An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool is capable of not only returning an highly accurate solution to the IOD problem, but also estimating a range of validity for the aforementioned solution in which the true orbit state should lie. Automatic domain splitting is then used on top of the IOD routines to ensure the local truncation error introduced by a polynomial representation of the state estimate remains below a predefined threshold to meet the specified requirements in accuracy. The algorithm is adapted to three types of ground based sensors, namely range radars, Doppler-only radars and optical telescopes by taking into account their different constraints in terms of available measurements and sensor noise. Its improved performance with respect to a Keplerian based IOD solution is finally demonstrated with large scale numerical simulations over a subset of tracked objects in low Earth orbit.
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Capturing and annotating Sign language datasets is a time consuming and costly process. Current datasets are orders of magnitude too small to successfully train unconstrained \acf{slt} models. As a result, research has turned to TV broadcast content as a source of large-scale training data, consisting of both the sign language interpreter and the associated audio subtitle. However, lack of sign language annotation limits the usability of this data and has led to the development of automatic annotation techniques such as sign spotting. These spottings are aligned to the video rather than the subtitle, which often results in a misalignment between the subtitle and spotted signs. In this paper we propose a method for aligning spottings with their corresponding subtitles using large spoken language models. Using a single modality means our method is computationally inexpensive and can be utilized in conjunction with existing alignment techniques. We quantitatively demonstrate the effectiveness of our method on the \acf{mdgs} and \acf{bobsl} datasets, recovering up to a 33.22 BLEU-1 score in word alignment.
The explosive growth of computation and energy cost of artificial intelligence has spurred strong interests in new computing modalities as potential alternatives to conventional electronic processors. Photonic processors that execute operations using photons instead of electrons, have promised to enable optical neural networks with ultra-low latency and power consumption. However, existing optical neural networks, limited by the underlying network designs, have achieved image recognition accuracy much lower than state-of-the-art electronic neural networks. In this work, we close this gap by introducing a large-kernel spatially-varying convolutional neural network learned via low-dimensional reparameterization techniques. We experimentally instantiate the network with a flat meta-optical system that encompasses an array of nanophotonic structures designed to induce angle-dependent responses. Combined with an extremely lightweight electronic backend with approximately 2K parameters we demonstrate a nanophotonic neural network reaches 73.80\% blind test classification accuracy on CIFAR-10 dataset, and, as such, the first time, an optical neural network outperforms the first modern digital neural network -- AlexNet (72.64\%) with 57M parameters, bringing optical neural network into modern deep learning era.
Homomorphically full graphs are those for which every homomorphic image is isomorphic to a subgraph. We extend the definition of homomorphically full to oriented graphs in two different ways. For the first of these, we show that homomorphically full oriented graphs arise as quasi-transitive orientations of homomorphically full graphs. This in turn yields an efficient recognition and construction algorithms for these homomorphically full oriented graphs. For the second one, we show that the related recognition problem is GI-hard, and that the problem of deciding if a graph admits a homomorphically full orientation is NP-complete. In doing so we show the problem of deciding if two given oriented cliques are isomorphic is GI-complete.
The problem of robust hypothesis testing is studied, where under the null and the alternative hypotheses, the data-generating distributions are assumed to be in some uncertainty sets, and the goal is to design a test that performs well under the worst-case distributions over the uncertainty sets. In this paper, uncertainty sets are constructed in a data-driven manner using kernel method, i.e., they are centered around empirical distributions of training samples from the null and alternative hypotheses, respectively; and are constrained via the distance between kernel mean embeddings of distributions in the reproducing kernel Hilbert space, i.e., maximum mean discrepancy (MMD). The Bayesian setting and the Neyman-Pearson setting are investigated. For the Bayesian setting where the goal is to minimize the worst-case error probability, an optimal test is firstly obtained when the alphabet is finite. When the alphabet is infinite, a tractable approximation is proposed to quantify the worst-case average error probability, and a kernel smoothing method is further applied to design test that generalizes to unseen samples. A direct robust kernel test is also proposed and proved to be exponentially consistent. For the Neyman-Pearson setting, where the goal is to minimize the worst-case probability of miss detection subject to a constraint on the worst-case probability of false alarm, an efficient robust kernel test is proposed and is shown to be asymptotically optimal. Numerical results are provided to demonstrate the performance of the proposed robust tests.
We introduce Branched Latent Neural Operators (BLNOs) to learn input-output maps encoding complex physical processes. A BLNO is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNOs leverage interpretable latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent generalization properties with small training datasets and short training times on a single processor. Indeed, their generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections, in place of a fully-connected structure, significantly reduce the number of tunable parameters. We show the capabilities of BLNOs in a challenging test case involving biophysically detailed electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a purkinje network for fast conduction and a heart-torso geometry. Specifically, we trained BLNOs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale, organ-level and electrical dyssynchrony. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNO, trained in less than 3 hours on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The mean square error is on the order of $10^{-4}$ on an independent test dataset comprised of 50 additional electrophysiology simulations. This paper provides a novel computational tool to build reliable and efficient reduced-order models for digital twinning in engineering applications.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
The information bottleneck (IB) method is a technique for extracting information that is relevant for predicting the target random variable from the source random variable, which is typically implemented by optimizing the IB Lagrangian that balances the compression and prediction terms. However, the IB Lagrangian is hard to optimize, and multiple trials for tuning values of Lagrangian multiplier are required. Moreover, we show that the prediction performance strictly decreases as the compression gets stronger during optimizing the IB Lagrangian. In this paper, we implement the IB method from the perspective of supervised disentangling. Specifically, we introduce Disentangled Information Bottleneck (DisenIB) that is consistent on compressing source maximally without target prediction performance loss (maximum compression). Theoretical and experimental results demonstrate that our method is consistent on maximum compression, and performs well in terms of generalization, robustness to adversarial attack, out-of-distribution detection, and supervised disentangling.
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected by a set of agents that communicate over a sparse network topology. After formulating the centralized GCN training problem, we first show how to make inference in a distributed scenario where the underlying data graph is split among different agents. Then, we propose a distributed gradient descent procedure to solve the GCN training problem. The resulting model distributes computation along three lines: during inference, during back-propagation, and during optimization. Convergence to stationary solutions of the GCN training problem is also established under mild conditions. Finally, we propose an optimization criterion to design the communication topology between agents in order to match with the graph describing data relationships. A wide set of numerical results validate our proposal. To the best of our knowledge, this is the first work combining graph convolutional neural networks with distributed optimization.
Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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