Providing formal safety and performance guarantees for autonomous systems is becoming increasingly important. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for providing these guarantees, since it can handle general nonlinear system dynamics, bounded adversarial system disturbances, and state and input constraints. However, it involves solving a PDE, whose computational and memory complexity scales exponentially with respect to the state dimensionality, making its direct use on large-scale systems intractable. A recently proposed method called DeepReach overcomes this challenge by leveraging a sinusoidal neural PDE solver for high-dimensional reachability problems, whose computational requirements scale with the complexity of the underlying reachable tube rather than the state space dimension. Unfortunately, neural networks can make errors and thus the computed solution may not be safe, which falls short of achieving our overarching goal to provide formal safety assurances. In this work, we propose a method to compute an error bound for the DeepReach solution. This error bound can then be used for reachable tube correction, resulting in a safe approximation of the true reachable tube. We also propose a scenario-based optimization approach to compute a probabilistic bound on this error correction for general nonlinear dynamical systems. We demonstrate the efficacy of the proposed approach in obtaining probabilistically safe reachable tubes for high-dimensional rocket-landing and multi-vehicle collision-avoidance problems.
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Headland maneuvering is a crucial aspect of unmanned field operations for autonomous agricultural vehicles (AAVs). While motion planning for headland turning in open fields has been extensively studied and integrated into commercial auto-guidance systems, the existing methods primarily address scenarios with ample headland space and thus may not work in more constrained headland geometries. Commercial orchards often contain narrow and irregularly shaped headlands, which may include static obstacles,rendering the task of planning a smooth and collision-free turning trajectory difficult. To address this challenge, we propose an optimization-based motion planning algorithm for headland turning under geometrical constraints imposed by field geometry and obstacles.
Performing automatic reformulations of a user's query is a popular paradigm used in information retrieval (IR) for improving effectiveness -- as exemplified by the pseudo-relevance feedback approaches, which expand the query in order to alleviate the vocabulary mismatch problem. Recent advancements in generative language models have demonstrated their ability in generating responses that are relevant to a given prompt. In light of this success, we seek to study the capacity of such models to perform query reformulation and how they compare with long-standing query reformulation methods that use pseudo-relevance feedback. In particular, we investigate two representative query reformulation frameworks, GenQR and GenPRF. GenQR directly reformulates the user's input query, while GenPRF provides additional context for the query by making use of pseudo-relevance feedback information. For each reformulation method, we leverage different techniques, including fine-tuning and direct prompting, to harness the knowledge of language models. The reformulated queries produced by the generative models are demonstrated to markedly benefit the effectiveness of a state-of-the-art retrieval pipeline on four TREC test collections (varying from TREC 2004 Robust to the TREC 2019 Deep Learning). Furthermore, our results indicate that our studied generative models can outperform various statistical query expansion approaches while remaining comparable to other existing complex neural query reformulation models, with the added benefit of being simpler to implement.
Multidimensional Voronoi constellations (VCs) are shown to be more power-efficient than quadrature amplitude modulation (QAM) formats given the same uncoded bit error rate, and also have higher achievable information rates. However, a coded modulation scheme to sustain these gains after forward error correction (FEC) coding is still lacking. This paper designs coded modulation schemes with soft-decision FEC codes for VCs, including bit-interleaved coded modulation (BICM) and multilevel coded modulation (MLCM), together with three bit-to-integer mapping algorithms and log-likelihood ratio calculation algorithms. Simulation results show that VCs can achieve up to 1.84 dB signal-to-noise ratio (SNR) gains over QAM with BICM, and up to 0.99 dB SNR gains over QAM with MLCM for the additive white Gaussian noise channel, with a surprisingly low complexity.
State-of-the-art performance in electroencephalography (EEG) decoding tasks is currently often achieved with either Deep-Learning (DL) or Riemannian-Geometry-based decoders (RBDs). Recently, there is growing interest in Deep Riemannian Networks (DRNs) possibly combining the advantages of both previous classes of methods. However, there are still a range of topics where additional insight is needed to pave the way for a more widespread application of DRNs in EEG. These include architecture design questions such as network size and end-to-end ability.How these factors affect model performance has not been explored. Additionally, it is not clear how the data within these networks is transformed, and whether this would correlate with traditional EEG decoding. Our study aims to lay the groundwork in the area of these topics through the analysis of DRNs for EEG with a wide range of hyperparameters. Networks were tested on two public EEG datasets and compared with state-of-the-art ConvNets. Here we propose end-to-end EEG SPDNet (EE(G)-SPDNet), and we show that this wide, end-to-end DRN can outperform the ConvNets, and in doing so use physiologically plausible frequency regions. We also show that the end-to-end approach learns more complex filters than traditional band-pass filters targeting the classical alpha, beta, and gamma frequency bands of the EEG, and that performance can benefit from channel specific filtering approaches. Additionally, architectural analysis revealed areas for further improvement due to the possible loss of Riemannian specific information throughout the network. Our study thus shows how to design and train DRNs to infer task-related information from the raw EEG without the need of handcrafted filterbanks and highlights the potential of end-to-end DRNs such as EE(G)-SPDNet for high-performance EEG decoding.
