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We study extensions of Sem\"enov arithmetic, the first-order theory of the structure $(\mathbb{N}, +, 2^x)$. It is well-knonw that this theory becomes undecidable when extended with regular predicates over tuples of number strings, such as the B\"uchi $V_2$-predicate. We therefore restrict ourselves to the existential theory of Sem\"enov arithmetic and show that this theory is decidable in EXPSPACE when extended with arbitrary regular predicates over tuples of number strings. Our approach relies on a reduction to the language emptiness problem for a restricted class of affine vector addition systems with states, which we show decidable in EXPSPACE. As an application of our results, we settle an open problem from the literature and show decidability of a class of string constraints involving length constraints.

Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and phenotypic spaces, especially through neutral mutations, helps us to better understand the progression of evolution and its algorithmic behaviour. In this study, we visualise the search trajectories of a genetic programming system as graph-based models, where nodes are genotypes/phenotypes and edges represent their mutational transitions. We also quantitatively measure the characteristics of phenotypes including their genotypic abundance (the requirement for neutrality) and Kolmogorov complexity. We connect these quantified metrics with search trajectory visualisations, and find that more complex phenotypes are under-represented by fewer genotypes and are harder for evolution to discover. Less complex phenotypes, on the other hand, are over-represented by genotypes, are easier to find, and frequently serve as stepping-stones for evolution.

This study aims to compare multiple deep learning-based forecasters for the task of predicting volatility using multivariate data. The paper evaluates a range of models, starting from simpler and shallower ones and progressing to deeper and more complex architectures. Additionally, the performance of these models is compared against naive predictions and variations of classical GARCH models. The prediction of volatility for five assets, namely S&P500, NASDAQ100, gold, silver, and oil, is specifically addressed using GARCH models, Multi-Layer Perceptrons, Recurrent Neural Networks, Temporal Convolutional Networks, and the Temporal Fusion Transformer. In the majority of cases, the Temporal Fusion Transformer, followed by variants of the Temporal Convolutional Network, outperformed classical approaches and shallow networks. These experiments were repeated, and the differences observed between the competing models were found to be statistically significant, thus providing strong encouragement for their practical application.

Due to the growing complexity of modern data centers, failures are not uncommon any more. Therefore, fault tolerance mechanisms play a vital role in fulfilling the availability requirements. Multiple availability models have been proposed to assess compute systems, among which Bayesian network models have gained popularity in industry and research due to its powerful modeling formalism. In particular, this work focuses on assessing the availability of redundant and replicated cloud computing services with Bayesian networks. So far, research on availability has only focused on modeling either infrastructure or communication failures in Bayesian networks, but have not considered both simultaneously. This work addresses practical modeling challenges of assessing the availability of large-scale redundant and replicated services with Bayesian networks, including cascading and common-cause failures from the surrounding infrastructure and communication network. In order to ease the modeling task, this paper introduces a high-level modeling formalism to build such a Bayesian network automatically. Performance evaluations demonstrate the feasibility of the presented Bayesian network approach to assess the availability of large-scale redundant and replicated services. This model is not only applicable in the domain of cloud computing it can also be applied for general cases of local and geo-distributed systems.

Dimension reduction is crucial in functional data analysis (FDA). The key tool to reduce the dimension of the data is functional principal component analysis. Existing approaches for functional principal component analysis usually involve the diagonalization of the covariance operator. With the increasing size and complexity of functional datasets, estimating the covariance operator has become more challenging. Therefore, there is a growing need for efficient methodologies to estimate the eigencomponents. Using the duality of the space of observations and the space of functional features, we propose to use the inner-product between the curves to estimate the eigenelements of multivariate and multidimensional functional datasets. The relationship between the eigenelements of the covariance operator and those of the inner-product matrix is established. We explore the application of these methodologies in several FDA settings and provide general guidance on their usability.

