Autonomous underwater vehicles (AUVs) are regularly used for deep ocean applications. Commonly, the autonomous navigation task is carried out by a fusion between two sensors: the inertial navigation system and the Doppler velocity log (DVL). The DVL operates by transmitting four acoustic beams to the sea floor, and once reflected back, the AUV velocity vector can be estimated. However, in real-life scenarios, such as an uneven seabed, sea creatures blocking the DVL's view and, roll/pitch maneuvers, the acoustic beams' reflection is resulting in a scenario known as DVL outage. Consequently, a velocity update is not available to bind the inertial solution drift. To cope with such situations, in this paper, we leverage our BeamsNet framework and propose a Set-Transformer-based BeamsNet (ST-BeamsNet) that utilizes inertial data readings and previous DVL velocity measurements to regress the current AUV velocity in case of a complete DVL outage. The proposed approach was evaluated using data from experiments held in the Mediterranean Sea with the Snapir AUV and was compared to a moving average (MA) estimator. Our ST-BeamsNet estimated the AUV velocity vector with an 8.547% speed error, which is 26% better than the MA approach.

Graph neural networks (GNNs) are widely used for modeling complex interactions between entities represented as vertices of a graph. Despite recent efforts to theoretically analyze the expressive power of GNNs, a formal characterization of their ability to model interactions is lacking. The current paper aims to address this gap. Formalizing strength of interactions through an established measure known as separation rank, we quantify the ability of certain GNNs to model interaction between a given subset of vertices and its complement, i.e. between sides of a given partition of input vertices. Our results reveal that the ability to model interaction is primarily determined by the partition's walk index -- a graph-theoretical characteristic that we define by the number of walks originating from the boundary of the partition. Experiments with common GNN architectures corroborate this finding. As a practical application of our theory, we design an edge sparsification algorithm named Walk Index Sparsification (WIS), which preserves the ability of a GNN to model interactions when input edges are removed. WIS is simple, computationally efficient, and markedly outperforms alternative methods in terms of induced prediction accuracy. More broadly, it showcases the potential of improving GNNs by theoretically analyzing the interactions they can model.

自动水下车辆（AUV）执行各种应用，例如海底映射和水下结构健康监测。通常，由多普勒速度日志（DVL）提供的惯性导航系统用于提供车辆的导航解决方案。在这种融合中，DVL提供了AUV的速度向量，从而确定导航解决方案的准确性并有助于估计导航状态。本文提出了BeamsNet，这是一个端到端的深度学习框架，用于回归估计的DVL速度向量，以提高速度向量估算的准确性，并可以替代基于模型的方法。提出了两个版本的BeamsNet，其输入与网络不同。第一个使用当前的DVL光束测量和惯性传感器数据，而另一个仅利用DVL数据，对回归过程进行了当前和过去的DVL测量值。进行了模拟和海上实验，以验证相对于基于模型的方法的拟议学习方法。使用地中海的Snapir AUV进行了海洋实验，收集了大约四个小时的DVL和惯性传感器数据。我们的结果表明，提出的方法在估计DVL速度矢量方面取得了超过60％的改善。

为了在深度学习中解释隐性正则化时，给予了矩阵和张量因子化的突出重点，这与简化的神经网络相对应。结果表明，这些模型分别表现出对低基质和张量排名的隐式趋势。当前的论文理论上绘制了更接近实际的深度学习，从理论上分析了分层张分解中的隐式正则化，该模型等同于某些深卷积神经网络。通过动态系统镜头，我们克服了与层次结构相关的挑战，并建立了对低层次张量级别的隐性正则化。这转化为相关卷积网络对区域的隐性正则化。受我们的理论的启发，我们设计了明确的正则化，阻碍了区域性，并证明了其在需要建筑变化的传统智慧的情况下，可以改善现代卷积网络在非本地任务上的性能。我们的工作突出了通过对其隐式正则化的理论分析来增强神经网络的潜力。

