The structure of linear dependence relations between coded symbols of a linear code, irrespective of specific coefficients involved, is referred to as the {\em topology} of the code. The specification of coefficients is referred to as an {\em instantiation} of the topology. In this paper, we propose a new block circulant topology $T_{[\mu,\lambda,\omega]}(\rho)$ parameterized by integers $\rho \geq 2$, $\omega \geq 1$, $\lambda \geq 2$, and $\mu$ a multiple of $\lambda$. In this topology, the code has $\mu$ local codes with $\rho$ parity-check (p-c) constraints and a total of $\mu\rho$ p-c equations fully define the code. Next, we construct a class of block circulant (BC) codes ${\cal C}_{\text{BC}}[\mu,\lambda,\omega,\rho]$ with blocklength $n=\mu(\rho+\omega)$, dimension $k=\mu\omega$ that instantiate $T_{[\mu,\lambda,\omega]}(\rho)$. Every local code of ${\cal C}_{\text{BC}}[\mu,\lambda,\omega,\rho]$ is a $[\rho+\lambda\omega,\lambda\omega,\rho+1]$ generalized Reed-Solomon (RS) code. The overlap between supports of local codes helps to enhance the minimum distance $\rho+1$ to $2\rho+1$, without compromising much on the rate. We provide an efficient, parallelizable decoding algorithm to correct $2\rho$ erasures when $\lambda=2$. Finally, we illustrate that the BC codes serve as a viable alternative to 2D RS codes in protocols designed to tackle blockchain networks' data availability (DA) problem. In these protocols, every node in a network of light nodes randomly queries symbols from a codeword stored in full nodes and verifies them using a cryptographic commitment scheme. For the same performance in tackling the DA problem, the BC code requires querying a smaller number of symbols than a comparable 2D RS code for a fixed high rate. Furthermore, the number of local codes in the BC code is typically smaller, yielding a reduction in the complexity of realizing the commitment scheme.
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In pool-based active learning, the learner is given an unlabeled data set and aims to efficiently learn the unknown hypothesis by querying the labels of the data points. This can be formulated as the classical Optimal Decision Tree (ODT) problem: Given a set of tests, a set of hypotheses, and an outcome for each pair of test and hypothesis, our objective is to find a low-cost testing procedure (i.e., decision tree) that identifies the true hypothesis. This optimization problem has been extensively studied under the assumption that each test generates a deterministic outcome. However, in numerous applications, for example, clinical trials, the outcomes may be uncertain, which renders the ideas from the deterministic setting invalid. In this work, we study a fundamental variant of the ODT problem in which some test outcomes are noisy, even in the more general case where the noise is persistent, i.e., repeating a test gives the same noisy output. Our approximation algorithms provide guarantees that are nearly best possible and hold for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades continuously with this number. We numerically evaluated our algorithms for identifying toxic chemicals and learning linear classifiers, and observed that our algorithms have costs very close to the information-theoretic minimum.
Representation-based retrieval models, so-called biencoders, estimate the relevance of a document to a query by calculating the similarity of their respective embeddings. Current state-of-the-art biencoders are trained using an expensive training regime involving knowledge distillation from a teacher model and batch-sampling. Instead of relying on a teacher model, we contribute a novel parameter-free loss function for self-supervision that exploits the pre-trained language modeling capabilities of the encoder model as a training signal, eliminating the need for batch sampling by performing implicit hard negative mining. We investigate the capabilities of our proposed approach through extensive ablation studies, demonstrating that self-distillation can match the effectiveness of teacher distillation using only 13.5% of the data, while offering a speedup in training time between 3x and 15x compared to parametrized losses. Code and data is made openly available.