Existing methods for video question answering (VideoQA) often suffer from spurious correlations between different modalities, leading to a failure in identifying the dominant visual evidence and the intended question. Moreover, these methods function as black boxes, making it difficult to interpret the visual scene during the QA process. In this paper, to discover critical video segments and frames that serve as the visual causal scene for generating reliable answers, we present a causal analysis of VideoQA and propose a framework for cross-modal causal relational reasoning, named Visual Causal Scene Refinement (VCSR). Particularly, a set of causal front-door intervention operations is introduced to explicitly find the visual causal scenes at both segment and frame levels. Our VCSR involves two essential modules: i) the Question-Guided Refiner (QGR) module, which refines consecutive video frames guided by the question semantics to obtain more representative segment features for causal front-door intervention; ii) the Causal Scene Separator (CSS) module, which discovers a collection of visual causal and non-causal scenes based on the visual-linguistic causal relevance and estimates the causal effect of the scene-separating intervention in a contrastive learning manner. Extensive experiments on the NExT-QA, Causal-VidQA, and MSRVTT-QA datasets demonstrate the superiority of our VCSR in discovering visual causal scene and achieving robust video question answering. The code is available at //github.com/YangLiu9208/VCSR.
Many efforts have been made to construct dialog systems for different types of conversations, such as task-oriented dialog (TOD) and open-domain dialog (ODD). To better mimic human-level conversations that usually fuse various dialog modes, it is essential to build a system that can effectively handle both TOD and ODD and access different knowledge sources. To address the lack of available data for the fused task, we propose a framework for automatically generating dialogues that combine knowledge-grounded ODDs and TODs in various settings. Additionally, we introduce a unified model PivotBot that is capable of appropriately adopting TOD and ODD modes and accessing different knowledge sources in order to effectively tackle the fused task. Evaluation results demonstrate the superior ability of the proposed model to switch seamlessly between TOD and ODD tasks.
We propose an unconditionally energy-stable, orthonormality-preserving, component-wise splitting iterative scheme for the Kohn-Sham gradient flow based model in the electronic structure calculation. We first study the scheme discretized in time but still continuous in space. The component-wise splitting iterative scheme changes one wave function at a time, similar to the Gauss-Seidel iteration for solving a linear equation system. Rigorous mathematical derivations are presented to show our proposed scheme indeed satisfies the desired properties. We then study the fully-discretized scheme, where the space is further approximated by a conforming finite element subspace. For the fully-discretized scheme, not only the preservation of orthogonality and normalization (together we called orthonormalization) can be quickly shown using the same idea as for the semi-discretized scheme, but also the highlight property of the scheme, i.e., the unconditional energy stability can be rigorously proven. The scheme allows us to use large time step sizes and deal with small systems involving only a single wave function during each iteration step. Several numerical experiments are performed to verify the theoretical analysis, where the number of iterations is indeed greatly reduced as compared to similar examples solved by the Kohn-Sham gradient flow based model in the literature.
The continuous dynamics of natural systems has been effectively modelled using Neural Ordinary Differential Equations (Neural ODEs). However, for accurate and meaningful predictions, it is crucial that the models follow the underlying rules or laws that govern these systems. In this work, we propose a self-adaptive penalty algorithm for Neural ODEs to enable modelling of constrained natural systems. The proposed self-adaptive penalty function can dynamically adjust the penalty parameters. The explicit introduction of prior knowledge helps to increase the interpretability of Neural ODE -based models. We validate the proposed approach by modelling three natural systems with prior knowledge constraints: population growth, chemical reaction evolution, and damped harmonic oscillator motion. The numerical experiments and a comparison with other penalty Neural ODE approaches and \emph{vanilla} Neural ODE, demonstrate the effectiveness of the proposed self-adaptive penalty algorithm for Neural ODEs in modelling constrained natural systems. Moreover, the self-adaptive penalty approach provides more accurate and robust models with reliable and meaningful predictions.
Graph Neural Networks (GNN) has demonstrated the superior performance in many challenging applications, including the few-shot learning tasks. Despite its powerful capacity to learn and generalize from few samples, GNN usually suffers from severe over-fitting and over-smoothing as the model becomes deep, which limit the model scalability. In this work, we propose a novel Attentive GNN to tackle these challenges, by incorporating a triple-attention mechanism, \ie node self-attention, neighborhood attention, and layer memory attention. We explain why the proposed attentive modules can improve GNN for few-shot learning with theoretical analysis and illustrations. Extensive experiments show that the proposed Attentive GNN outperforms the state-of-the-art GNN-based methods for few-shot learning over the mini-ImageNet and Tiered-ImageNet datasets, with both inductive and transductive settings.
Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model---namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)---which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.
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