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We study the problem of blind super-resolution, which can be formulated as a low-rank matrix recovery problem via vectorized Hankel lift (VHL). The previous gradient descent method based on VHL named PGD-VHL relies on additional regularization such as the projection and balancing penalty, exhibiting a suboptimal iteration complexity. In this paper, we propose a simpler unconstrained optimization problem without the above two types of regularization and develop two new and provable gradient methods named VGD-VHL and ScalGD-VHL. A novel and sharp analysis is provided for the theoretical guarantees of our algorithms, which demonstrates that our methods offer lower iteration complexity than PGD-VHL. In addition, ScalGD-VHL has the lowest iteration complexity while being independent of the condition number. Furthermore, our novel analysis reveals that the blind super-resolution problem is less incoherence-demanding, thereby eliminating the necessity for incoherent projections to achieve linear convergence. Empirical results illustrate that our methods exhibit superior computational efficiency while achieving comparable recovery performance to prior arts.

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This paper presents a comprehensive hazard analysis, risk assessment, and loss evaluation for an Evasive Minimum Risk Maneuvering (EMRM) system designed for autonomous vehicles. The EMRM system is engineered to enhance collision avoidance and mitigate loss severity by drawing inspiration from professional drivers who perform aggressive maneuvers while maintaining stability for effective risk mitigation. Recent advancements in autonomous vehicle technology demonstrate a growing capability for high-performance maneuvers. This paper discusses a comprehensive safety verification process and establishes a clear safety goal to enhance testing validation. The study systematically identifies potential hazards and assesses their risks to overall safety and the protection of vulnerable road users. A novel loss evaluation approach is introduced, focusing on the impact of mitigation maneuvers on loss severity. Additionally, the proposed mitigation integrity level can be used to verify the minimum-risk maneuver feature. This paper applies a verification method to evasive maneuvering, contributing to the development of more reliable active safety features in autonomous driving systems.

We study gradient descent (GD) dynamics on logistic regression problems with large, constant step sizes. For linearly-separable data, it is known that GD converges to the minimizer with arbitrarily large step sizes, a property which no longer holds when the problem is not separable. In fact, the behaviour can be much more complex -- a sequence of period-doubling bifurcations begins at the critical step size $2/\lambda$, where $\lambda$ is the largest eigenvalue of the Hessian at the solution. Using a smaller-than-critical step size guarantees convergence if initialized nearby the solution: but does this suffice globally? In one dimension, we show that a step size less than $1/\lambda$ suffices for global convergence. However, for all step sizes between $1/\lambda$ and the critical step size $2/\lambda$, one can construct a dataset such that GD converges to a stable cycle. In higher dimensions, this is actually possible even for step sizes less than $1/\lambda$. Our results show that although local convergence is guaranteed for all step sizes less than the critical step size, global convergence is not, and GD may instead converge to a cycle depending on the initialization.

Backdoor attacks allow an attacker to embed a specific vulnerability in a machine learning algorithm, activated when an attacker-chosen pattern is presented, causing a specific misprediction. The need to identify backdoors in biometric scenarios has led us to propose a novel technique with different trade-offs. In this paper we propose to use model pairs on open-set classification tasks for detecting backdoors. Using a simple linear operation to project embeddings from a probe model's embedding space to a reference model's embedding space, we can compare both embeddings and compute a similarity score. We show that this score, can be an indicator for the presence of a backdoor despite models being of different architectures, having been trained independently and on different datasets. This technique allows for the detection of backdoors on models designed for open-set classification tasks, which is little studied in the literature. Additionally, we show that backdoors can be detected even when both models are backdoored. The source code is made available for reproducibility purposes.

We study the problem of fairly and efficiently allocating indivisible goods among agents with additive valuation functions. Envy-freeness up to one good (EF1) is a well-studied fairness notion for indivisible goods, while Pareto optimality (PO) and its stronger variant, fractional Pareto optimality (fPO), are widely recognized efficiency criteria. Although each property is straightforward to achieve individually, simultaneously ensuring both fairness and efficiency is challenging. Caragiannis et al.~\cite{caragiannis2019unreasonable} established the surprising result that maximizing Nash social welfare yields an allocation that is both EF1 and PO; however, since maximizing Nash social welfare is NP-hard, this approach does not provide an efficient algorithm. To overcome this barrier, Barman, Krishnamurthy, and Vaish~\cite{barman2018finding} designed a pseudo-polynomial time algorithm to compute an EF1 and PO allocation, and showed the existence of EF1 and fPO allocations. Nevertheless, the latter existence proof relies on a non-constructive convergence argument and does not directly yield an efficient algorithm for finding EF1 and fPO allocations. Whether a polynomial-time algorithm exists for finding an EF1 and PO (or fPO) allocation remains an important open problem. In this paper, we propose a polynomial-time algorithm to compute an allocation that achieves both EF1 and fPO under additive valuation functions when the number of agents is fixed. Our primary idea is to avoid processing the entire instance at once; instead, we sequentially add agents to the instance and construct an allocation that satisfies EF1 and fPO at each step.

