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We propose a theory for matrix completion that goes beyond the low-rank structure commonly considered in the literature and applies to general matrices of low description complexity. Specifically, complexity of the sets of matrices encompassed by the theory is measured in terms of Hausdorff and upper Minkowski dimensions. Our goal is the characterization of the number of linear measurements, with an emphasis on rank-$1$ measurements, needed for the existence of an algorithm that yields reconstruction, either perfect, with probability 1, or with arbitrarily small probability of error, depending on the setup. Concretely, we show that matrices taken from a set $\mathcal{U}$ such that $\mathcal{U}-\mathcal{U}$ has Hausdorff dimension $s$ can be recovered from $k>s$ measurements, and random matrices supported on a set $\mathcal{U}$ of Hausdorff dimension $s$ can be recovered with probability 1 from $k>s$ measurements. What is more, we establish the existence of recovery mappings that are robust against additive perturbations or noise in the measurements. Concretely, we show that there are $\beta$-H\"older continuous mappings recovering matrices taken from a set of upper Minkowski dimension $s$ from $k>2s/(1-\beta)$ measurements and, with arbitrarily small probability of error, random matrices supported on a set of upper Minkowski dimension $s$ from $k>s/(1-\beta)$ measurements. The numerous concrete examples we consider include low-rank matrices, sparse matrices, QR decompositions with sparse R-components, and matrices of fractal nature.

The convergence of deterministic policy gradient under the Hadamard parameterization is studied in the tabular setting and the linear convergence of the algorithm is established. To this end, we first show that the error decreases at an $O(\frac{1}{k})$ rate for all the iterations. Based on this result, we further show that the algorithm has a faster local linear convergence rate after $k_0$ iterations, where $k_0$ is a constant that only depends on the MDP problem and the initialization. To show the local linear convergence of the algorithm, we have indeed established the contraction of the sub-optimal probability $b_s^k$ (i.e., the probability of the output policy $\pi^k$ on non-optimal actions) when $k\ge k_0$.

Figures of speech such as metaphors, similes, and idioms are integral parts of human communication. They are ubiquitous in many forms of discourse, allowing people to convey complex, abstract ideas and evoke emotion. As figurative forms are often conveyed through multiple modalities (e.g., both text and images), understanding multimodal figurative language is an important AI challenge, weaving together profound vision, language, commonsense and cultural knowledge. In this work, we develop the Image Recognition of Figurative Language (IRFL) dataset. We leverage human annotation and an automatic pipeline we created to generate a multimodal dataset, and introduce two novel tasks as a benchmark for multimodal figurative language understanding. We experimented with state-of-the-art vision and language models and found that the best (22%) performed substantially worse than humans (97%). We release our dataset, benchmark, and code, in hopes of driving the development of models that can better understand figurative language.

An initial procedure in text-as-data applications is text preprocessing. One of the typical steps, which can substantially facilitate computations, consists in removing infrequent words believed to provide limited information about the corpus. Despite popularity of vocabulary pruning, not many guidelines on how to implement it are available in the literature. The aim of the paper is to fill this gap by examining the effects of removing infrequent words for the quality of topics estimated using Latent Dirichlet Allocation. The analysis is based on Monte Carlo experiments taking into account different criteria for infrequent terms removal and various evaluation metrics. The results indicate that pruning is beneficial and that the share of vocabulary which might be eliminated can be quite considerable.

The subrank of tensors is a measure of how much a tensor can be ''diagonalized''. This parameter was introduced by Strassen to study fast matrix multiplication algorithms in algebraic complexity theory and is closely related to many central tensor parameters (e.g. slice rank, partition rank, analytic rank, geometric rank, G-stable rank) and problems in combinatorics, computer science and quantum information theory. Strassen (J. Reine Angew. Math., 1988) proved that there is a gap in the subrank when taking large powers under the tensor product: either the subrank of all powers is at most one, or it grows as a power of a constant strictly larger than one. In this paper, we precisely determine this constant for tensors of any order. Additionally, for tensors of order three, we prove that there is a second gap in the possible rates of growth. Our results strengthen the recent work of Costa and Dalai (J. Comb. Theory, Ser. A, 2021), who proved a similar gap for the slice rank. Our theorem on the subrank has wider applications by implying such gaps not only for the slice rank, but for any ``normalized monotone''. In order to prove the main result, we characterize when a tensor has a very structured tensor (the W-tensor) in its orbit closure. Our methods include degenerations in Grassmanians, which may be of independent interest.