The evolution of semantic segmentation has long been dominated by learning more discriminative image representations for classifying each pixel. Despite the prominent advancements, the priors of segmentation masks themselves, e.g., geometric and semantic constraints, are still under-explored. In this paper, we propose to ameliorate the semantic segmentation quality of existing discriminative approaches with a mask prior modeled by a recently-developed denoising diffusion generative model. Beginning with a unified architecture that adapts diffusion models for mask prior modeling, we focus this work on a specific instantiation with discrete diffusion and identify a variety of key design choices for its successful application. Our exploratory analysis revealed several important findings, including: (1) a simple integration of diffusion models into semantic segmentation is not sufficient, and a poorly-designed diffusion process might lead to degradation in segmentation performance; (2) during the training, the object to which noise is added is more important than the type of noise; (3) during the inference, the strict diffusion denoising scheme may not be essential and can be relaxed to a simpler scheme that even works better. We evaluate the proposed prior modeling with several off-the-shelf segmentors, and our experimental results on ADE20K and Cityscapes demonstrate that our approach could achieve competitively quantitative performance and more appealing visual quality.

Knowledge graphs represent factual knowledge about the world as relationships between concepts and are critical for intelligent decision making in enterprise applications. New knowledge is inferred from the existing facts in the knowledge graphs by encoding the concepts and relations into low-dimensional feature vector representations. The most effective representations for this task, called Knowledge Graph Embeddings (KGE), are learned through neural network architectures. Due to their impressive predictive performance, they are increasingly used in high-impact domains like healthcare, finance and education. However, are the black-box KGE models adversarially robust for use in domains with high stakes? This thesis argues that state-of-the-art KGE models are vulnerable to data poisoning attacks, that is, their predictive performance can be degraded by systematically crafted perturbations to the training knowledge graph. To support this argument, two novel data poisoning attacks are proposed that craft input deletions or additions at training time to subvert the learned model's performance at inference time. These adversarial attacks target the task of predicting the missing facts in knowledge graphs using KGE models, and the evaluation shows that the simpler attacks are competitive with or outperform the computationally expensive ones. The thesis contributions not only highlight and provide an opportunity to fix the security vulnerabilities of KGE models, but also help to understand the black-box predictive behaviour of KGE models.

Interpretability methods are developed to understand the working mechanisms of black-box models, which is crucial to their responsible deployment. Fulfilling this goal requires both that the explanations generated by these methods are correct and that people can easily and reliably understand them. While the former has been addressed in prior work, the latter is often overlooked, resulting in informal model understanding derived from a handful of local explanations. In this paper, we introduce explanation summary (ExSum), a mathematical framework for quantifying model understanding, and propose metrics for its quality assessment. On two domains, ExSum highlights various limitations in the current practice, helps develop accurate model understanding, and reveals easily overlooked properties of the model. We also connect understandability to other properties of explanations such as human alignment, robustness, and counterfactual minimality and plausibility.

Multi-stage ranking pipelines have been a practical solution in modern search systems, where the first-stage retrieval is to return a subset of candidate documents, and latter stages attempt to re-rank those candidates. Unlike re-ranking stages going through quick technique shifts during past decades, the first-stage retrieval has long been dominated by classical term-based models. Unfortunately, these models suffer from the vocabulary mismatch problem, which may block re-ranking stages from relevant documents at the very beginning. Therefore, it has been a long-term desire to build semantic models for the first-stage retrieval that can achieve high recall efficiently. Recently, we have witnessed an explosive growth of research interests on the first-stage semantic retrieval models. We believe it is the right time to survey current status, learn from existing methods, and gain some insights for future development. In this paper, we describe the current landscape of the first-stage retrieval models under a unified framework to clarify the connection between classical term-based retrieval methods, early semantic retrieval methods and neural semantic retrieval methods. Moreover, we identify some open challenges and envision some future directions, with the hope of inspiring more researches on these important yet less investigated topics.

We consider the problem of zero-shot recognition: learning a visual classifier for a category with zero training examples, just using the word embedding of the category and its relationship to other categories, which visual data are provided. The key to dealing with the unfamiliar or novel category is to transfer knowledge obtained from familiar classes to describe the unfamiliar class. In this paper, we build upon the recently introduced Graph Convolutional Network (GCN) and propose an approach that uses both semantic embeddings and the categorical relationships to predict the classifiers. Given a learned knowledge graph (KG), our approach takes as input semantic embeddings for each node (representing visual category). After a series of graph convolutions, we predict the visual classifier for each category. During training, the visual classifiers for a few categories are given to learn the GCN parameters. At test time, these filters are used to predict the visual classifiers of unseen categories. We show that our approach is robust to noise in the KG. More importantly, our approach provides significant improvement in performance compared to the current state-of-the-art results (from 2 ~ 3% on some metrics to whopping 20% on a few).