data using approximate nearest neighbor (ANN) solutions, particularly locality-sensitive hashing. We consider the problem of set retrieval from an input set query. Such retrieval problem requires: 1) an efficient mechanism to calculate the distances/dissimilarities between sets, and 2) an appropriate data structure for fast nearest neighbor search. To that end, we propose Sliced-Wasserstein set embedding as a computationally efficient "set-2-vector" mechanism that enables downstream ANN, with theoretical guarantees. The set elements are treated as samples from an unknown underlying distribution, and the Sliced-Wasserstein distance is used to compare sets. We demonstrate the effectiveness of our algorithm, denoted as Set-LOcality Sensitive Hashing (SLOSH), on various set retrieval datasets and compare our proposed embedding with standard set embedding approaches, including Generalized Mean (GeM) embedding/pooling, Featurewise Sort Pooling (FSPool), and Covariance Pooling and show consistent improvement in retrieval results. The code for replicating our results is available here: \href{https://github.com/mint-vu/SLOSH}{https://github.com/mint-vu/SLOSH}.