The allure of aesthetic appeal in images captivates our senses, yet the underlying intricacies of aesthetic preferences remain elusive. In this study, we pioneer a novel perspective by utilizing machine learning models that focus on aesthetic attributes known to influence preferences. Through a data mining approach, our models process these attributes as inputs to predict the aesthetic scores of images. Moreover, to delve deeper and obtain interpretable explanations regarding the factors driving aesthetic preferences, we utilize the popular Explainable AI (XAI) technique known as SHapley Additive exPlanations (SHAP). Our methodology involves employing various machine learning models, including Random Forest, XGBoost, Support Vector Regression, and Multilayer Perceptron, to compare their performances in accurately predicting aesthetic scores, and consistently observing results in conjunction with SHAP. We conduct experiments on three image aesthetic benchmarks, providing insights into the roles of attributes and their interactions. Ultimately, our study aims to shed light on the complex nature of aesthetic preferences in images through machine learning and provides a deeper understanding of the attributes that influence aesthetic judgements.

We investigate how the potential use of algorithms and demonstrative evidence may affect potential jurors' feelings of reliability, credibility, and understanding of expert witnesses and presented evidence. The use of statistical methods in forensic science is motivated by a lack of scientific validity and error rate issues present in many forensic analysis methods. We explore how this new method may be perceived in the courtroom - where individuals unfamiliar with advanced statistical methods are asked to evaluate its use in order to assess guilt. In the course of our initial study, we discovered issues in scale compression of responses and survey format. We visually compare participants' notes to the provided transcript by highlighting phrase frequency based on collocations.

In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.

In the past decade, we have witnessed the rise of deep learning to dominate the field of artificial intelligence. Advances in artificial neural networks alongside corresponding advances in hardware accelerators with large memory capacity, together with the availability of large datasets enabled researchers and practitioners alike to train and deploy sophisticated neural network models that achieve state-of-the-art performance on tasks across several fields spanning computer vision, natural language processing, and reinforcement learning. However, as these neural networks become bigger, more complex, and more widely used, fundamental problems with current deep learning models become more apparent. State-of-the-art deep learning models are known to suffer from issues that range from poor robustness, inability to adapt to novel task settings, to requiring rigid and inflexible configuration assumptions. Ideas from collective intelligence, in particular concepts from complex systems such as self-organization, emergent behavior, swarm optimization, and cellular systems tend to produce solutions that are robust, adaptable, and have less rigid assumptions about the environment configuration. It is therefore natural to see these ideas incorporated into newer deep learning methods. In this review, we will provide a historical context of neural network research's involvement with complex systems, and highlight several active areas in modern deep learning research that incorporate the principles of collective intelligence to advance its current capabilities. To facilitate a bi-directional flow of ideas, we also discuss work that utilize modern deep learning models to help advance complex systems research. We hope this review can serve as a bridge between complex systems and deep learning communities to facilitate the cross pollination of ideas and foster new collaborations across disciplines.

AI is undergoing a paradigm shift with the rise of models (e.g., BERT, DALL-E, GPT-3) that are trained on broad data at scale and are adaptable to a wide range of downstream tasks. We call these models foundation models to underscore their critically central yet incomplete character. This report provides a thorough account of the opportunities and risks of foundation models, ranging from their capabilities (e.g., language, vision, robotics, reasoning, human interaction) and technical principles(e.g., model architectures, training procedures, data, systems, security, evaluation, theory) to their applications (e.g., law, healthcare, education) and societal impact (e.g., inequity, misuse, economic and environmental impact, legal and ethical considerations). Though foundation models are based on standard deep learning and transfer learning, their scale results in new emergent capabilities,and their effectiveness across so many tasks incentivizes homogenization. Homogenization provides powerful leverage but demands caution, as the defects of the foundation model are inherited by all the adapted models downstream. Despite the impending widespread deployment of foundation models, we currently lack a clear understanding of how they work, when they fail, and what they are even capable of due to their emergent properties. To tackle these questions, we believe much of the critical research on foundation models will require deep interdisciplinary collaboration commensurate with their fundamentally sociotechnical nature.