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In nonsmooth, nonconvex stochastic optimization, understanding the uniform convergence of subdifferential mappings is crucial for analyzing stationary points of sample average approximations of risk as they approach the population risk. Yet, characterizing this convergence remains a fundamental challenge. This work introduces a novel perspective by connecting the uniform convergence of subdifferential mappings to that of subgradient mappings as empirical risk converges to the population risk. We prove that, for stochastic weakly-convex objectives, and within any open set, a uniform bound on the convergence of subgradients -- chosen arbitrarily from the corresponding subdifferential sets -- translates to a uniform bound on the convergence of the subdifferential sets itself, measured by the Hausdorff metric. Using this technique, we derive uniform convergence rates for subdifferential sets of stochastic convex-composite objectives. Our results do not rely on key distributional assumptions in the literature, which require the population and finite sample subdifferentials to be continuous in the Hausdorff metric, yet still provide tight convergence rates. These guarantees lead to new insights into the nonsmooth landscapes of such objectives within finite samples.

Citation practices are crucial in shaping the structure of scientific knowledge, yet they are often influenced by contemporary norms and biases. The emergence of Large Language Models (LLMs) like GPT-4 introduces a new dynamic to these practices. Interestingly, the characteristics and potential biases of references recommended by LLMs that entirely rely on their parametric knowledge, and not on search or retrieval-augmented generation, remain unexplored. Here, we analyze these characteristics in an experiment using a dataset of 166 papers from AAAI, NeurIPS, ICML, and ICLR, published after GPT-4's knowledge cut-off date, encompassing 3,066 references in total. In our experiment, GPT-4 was tasked with suggesting scholarly references for the anonymized in-text citations within these papers. Our findings reveal a remarkable similarity between human and LLM citation patterns, but with a more pronounced high citation bias in GPT-4, which persists even after controlling for publication year, title length, number of authors, and venue. Additionally, we observe a large consistency between the characteristics of GPT-4's existing and non-existent generated references, indicating the model's internalization of citation patterns. By analyzing citation graphs, we show that the references recommended by GPT-4 are embedded in the relevant citation context, suggesting an even deeper conceptual internalization of the citation networks. While LLMs can aid in citation generation, they may also amplify existing biases and introduce new ones, potentially skewing scientific knowledge dissemination. Our results underscore the need for identifying the model's biases and for developing balanced methods to interact with LLMs in general.

Semi-supervised anomaly detection, which aims to improve the performance of the anomaly detector by using a small amount of anomaly data in addition to unlabeled data, has attracted attention. Existing semi-supervised approaches assume that unlabeled data are mostly normal. They train the anomaly detector to minimize the anomaly scores for the unlabeled data, and to maximize those for the anomaly data. However, in practice, the unlabeled data are often contaminated with anomalies. This weakens the effect of maximizing the anomaly scores for anomalies, and prevents us from improving the detection performance. To solve this problem, we propose the positive-unlabeled autoencoder, which is based on positive-unlabeled learning and the anomaly detector such as the autoencoder. With our approach, we can approximate the anomaly scores for normal data using the unlabeled and anomaly data. Therefore, without the labeled normal data, we can train the anomaly detector to minimize the anomaly scores for normal data, and to maximize those for the anomaly data. In addition, our approach is applicable to various anomaly detectors such as the DeepSVDD. Experiments on various datasets show that our approach achieves better detection performance than existing approaches.

Patient datasets contain confidential information which is protected by laws and regulations such as HIPAA and GDPR. Ensuring comprehensive patient information necessitates privacy-preserving entity resolution (PPER), which identifies identical patient entities across multiple databases from different healthcare organizations while maintaining data privacy. Existing methods often lack cryptographic security or are computationally impractical for real-world datasets. We introduce a PPER pipeline based on AMPPERE, a secure abstract computation model utilizing cryptographic tools like homomorphic encryption. Our tailored approach incorporates extensive parallelization techniques and optimal parameters specifically for patient datasets. Experimental results demonstrate the proposed method's effectiveness in terms of accuracy and efficiency compared to various baselines.

