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A fundamental question in computational geometry is for a dynamic collection of geometric objects in Euclidean space, whether it is possible to maintain a maximum independent set in polylogarithmic update time. Already, for a set of intervals, it is known that no dynamic algorithm can maintain an exact maximum independent set with sublinear update time. Therefore, the typical objective is to explore the trade-off between update time and solution size. Substantial efforts have been made in recent years to understand this question for various families of geometric objects, such as intervals, hypercubes, hyperrectangles, and fat objects. We present the first fully dynamic approximation algorithm for disks of arbitrary radii in the plane that maintains a constant-factor approximate maximum independent set in polylogarithmic update time. First, we show that for a fully dynamic set of $n$ unit disks in the plane, a $12$-approximate maximum independent set can be maintained with worst-case update time $O(\log^2 n)$, and optimal output-sensitive reporting. Moreover, this result generalizes to fat objects of comparable sizes in any fixed dimension $d$, where the approximation ratio depends on the dimension and the fatness parameter. Our main result is that for a fully dynamic set of disks of arbitrary radii in the plane, an $O(1)$-approximate maximum independent set can be maintained in polylogarithmic expected amortized update time.

With the explosive growth of textual information, summarization systems have become increasingly important. This work aims to concisely indicate the current state of the art in abstractive text summarization. As part of this, we outline the current paradigm shifts towards pre-trained encoder-decoder models and large autoregressive language models. Additionally, we delve further into the challenges of evaluating summarization systems and the potential of instruction-tuned models for zero-shot summarization. Finally, we provide a brief overview of how summarization systems are currently being integrated into commercial applications.

With the rapid development of cloud computing and big data technologies, storage systems have become a fundamental building block of datacenters, incorporating hardware innovations such as flash solid state drives and non-volatile memories, as well as software infrastructures such as RAID and distributed file systems. Despite the growing popularity and interests in storage, designing and implementing reliable storage systems remains challenging, due to their performance instability and prevailing hardware failures. Proactive prediction greatly strengthens the reliability of storage systems. There are two dimensions of prediction: performance and failure. Ideally, through detecting in advance the slow IO requests, and predicting device failures before they really happen, we can build storage systems with especially low tail latency and high availability. While its importance is well recognized, such proactive prediction in storage systems, on the other hand, is particularly difficult. To move towards predictability of storage systems, various mechanisms and field studies have been proposed in the past few years. In this report, we present a survey of these mechanisms and field studies, focusing on machine learning based black-box approaches. Based on three representative research works, we discuss where and how machine learning should be applied in this field. The strengths and limitations of each research work are also evaluated in detail.

Answering temporal CQs over temporalized Description Logic knowledge bases (TKB) is a main technique to realize ontology-based situation recognition. In case the collected data in such a knowledge base is inaccurate, important query answers can be missed. In this paper we introduce the TKB Alignment problem, which computes a variant of the TKB that minimally changes the TKB, but entails the given temporal CQ and is in that sense (cost-)optimal. We investigate this problem for ALC TKBs and conjunctive queries with LTL operators and devise a solution technique to compute (cost-optimal) alignments of TKBs that extends techniques for the alignment problem for propositional LTL over finite traces.

Large Language Models (LLMs) have demonstrated remarkable abilities across numerous disciplines, primarily assessed through tasks in language generation, knowledge utilization, and complex reasoning. However, their alignment with human emotions and values, which is critical for real-world applications, has not been systematically evaluated. Here, we assessed LLMs' Emotional Intelligence (EI), encompassing emotion recognition, interpretation, and understanding, which is necessary for effective communication and social interactions. Specifically, we first developed a novel psychometric assessment focusing on Emotion Understanding (EU), a core component of EI, suitable for both humans and LLMs. This test requires evaluating complex emotions (e.g., surprised, joyful, puzzled, proud) in realistic scenarios (e.g., despite feeling underperformed, John surprisingly achieved a top score). With a reference frame constructed from over 500 adults, we tested a variety of mainstream LLMs. Most achieved above-average EQ scores, with GPT-4 exceeding 89% of human participants with an EQ of 117. Interestingly, a multivariate pattern analysis revealed that some LLMs apparently did not reply on the human-like mechanism to achieve human-level performance, as their representational patterns were qualitatively distinct from humans. In addition, we discussed the impact of factors such as model size, training method, and architecture on LLMs' EQ. In summary, our study presents one of the first psychometric evaluations of the human-like characteristics of LLMs, which may shed light on the future development of LLMs aiming for both high intellectual and emotional intelligence. Project website: //emotional-intelligence.github.io/

Momentum is known to accelerate the convergence of gradient descent in strongly convex settings without stochastic gradient noise. In stochastic optimization, such as training neural networks, folklore suggests that momentum may help deep learning optimization by reducing the variance of the stochastic gradient update, but previous theoretical analyses do not find momentum to offer any provable acceleration. Theoretical results in this paper clarify the role of momentum in stochastic settings where the learning rate is small and gradient noise is the dominant source of instability, suggesting that SGD with and without momentum behave similarly in the short and long time horizons. Experiments show that momentum indeed has limited benefits for both optimization and generalization in practical training regimes where the optimal learning rate is not very large, including small- to medium-batch training from scratch on ImageNet and fine-tuning language models on downstream tasks.

Large Language Models (LLMs) have shown excellent generalization capabilities that have led to the development of numerous models. These models propose various new architectures, tweaking existing architectures with refined training strategies, increasing context length, using high-quality training data, and increasing training time to outperform baselines. Analyzing new developments is crucial for identifying changes that enhance training stability and improve generalization in LLMs. This survey paper comprehensively analyses the LLMs architectures and their categorization, training strategies, training datasets, and performance evaluations and discusses future research directions. Moreover, the paper also discusses the basic building blocks and concepts behind LLMs, followed by a complete overview of LLMs, including their important features and functions. Finally, the paper summarizes significant findings from LLM research and consolidates essential architectural and training strategies for developing advanced LLMs. Given the continuous advancements in LLMs, we intend to regularly update this paper by incorporating new sections and featuring the latest LLM models.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

We describe the new field of mathematical analysis of deep learning. This field emerged around a list of research questions that were not answered within the classical framework of learning theory. These questions concern: the outstanding generalization power of overparametrized neural networks, the role of depth in deep architectures, the apparent absence of the curse of dimensionality, the surprisingly successful optimization performance despite the non-convexity of the problem, understanding what features are learned, why deep architectures perform exceptionally well in physical problems, and which fine aspects of an architecture affect the behavior of a learning task in which way. We present an overview of modern approaches that yield partial answers to these questions. For selected approaches, we describe the main ideas in more detail.

Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.