We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and other spectral characteristics. Our motivation comes from the study of almost-periodic operators, particularly those that arise as models of quasicrystals. Such operators are known for intricate hierarchical patterns and often display delicate spectral properties, such as Cantor spectra, which are significant in studying quantum mechanical systems and materials science. We propose a series of algorithms that compute these properties under different assumptions and explore their theoretical implications through the Solvability Complexity Index (SCI) hierarchy. This approach provides a rigorous framework for understanding the computational feasibility of these problems, proving algorithmic optimality, and enhancing the precision of spectral analysis in practical settings. For example, we show that our methods are optimal by proving certain lower bounds (impossibility results) for the class of limit-periodic Schr\"odinger operators. We demonstrate our methods through state-of-the-art computations for aperiodic systems in one and two dimensions, effectively capturing these complex spectral characteristics. The results contribute significantly to connecting theoretical and computational aspects of spectral theory, offering insights that bridge the gap between abstract mathematical concepts and their practical applications in physical sciences and engineering. Based on our work, we conclude with conjectures and open problems regarding the spectral properties of specific models.
The shuffle model of Differential Privacy (DP) is an enhanced privacy protocol which introduces an intermediate trusted server between local users and a central data curator. It significantly amplifies the central DP guarantee by anonymizing and shuffling the local randomized data. Yet, deriving a tight privacy bound is challenging due to its complicated randomization protocol. While most existing work are focused on unified local privacy settings, this work focuses on deriving the central privacy bound for a more practical setting where personalized local privacy is required by each user. To bound the privacy after shuffling, we first need to capture the probability of each user generating clones of the neighboring data points. Second, we need to quantify the indistinguishability between two distributions of the number of clones on neighboring datasets. Existing works either inaccurately capture the probability, or underestimate the indistinguishability between neighboring datasets. Motivated by this, we develop a more precise analysis, which yields a general and tighter bound for arbitrary DP mechanisms. Firstly, we derive the clone-generating probability by hypothesis testing %from a randomizer-specific perspective, which leads to a more accurate characterization of the probability. Secondly, we analyze the indistinguishability in the context of $f$-DP, where the convexity of the distributions is leveraged to achieve a tighter privacy bound. Theoretical and numerical results demonstrate that our bound remarkably outperforms the existing results in the literature.
Developing an effective evaluation metric is crucial for accurately and swiftly measuring LiDAR perception performance. One major issue is the lack of metrics that can simultaneously generate fast and accurate evaluations based on either object detection or point cloud data. In this study, we propose a novel LiDAR perception entropy metric based on the probability of vehicle grid occupancy. This metric reflects the influence of point cloud distribution on vehicle detection performance. Based on this, we also introduce a LiDAR deployment optimization model, which is solved using a differential evolution-based particle swarm optimization algorithm. A comparative experiment demonstrated that the proposed PE-VGOP offers a correlation of more than 0.98 with vehicle detection ground truth in evaluating LiDAR perception performance. Furthermore, compared to the base deployment, field experiments indicate that the proposed optimization model can significantly enhance the perception capabilities of various types of LiDARs, including RS-16, RS-32, and RS-80. Notably, it achieves a 25% increase in detection Recall for the RS-32 LiDAR.
Writing, as an omnipresent form of human communication, permeates nearly every aspect of contemporary life. Consequently, inaccuracies or errors in written communication can lead to profound consequences, ranging from financial losses to potentially life-threatening situations. Spelling mistakes, among the most prevalent writing errors, are frequently encountered due to various factors. This research aims to identify and rectify diverse spelling errors in text using neural networks, specifically leveraging the Bidirectional Encoder Representations from Transformers (BERT) masked language model. To achieve this goal, we compiled a comprehensive dataset encompassing both non-real-word and real-word errors after categorizing different types of spelling mistakes. Subsequently, multiple pre-trained BERT models were employed. To ensure optimal performance in correcting misspelling errors, we propose a combined approach utilizing the BERT masked language model and Levenshtein distance. The results from our evaluation data demonstrate that the system presented herein exhibits remarkable capabilities in identifying and rectifying spelling mistakes, often surpassing existing systems tailored for the Persian language.
