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In this paper, we focus on the solution of online optimization problems that arise often in signal processing and machine learning, in which we have access to streaming sources of data. We discuss algorithms for online optimization based on the prediction-correction paradigm, both in the primal and dual space. In particular, we leverage the typical regularized least-squares structure appearing in many signal processing problems to propose a novel and tailored prediction strategy, which we call extrapolation-based. By using tools from operator theory, we then analyze the convergence of the proposed methods as applied both to primal and dual problems, deriving an explicit bound for the tracking error, that is, the distance from the time-varying optimal solution. We further discuss the empirical performance of the algorithm when applied to signal processing, machine learning, and robotics problems.

Let a polytope $P$ be defined by a system $A x \leq b$. We consider the problem of counting the number of integer points inside $P$, assuming that $P$ is $\Delta$-modular, where the polytope $P$ is called $\Delta$-modular if all the rank sub-determinants of $A$ are bounded by $\Delta$ in the absolute value. We present a new FPT-algorithm, parameterized by $\Delta$ and by the maximal number of vertices in $P$, where the maximum is taken by all r.h.s. vectors $b$. We show that our algorithm is more efficient for $\Delta$-modular problems than the approach of A. Barvinok et al. To this end, we do not directly compute the short rational generating function for $P \cap Z^n$, which is commonly used for the considered problem. Instead, we use the dynamic programming principle to compute its particular representation in the form of exponential series that depends on a single variable. We completely do not rely to the Barvinok's unimodular sign decomposition technique. Using our new complexity bound, we consider different special cases that may be of independent interest. For example, we give FPT-algorithms for counting the integer points number in $\Delta$-modular simplices and similar polytopes that have $n + O(1)$ facets. As a special case, for any fixed $m$, we give an FPT-algorithm to count solutions of the unbounded $m$-dimensional $\Delta$-modular subset-sum problem.

Language has a strong influence on our perceptions of time and rewards. This raises the question of whether large language models, when asked in different languages, show different preferences for rewards over time and if their choices are similar to those of humans. In this study, we analyze the responses of GPT-3.5 (hereafter referred to as GPT) to prompts in multiple languages, exploring preferences between smaller, sooner rewards and larger, later rewards. Our results show that GPT displays greater patience when prompted in languages with weak future tense references (FTR), such as German and Mandarin, compared to languages with strong FTR, like English and French. These findings are consistent with existing literature and suggest a correlation between GPT's choices and the preferences of speakers of these languages. However, further analysis reveals that the preference for earlier or later rewards does not systematically change with reward gaps, indicating a lexicographic preference for earlier payments. While GPT may capture intriguing variations across languages, our findings indicate that the choices made by these models do not correspond to those of human decision-makers.

Given a function $f$ on $\mathbb{F}_2^n$, we study the following problem. What is the largest affine subspace $\mathcal{U}$ such that when restricted to $\mathcal{U}$, all the non-trivial Fourier coefficients of $f$ are very small? For the natural class of bounded Fourier degree $d$ functions $f:\mathbb{F}_2^n \to [-1,1]$, we show that there exists an affine subspace of dimension at least $ \tilde\Omega(n^{1/d!}k^{-2})$, wherein all of $f$'s nontrivial Fourier coefficients become smaller than $ 2^{-k}$. To complement this result, we show the existence of degree $d$ functions with coefficients larger than $2^{-d\log n}$ when restricted to any affine subspace of dimension larger than $\Omega(dn^{1/(d-1)})$. In addition, we give explicit examples of functions with analogous but weaker properties. Along the way, we provide multiple characterizations of the Fourier coefficients of functions restricted to subspaces of $\mathbb{F}_2^n$ that may be useful in other contexts. Finally, we highlight applications and connections of our results to parity kill number and affine dispersers.

Speech AI Technologies are largely trained on publicly available datasets or by the massive web-crawling of speech. In both cases, data acquisition focuses on minimizing collection effort, without necessarily taking the data subjects' protection or user needs into consideration. This results to models that are not robust when used on users who deviate from the dominant demographics in the training set, discriminating individuals having different dialects, accents, speaking styles, and disfluencies. In this talk, we use automatic speech recognition as a case study and examine the properties that ethical speech datasets should possess towards responsible AI applications. We showcase diversity issues, inclusion practices, and necessary considerations that can improve trained models, while facilitating model explainability and protecting users and data subjects. We argue for the legal & privacy protection of data subjects, targeted data sampling corresponding to user demographics & needs, appropriate meta data that ensure explainability & accountability in cases of model failure, and the sociotechnical \& situated model design. We hope this talk can inspire researchers \& practitioners to design and use more human-centric datasets in speech technologies and other domains, in ways that empower and respect users, while improving machine learning models' robustness and utility.

Recent years have witnessed a proliferation of valuable original natural language contents found in subscription-based media outlets, web novel platforms, and outputs of large language models. Without proper security measures, however, these contents are susceptible to illegal piracy and potential misuse. This calls for a secure watermarking system to guarantee copyright protection through leakage tracing or ownership identification. To effectively combat piracy and protect copyrights, a watermarking framework should be able not only to embed adequate bits of information but also extract the watermarks in a robust manner despite possible corruption. In this work, we explore ways to advance both payload and robustness by following a well-known proposition from image watermarking and identify features in natural language that are invariant to minor corruption. Through a systematic analysis of the possible sources of errors, we further propose a corruption-resistant infill model. Our full method improves upon the previous work on robustness by +16.8% point on average on four datasets, three corruption types, and two corruption ratios. Code available at //github.com/bangawayoo/nlp-watermarking.

Knowledge graph embedding (KGE) is a increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

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.

Deep learning models on graphs have achieved remarkable performance in various graph analysis tasks, e.g., node classification, link prediction and graph clustering. However, they expose uncertainty and unreliability against the well-designed inputs, i.e., adversarial examples. Accordingly, various studies have emerged for both attack and defense addressed in different graph analysis tasks, leading to the arms race in graph adversarial learning. For instance, the attacker has poisoning and evasion attack, and the defense group correspondingly has preprocessing- and adversarial- based methods. Despite the booming works, there still lacks a unified problem definition and a comprehensive review. To bridge this gap, we investigate and summarize the existing works on graph adversarial learning tasks systemically. Specifically, we survey and unify the existing works w.r.t. attack and defense in graph analysis tasks, and give proper definitions and taxonomies at the same time. Besides, we emphasize the importance of related evaluation metrics, and investigate and summarize them comprehensively. Hopefully, our works can serve as a reference for the relevant researchers, thus providing assistance for their studies. More details of our works are available at //github.com/gitgiter/Graph-Adversarial-Learning.

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.