Preferences are a pivotal component in practical reasoning, especially in tasks that involve decision-making over different options or courses of action that could be pursued. In this work, we focus on repairing and querying inconsistent knowledge bases in the form of graph databases, which involves finding a way to solve conflicts in the knowledge base and considering answers that are entailed from every possible repair, respectively. Without a priori domain knowledge, all possible repairs are equally preferred. Though that may be adequate for some settings, it seems reasonable to establish and exploit some form of preference order among the potential repairs. We study the problem of computing prioritized repairs over graph databases with data values, using a notion of consistency based on GXPath expressions as integrity constraints. We present several preference criteria based on the standard subset repair semantics, incorporating weights, multisets, and set-based priority levels. We show that it is possible to maintain the same computational complexity as in the case where no preference criterion is available for exploitation. Finally, we explore the complexity of consistent query answering in this setting and obtain tight lower and upper bounds for all the preference criteria introduced.

Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant challenges. In particular, extending support vector machines to hyperbolic spaces is in general a constrained non-convex optimization problem. Previous and popular attempts to solve hyperbolic SVMs, primarily using projected gradient descent, are generally sensitive to hyperparameters and initializations, often leading to suboptimal solutions. In this work, by first rewriting the problem into a polynomial optimization, we apply semidefinite relaxation and sparse moment-sum-of-squares relaxation to effectively approximate the optima. From extensive empirical experiments, these methods are shown to perform better than the projected gradient descent approach.

Quantum computing holds the potential to solve problems that are practically unsolvable by classical computers due to its ability to significantly reduce time complexity. We aim to harness this potential to enhance ray casting, a pivotal technique in computer graphics for simplifying the rendering of 3D objects. To perform ray casting in a quantum computer, we need to encode the defining parameters of primitives into qubits. However, during the current noisy intermediate-scale quantum (NISQ) era, challenges arise from the limited number of qubits and the impact of noise when executing multiple gates. Through logic optimization, we reduced the depth of quantum circuits as well as the number of gates and qubits. As a result, the event count of correct measurements from an IBM quantum computer significantly exceeded that of incorrect measurements.

A white noise signal can access any possible configuration of values, though statistically over many samples tends to a uniform spectral distribution, and is highly unlikely to produce intelligible sound. But how unlikely? The probability that white noise generates a music-like signal over different durations is analyzed, based on some necessary features observed in real music audio signals such as mostly proximate movement and zero crossing rate. Given the mathematical results, the rarity of music as a signal is considered overall. The applicability of this study is not just to show that music has a precious rarity value, but that examination of the size of music relative to the overall size of audio signal space provides information to inform new generations of algorithmic music system (which are now often founded on audio signal generation directly, and may relate to white noise via such machine learning processes as diffusion). Estimated upper bounds on the rarity of music to the size of various physical and musical spaces are compared, to better understand the magnitude of the results (pun intended). Underlying the research are the questions `how much music is still out there?' and `how much music could a machine learning process actually reach?'.

Graphs are important data representations for describing objects and their relationships, which appear in a wide diversity of real-world scenarios. As one of a critical problem in this area, graph generation considers learning the distributions of given graphs and generating more novel graphs. Owing to their wide range of applications, generative models for graphs, which have a rich history, however, are traditionally hand-crafted and only capable of modeling a few statistical properties of graphs. Recent advances in deep generative models for graph generation is an important step towards improving the fidelity of generated graphs and paves the way for new kinds of applications. This article provides an extensive overview of the literature in the field of deep generative models for graph generation. Firstly, the formal definition of deep generative models for the graph generation and the preliminary knowledge are provided. Secondly, taxonomies of deep generative models for both unconditional and conditional graph generation are proposed respectively; the existing works of each are compared and analyzed. After that, an overview of the evaluation metrics in this specific domain is provided. Finally, the applications that deep graph generation enables are summarized and five promising future research directions are highlighted.

Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social networks and recommendation systems. Despite the plethora of different models for deep learning on graphs, few approaches have been proposed thus far for dealing with graphs that present some sort of dynamic nature (e.g. evolving features or connectivity over time). In this paper, we present Temporal Graph Networks (TGNs), a generic, efficient framework for deep learning on dynamic graphs represented as sequences of timed events. Thanks to a novel combination of memory modules and graph-based operators, TGNs are able to significantly outperform previous approaches being at the same time more computationally efficient. We furthermore show that several previous models for learning on dynamic graphs can be cast as specific instances of our framework. We perform a detailed ablation study of different components of our framework and devise the best configuration that achieves state-of-the-art performance on several transductive and inductive prediction tasks for dynamic graphs.