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We present CAFA-evaluator, a powerful Python program designed to evaluate the performance of prediction methods on targets with hierarchical concept dependencies. It generalizes multi-label evaluation to modern ontologies where the prediction targets are drawn from a directed acyclic graph and achieves high efficiency by leveraging matrix computation and topological sorting. The program requirements include a small number of standard Python libraries, making CAFA-evaluator easy to maintain. The code replicates the Critical Assessment of protein Function Annotation (CAFA) benchmarking, which evaluates predictions of the consistent subgraphs in Gene Ontology. Owing to its reliability and accuracy, the organizers have selected CAFA-evaluator as the official CAFA evaluation software.

In this study, we address the challenge of constructing continuous three-dimensional (3D) models that accurately represent uncertain surfaces, derived from noisy and incomplete LiDAR scanning data. Building upon our prior work, which utilized the Gaussian Process (GP) and Gaussian Mixture Model (GMM) for structured building models, we introduce a more generalized approach tailored for complex surfaces in urban scenes, where four-dimensional (4D) GMM Regression and GP with derivative observations are applied. A Hierarchical GMM (HGMM) is employed to optimize the number of GMM components and speed up the GMM training. With the prior map obtained from HGMM, GP inference is followed for the refinement of the final map. Our approach models the implicit surface of the geo-object and enables the inference of the regions that are not completely covered by measurements. The integration of GMM and GP yields well-calibrated uncertainty estimates alongside the surface model, enhancing both accuracy and reliability. The proposed method is evaluated on the real data collected by a mobile mapping system. Compared to the performance in mapping accuracy and uncertainty quantification of other methods such as Gaussian Process Implicit Surface map (GPIS) and log-Gaussian Process Implicit Surface map (Log-GPIS), the proposed method achieves lower RMSEs, higher log-likelihood values and fewer computational costs for the evaluated datasets.

In this paper, we propose a new framework for online 3D scene perception. Conventional 3D scene perception methods are offline, i.e., take an already reconstructed 3D scene geometry as input, which is not applicable in robotic applications where the input data is streaming RGB-D videos rather than a complete 3D scene reconstructed from pre-collected RGB-D videos. To deal with online 3D scene perception tasks where data collection and perception should be performed simultaneously, the model should be able to process 3D scenes frame by frame and make use of the temporal information. To this end, we propose an adapter-based plug-and-play module for the backbone of 3D scene perception model, which constructs memory to cache and aggregate the extracted RGB-D features to empower offline models with temporal learning ability. Specifically, we propose a queued memory mechanism to cache the supporting point cloud and image features. Then we devise aggregation modules which directly perform on the memory and pass temporal information to current frame. We further propose 3D-to-2D adapter to enhance image features with strong global context. Our adapters can be easily inserted into mainstream offline architectures of different tasks and significantly boost their performance on online tasks. Extensive experiments on ScanNet and SceneNN datasets demonstrate our approach achieves leading performance on three 3D scene perception tasks compared with state-of-the-art online methods by simply finetuning existing offline models, without any model and task-specific designs. \href{//xuxw98.github.io/Online3D/}{Project page}.

In this work, we study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). LTL is a rich and expressive logic that can specify important properties of programs. This includes, but is not limited to, termination, safety, liveness, progress, recurrence and reach-avoid properties. We first present novel sound and complete witnesses for LTL verification over imperative programs. Our witnesses are applicable to both universal (all runs) and existential (some run) settings. We then consider polynomial arithmetic programs, i.e. programs in which every assignment and guard consists only of polynomial expressions, with specifications as LTL formulas in which atomic propositions are polynomial constraints. For this setting, we provide an efficient algorithm to automatically synthesize such LTL witnesses. Our synthesis procedure is both sound and semi-complete, i.e. complete for any fixed polynomial degree in the templates. In other words, we provide the first template-based approach for polynomial programs that can handle any LTL formula as its specification. Our approach has termination guarantees with sub-exponential time complexity and generalizes and unifies previous methods for termination, safety and reachability, since they are expressible in LTL. Finally, we present experimental results demonstrating the effectiveness of our approach and that it can handle programs which were beyond the reach of previous state-of-the-art tools.

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling high-dimensional partial differential equations (PDEs), challenges arise when applying quadrature rules for accurate integral evaluation in the BGK operator, which can compromise the mesh-free benefit and increase computational costs. To address this, we leverage the canonical polyadic decomposition structure of SPINNs and the linear nature of moment calculation, achieving a substantial reduction in computational expense for quadrature rule application. The multi-scale nature of the particle density function poses difficulties in precisely approximating macroscopic moments using neural networks. To improve SPINN training, we introduce the integration of Gaussian functions into SPINNs, coupled with a relative loss approach. This modification enables SPINNs to decay as rapidly as Maxwellian distributions, thereby enhancing the accuracy of macroscopic moment approximations. The relative loss design further ensures that both large and small-scale features are effectively captured by the SPINNs. The efficacy of our approach is demonstrated through a series of five numerical experiments, including the solution to a challenging 3D Riemann problem. These results highlight the potential of our novel method in efficiently and accurately addressing complex challenges in computational physics.