Analysis of 3D segmentation models, especially in the context of medical imaging, is often limited to segmentation performance metrics that overlook the crucial aspect of explainability and bias. Currently, effectively explaining these models with saliency maps is challenging due to the high dimensions of input images multiplied by the ever-growing number of segmented class labels. To this end, we introduce Agg^2Exp, a methodology for aggregating fine-grained voxel attributions of the segmentation model's predictions. Unlike classical explanation methods that primarily focus on the local feature attribution, Agg^2Exp enables a more comprehensive global view on the importance of predicted segments in 3D images. Our benchmarking experiments show that gradient-based voxel attributions are more faithful to the model's predictions than perturbation-based explanations. As a concrete use-case, we apply Agg^2Exp to discover knowledge acquired by the Swin UNEt TRansformer model trained on the TotalSegmentator v2 dataset for segmenting anatomical structures in computed tomography medical images. Agg^2Exp facilitates the explanatory analysis of large segmentation models beyond their predictive performance.
Given the diverse array of physical systems available for quantum computing and the absence of a well-defined quantum internet protocol stack, the design and optimisation of quantum networking protocols remain largely unexplored. To address this, we introduce an approach that facilitates the establishment of paths capable of delivering end-to-end fidelity above a specified threshold, without requiring detailed knowledge of the quantum network properties, which we call the 'grey box approach'. In this study, we define algorithms that are specific instances of this approach and evaluate them in comparison to Dijkstra shortest path algorithm and a fully knowledge-aware algorithm through simulations. Our results demonstrate that one of the grey box algorithms consistently outperforms the other methods in delivering paths above the fidelity threshold, across various network topologies and the number of source-destination pairs involved, while maintaining significant levels of fairness among the users and being robust to inaccurate estimations of the expected end-to-end fidelity.
A community reveals the features and connections of its members that are different from those in other communities in a network. Detecting communities is of great significance in network analysis. Despite the classical spectral clustering and statistical inference methods, we notice a significant development of deep learning techniques for community detection in recent years with their advantages in handling high dimensional network data. Hence, a comprehensive overview of community detection's latest progress through deep learning is timely to both academics and practitioners. This survey devises and proposes a new taxonomy covering different categories of the state-of-the-art methods, including deep learning-based models upon deep neural networks, deep nonnegative matrix factorization and deep sparse filtering. The main category, i.e., deep neural networks, is further divided into convolutional networks, graph attention networks, generative adversarial networks and autoencoders. The survey also summarizes the popular benchmark data sets, model evaluation metrics, and open-source implementations to address experimentation settings. We then discuss the practical applications of community detection in various domains and point to implementation scenarios. Finally, we outline future directions by suggesting challenging topics in this fast-growing deep learning field.
Knowledge graphs capture interlinked information between entities and they represent an attractive source of structured information that can be harnessed for recommender systems. However, existing recommender engines use knowledge graphs by manually designing features, do not allow for end-to-end training, or provide poor scalability. Here we propose Knowledge Graph Convolutional Networks (KGCN), an end-to-end trainable framework that harnesses item relationships captured by the knowledge graph to provide better recommendations. Conceptually, KGCN computes user-specific item embeddings by first applying a trainable function that identifies important knowledge graph relations for a given user and then transforming the knowledge graph into a user-specific weighted graph. Then, KGCN applies a graph convolutional neural network that computes an embedding of an item node by propagating and aggregating knowledge graph neighborhood information. Moreover, to provide better inductive bias KGCN uses label smoothness (LS), which provides regularization over edge weights and we prove that it is equivalent to label propagation scheme on a graph. Finally, We unify KGCN and LS regularization, and present a scalable minibatch implementation for KGCN-LS model. Experiments show that KGCN-LS outperforms strong baselines in four datasets. KGCN-LS also achieves great performance in sparse scenarios and is highly scalable with respect to the knowledge graph size.
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