在深度学习中的优化分析是连续的，专注于（变体）梯度流动，或离散，直接处理（变体）梯度下降。梯度流程可符合理论分析，但是风格化并忽略计算效率。它代表梯度下降的程度是深度学习理论的一个开放问题。目前的论文研究了这个问题。将梯度下降视为梯度流量初始值问题的近似数值问题，发现近似程度取决于梯度流动轨迹周围的曲率。然后，我们表明，在具有均匀激活的深度神经网络中，梯度流动轨迹享有有利的曲率，表明它们通过梯度下降近似地近似。该发现允许我们将深度线性神经网络的梯度流分析转换为保证梯度下降，其几乎肯定会在随机初始化下有效地收敛到全局最小值。实验表明，在简单的深度神经网络中，具有传统步长的梯度下降确实接近梯度流。我们假设梯度流动理论将解开深入学习背后的奥秘。

Efforts to understand the generalization mystery in deep learning have led to the belief that gradient-based optimization induces a form of implicit regularization, a bias towards models of low "complexity." We study the implicit regularization of gradient descent over deep linear neural networks for matrix completion and sensing, a model referred to as deep matrix factorization. Our first finding, supported by theory and experiments, is that adding depth to a matrix factorization enhances an implicit tendency towards low-rank solutions, oftentimes leading to more accurate recovery. Secondly, we present theoretical and empirical arguments questioning a nascent view by which implicit regularization in matrix factorization can be captured using simple mathematical norms. Our results point to the possibility that the language of standard regularizers may not be rich enough to fully encompass the implicit regularization brought forth by gradient-based optimization.

Conventional wisdom in deep learning states that increasing depth improves expressiveness but complicates optimization. This paper suggests that, sometimes, increasing depth can speed up optimization. The effect of depth on optimization is decoupled from expressiveness by focusing on settings where additional layers amount to overparameterization -linear neural networks, a wellstudied model. Theoretical analysis, as well as experiments, show that here depth acts as a preconditioner which may accelerate convergence. Even on simple convex problems such as linear regression with p loss, p > 2, gradient descent can benefit from transitioning to a non-convex overparameterized objective, more than it would from some common acceleration schemes. We also prove that it is mathematically impossible to obtain the acceleration effect of overparametrization via gradients of any regularizer.

Classical methods for acoustic scene mapping require the estimation of time difference of arrival (TDOA) between microphones. Unfortunately, TDOA estimation is very sensitive to reverberation and additive noise. We introduce an unsupervised data-driven approach that exploits the natural structure of the data. Our method builds upon local conformal autoencoders (LOCA) - an offline deep learning scheme for learning standardized data coordinates from measurements. Our experimental setup includes a microphone array that measures the transmitted sound source at multiple locations across the acoustic enclosure. We demonstrate that LOCA learns a representation that is isometric to the spatial locations of the microphones. The performance of our method is evaluated using a series of realistic simulations and compared with other dimensionality-reduction schemes. We further assess the influence of reverberation on the results of LOCA and show that it demonstrates considerable robustness.

Software Defect Prediction aims at predicting which software modules are the most probable to contain defects. The idea behind this approach is to save time during the development process by helping find bugs early. Defect Prediction models are based on historical data. Specifically, one can use data collected from past software distributions, or Versions, of the same target application under analysis. Defect Prediction based on past versions is called Cross Version Defect Prediction (CVDP). Traditionally, Static Code Metrics are used to predict defects. In this work, we use the Class Dependency Network (CDN) as another predictor for defects, combined with static code metrics. CDN data contains structural information about the target application being analyzed. Usually, CDN data is analyzed using different handcrafted network measures, like Social Network metrics. Our approach uses network embedding techniques to leverage CDN information without having to build the metrics manually. In order to use the embeddings between versions, we incorporate different embedding alignment techniques. To evaluate our approach, we performed experiments on 24 software release pairs and compared it against several benchmark methods. In these experiments, we analyzed the performance of two different graph embedding techniques, three anchor selection approaches, and two alignment techniques. We also built a meta-model based on two different embeddings and achieved a statistically significant improvement in AUC of 4.7% (p < 0.002) over the baseline method.

We consider a long-term average profit maximizing admission control problem in an M/M/1 queuing system with a known arrival rate but an unknown service rate. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue-length of the system. \cite[Econometrica]{Naor} showed that if all the parameters of the model are known, then it is optimal to use a static threshold policy - admit if the queue-length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full information model of \cite{Naor}. We show that the algorithm achieves an $O(1)$ regret when all optimal thresholds with full information are non-zero, and achieves an $O(\ln^{3+\epsilon}(N))$ regret in the case that an optimal threshold with full information is $0$ (i.e., an optimal policy is to reject all arrivals), where $N$ is the number of arrivals and $\epsilon>0$.