In this paper, we apply the Paired-Explicit Runge-Kutta (P-ERK) schemes by Vermeire et. al. (2019, 2022) to dynamically partitioned systems arising from adaptive mesh refinement. The P-ERK schemes enable multirate time-integration with no changes in the spatial discretization methodology, making them readily implementable in existing codes that employ a method-of-lines approach. We show that speedup compared to a range of state of the art Runge-Kutta methods can be realized, despite additional overhead due to the dynamic re-assignment of flagging variables and restricting nonlinear stability properties. The effectiveness of the approach is demonstrated for a range of simulation setups for viscous and inviscid convection-dominated compressible flows for which we provide a reproducibility repository. In addition, we perform a thorough investigation of the nonlinear stability properties of the Paired-Explicit Runge-Kutta schemes regarding limitations due to the violation of monotonicity properties of the underlying spatial discretization. Furthermore, we present a novel approach for estimating the relevant eigenvalues of large Jacobians required for the optimization of stability polynomials.

In this paper, we look at cross-domain few-shot classification which presents the challenging task of learning new classes in unseen domains with few labelled examples. Existing methods, though somewhat effective, encounter several limitations, which we address in this work through two significant improvements. First, to address overfitting associated with fine-tuning a large number of parameters on small datasets, we introduce a lightweight parameter-efficient adaptation strategy. This strategy employs a linear transformation of pre-trained features, significantly reducing the trainable parameter count. Second, we replace the traditional nearest centroid classifier with a variance-aware loss function, enhancing the model's sensitivity to the inter- and intra-class variances within the training set for improved clustering in feature space. Empirical evaluations on the Meta-Dataset benchmark showcase that our approach not only improves accuracy up to 7.7% and 5.3% on seen and unseen datasets respectively but also achieves this performance while being at least ~3x more parameter-efficient than existing methods, establishing a new state-of-the-art in cross-domain few-shot learning. Our code can be found at //github.com/rashindrie/DIPA.

In this paper, we study the problem of unsupervised graph representation learning by harnessing the control properties of dynamical networks defined on graphs. Our approach introduces a novel framework for contrastive learning, a widely prevalent technique for unsupervised representation learning. A crucial step in contrastive learning is the creation of 'augmented' graphs from the input graphs. Though different from the original graphs, these augmented graphs retain the original graph's structural characteristics. Here, we propose a unique method for generating these augmented graphs by leveraging the control properties of networks. The core concept revolves around perturbing the original graph to create a new one while preserving the controllability properties specific to networks and graphs. Compared to the existing methods, we demonstrate that this innovative approach enhances the effectiveness of contrastive learning frameworks, leading to superior results regarding the accuracy of the classification tasks. The key innovation lies in our ability to decode the network structure using these control properties, opening new avenues for unsupervised graph representation learning.

In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving on the broad class of homogeneous spaces (encompassing all vector spaces, Lie groups, and spheres of any dimension). In this setting, the transitive action of a Lie group on the configuration manifold enables an intrinsic description of the tracking error as an element of the state space, even in the absence of a group structure on the configuration manifold itself (e.g., for $\mathbb{S}^2$). Such an error state facilitates the design of a generalized control policy depending smoothly on state and time that drives this geometric tracking error to a designated origin from almost every initial condition, thereby guaranteeing almost global convergence to the reference trajectory. Moreover, the proposed controller simplifies naturally when specialized to a Lie group or the $n$-sphere. In summary, we propose a unified, intrinsic controller guaranteeing almost global asymptotic trajectory tracking for fully-actuated mechanical systems evolving on a broader class of manifolds. We apply the method to an axisymmetric satellite and an omnidirectional aerial robot.

In this paper, we propose the joint learning attention and recurrent neural network (RNN) models for multi-label classification. While approaches based on the use of either model exist (e.g., for the task of image captioning), training such existing network architectures typically require pre-defined label sequences. For multi-label classification, it would be desirable to have a robust inference process, so that the prediction error would not propagate and thus affect the performance. Our proposed model uniquely integrates attention and Long Short Term Memory (LSTM) models, which not only addresses the above problem but also allows one to identify visual objects of interests with varying sizes without the prior knowledge of particular label ordering. More importantly, label co-occurrence information can be jointly exploited by our LSTM model. Finally, by advancing the technique of beam search, prediction of multiple labels can be efficiently achieved by our proposed network model.