Understanding the neural basis of behavior is a fundamental goal in neuroscience. Current research in large-scale neuro-behavioral data analysis often relies on decoding models, which quantify behavioral information in neural data but lack details on behavior encoding. This raises an intriguing scientific question: ``how can we enable in-depth exploration of neural representations in behavioral tasks, revealing interpretable neural dynamics associated with behaviors''. However, addressing this issue is challenging due to the varied behavioral encoding across different brain regions and mixed selectivity at the population level. To tackle this limitation, our approach, named ``BeNeDiff'', first identifies a fine-grained and disentangled neural subspace using a behavior-informed latent variable model. It then employs state-of-the-art generative diffusion models to synthesize behavior videos that interpret the neural dynamics of each latent factor. We validate the method on multi-session datasets containing widefield calcium imaging recordings across the dorsal cortex. Through guiding the diffusion model to activate individual latent factors, we verify that the neural dynamics of latent factors in the disentangled neural subspace provide interpretable quantifications of the behaviors of interest. At the same time, the neural subspace in BeNeDiff demonstrates high disentanglement and neural reconstruction quality.

In missions constrained by finite resources, efficient data collection is critical. Informative path planning, driven by automated decision-making, optimizes exploration by reducing the costs associated with accurate characterization of a target in an environment. Previous implementations of active learning did not consider the action cost for regression problems or only considered the action cost for classification problems. This paper analyzes an AL algorithm for Gaussian Process regression while incorporating action cost. The algorithm's performance is compared on various regression problems to include terrain mapping on diverse simulated surfaces along metrics of root mean square error, samples and distance until convergence, and model variance upon convergence. The cost-dependent acquisition policy doesn't organically optimize information gain over distance. Instead, the traditional uncertainty metric with a distance constraint best minimizes root-mean-square error over trajectory distance. This studys impact is to provide insight into incorporating action cost with AL methods to optimize exploration under realistic mission constraints.

Recent artificial intelligence (AI) systems have reached milestones in "grand challenges" ranging from Go to protein-folding. The capability to retrieve medical knowledge, reason over it, and answer medical questions comparably to physicians has long been viewed as one such grand challenge. Large language models (LLMs) have catalyzed significant progress in medical question answering; Med-PaLM was the first model to exceed a "passing" score in US Medical Licensing Examination (USMLE) style questions with a score of 67.2% on the MedQA dataset. However, this and other prior work suggested significant room for improvement, especially when models' answers were compared to clinicians' answers. Here we present Med-PaLM 2, which bridges these gaps by leveraging a combination of base LLM improvements (PaLM 2), medical domain finetuning, and prompting strategies including a novel ensemble refinement approach. Med-PaLM 2 scored up to 86.5% on the MedQA dataset, improving upon Med-PaLM by over 19% and setting a new state-of-the-art. We also observed performance approaching or exceeding state-of-the-art across MedMCQA, PubMedQA, and MMLU clinical topics datasets. We performed detailed human evaluations on long-form questions along multiple axes relevant to clinical applications. In pairwise comparative ranking of 1066 consumer medical questions, physicians preferred Med-PaLM 2 answers to those produced by physicians on eight of nine axes pertaining to clinical utility (p < 0.001). We also observed significant improvements compared to Med-PaLM on every evaluation axis (p < 0.001) on newly introduced datasets of 240 long-form "adversarial" questions to probe LLM limitations. While further studies are necessary to validate the efficacy of these models in real-world settings, these results highlight rapid progress towards physician-level performance in medical question answering.

Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.

Incompleteness is a common problem for existing knowledge graphs (KGs), and the completion of KG which aims to predict links between entities is challenging. Most existing KG completion methods only consider the direct relation between nodes and ignore the relation paths which contain useful information for link prediction. Recently, a few methods take relation paths into consideration but pay less attention to the order of relations in paths which is important for reasoning. In addition, these path-based models always ignore nonlinear contributions of path features for link prediction. To solve these problems, we propose a novel KG completion method named OPTransE. Instead of embedding both entities of a relation into the same latent space as in previous methods, we project the head entity and the tail entity of each relation into different spaces to guarantee the order of relations in the path. Meanwhile, we adopt a pooling strategy to extract nonlinear and complex features of different paths to further improve the performance of link prediction. Experimental results on two benchmark datasets show that the proposed model OPTransE performs better than state-of-the-art methods.

Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.

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