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Quantum Relative Entropy (QRE) programming is a recently popular and challenging class of convex optimization problems with significant applications in quantum computing and quantum information theory. We are interested in modern interior point (IP) methods based on optimal self-concordant barriers for the QRE cone. A range of theoretical and numerical challenges associated with such barrier functions and the QRE cones have hindered the scalability of IP methods. To address these challenges, we propose a series of numerical and linear algebraic techniques and heuristics aimed at enhancing the efficiency of gradient and Hessian computations for the self-concordant barrier function, solving linear systems, and performing matrix-vector products. We also introduce and deliberate about some interesting concepts related to QRE such as symmetric quantum relative entropy (SQRE). We also introduce a two-phase method for performing facial reduction that can significantly improve the performance of QRE programming. Our new techniques have been implemented in the latest version (DDS 2.2) of the software package DDS. In addition to handling QRE constraints, DDS accepts any combination of several other conic and non-conic convex constraints. Our comprehensive numerical experiments encompass several parts including 1) a comparison of DDS 2.2 with Hypatia for the nearest correlation matrix problem, 2) using DDS for combining QRE constraints with various other constraint types, and 3) calculating the key rate for quantum key distribution (QKD) channels and presenting results for several QKD protocols.

Contextualized embeddings are the preferred tool for modeling Lexical Semantic Change (LSC). Current evaluations typically focus on a specific task known as Graded Change Detection (GCD). However, performance comparison across work are often misleading due to their reliance on diverse settings. In this paper, we evaluate state-of-the-art models and approaches for GCD under equal conditions. We further break the LSC problem into Word-in-Context (WiC) and Word Sense Induction (WSI) tasks, and compare models across these different levels. Our evaluation is performed across different languages on eight available benchmarks for LSC, and shows that (i) APD outperforms other approaches for GCD; (ii) XL-LEXEME outperforms other contextualized models for WiC, WSI, and GCD, while being comparable to GPT-4; (iii) there is a clear need for improving the modeling of word meanings, as well as focus on how, when, and why these meanings change, rather than solely focusing on the extent of semantic change.

The moving discontinuous Galerkin method with interface condition enforcement (MDG-ICE) is a high-order, r-adaptive method that treats the grid as a variable and weakly enforces the conservation law, constitutive law, and corresponding interface conditions in order to implicitly fit high-gradient flow features. In this paper, we develop an optimization solver based on the Levenberg-Marquardt algorithm that features an anisotropic, locally adaptive penalty method to enhance robustness and prevent cell degeneration in the computation of hypersonic, viscous flows. Specifically, we incorporate an anisotropic grid regularization based on the mesh-implied metric that inhibits grid motion in directions with small element length scales, an element shape regularization that inhibits nonlinear deformations of the high-order elements, and a penalty regularization that penalizes degenerate elements. Additionally, we introduce a procedure for locally scaling the regularization operators in an adaptive, elementwise manner in order to maintain grid validity. We apply the proposed MDG-ICE formulation to two- and three-dimensional test cases involving viscous shocks and/or boundary layers, including Mach 17.6 hypersonic viscous flow over a circular cylinder and Mach 5 hypersonic viscous flow over a sphere, which are very challenging test cases for conventional numerical schemes on simplicial grids. Even without artificial dissipation, the computed solutions are free from spurious oscillations and yield highly symmetric surface heat-flux profiles.

Users of natural language interfaces, generally powered by Large Language Models (LLMs),often must repeat their preferences each time they make a similar request. We describe an approach to LLM-based dialogue modeling in which persistent user constraints and preferences -- collectively termed standing instructions -- as additional context for such interfaces. For example, when a user states "I'm hungry", a previously expressed preference for Persian food can be automatically added to the LLM prompt, influencing the search for relevant restaurants. We develop NLSI, a language-to-program dataset consisting of over 2.4K dialogues spanning 17 domains, where each dialogue is paired with a user profile (a set of users specific standing instructions) and corresponding structured representations (API calls). A key challenge in NLSI is to identify which subset of the standing instructions is applicable to a given dialogue. NLSI contains diverse phenomena, from simple preferences to interdependent instructions such as triggering a hotel search whenever the user is booking tickets to an event. We conduct experiments on NLSI using prompting with large language models and various retrieval approaches, achieving a maximum of 44.7% exact match on API prediction. Our results demonstrate the challenges in identifying the relevant standing instructions and their interpretation into API calls.

Deep Residual Neural Networks (ResNets) have demonstrated remarkable success across a wide range of real-world applications. In this paper, we identify a suitable scaling factor (denoted by $\alpha$) on the residual branch of deep wide ResNets to achieve good generalization ability. We show that if $\alpha$ is a constant, the class of functions induced by Residual Neural Tangent Kernel (RNTK) is asymptotically not learnable, as the depth goes to infinity. We also highlight a surprising phenomenon: even if we allow $\alpha$ to decrease with increasing depth $L$, the degeneration phenomenon may still occur. However, when $\alpha$ decreases rapidly with $L$, the kernel regression with deep RNTK with early stopping can achieve the minimax rate provided that the target regression function falls in the reproducing kernel Hilbert space associated with the infinite-depth RNTK. Our simulation studies on synthetic data and real classification tasks such as MNIST, CIFAR10 and CIFAR100 support our theoretical criteria for choosing $\alpha$.

Large Language Models (LLMs) have unlocked new capabilities and applications; however, evaluating the alignment with human preferences still poses significant challenges. To address this issue, we introduce Chatbot Arena, an open platform for evaluating LLMs based on human preferences. Our methodology employs a pairwise comparison approach and leverages input from a diverse user base through crowdsourcing. The platform has been operational for several months, amassing over 240K votes. This paper describes the platform, analyzes the data we have collected so far, and explains the tried-and-true statistical methods we are using for efficient and accurate evaluation and ranking of models. We confirm that the crowdsourced questions are sufficiently diverse and discriminating and that the crowdsourced human votes are in good agreement with those of expert raters. These analyses collectively establish a robust foundation for the credibility of Chatbot Arena. Because of its unique value and openness, Chatbot Arena has emerged as one of the most referenced LLM leaderboards, widely cited by leading LLM developers and companies. Our demo is publicly available at \url{//chat.lmsys.org}.

Large language models (LLMs) need to serve everyone, including a global majority of non-English speakers. However, most LLMs today, and open LLMs in particular, are often intended for use in just English (e.g. Llama2, Mistral) or a small handful of high-resource languages (e.g. Mixtral, Qwen). Recent research shows that, despite limits in their intended use, people prompt LLMs in many different languages. Therefore, in this paper, we investigate the basic multilingual capabilities of state-of-the-art open LLMs beyond their intended use. For this purpose, we introduce MultiQ, a new silver standard benchmark for basic open-ended question answering with 27.4k test questions across a typologically diverse set of 137 languages. With MultiQ, we evaluate language fidelity, i.e.\ whether models respond in the prompted language, and question answering accuracy. All LLMs we test respond faithfully and/or accurately for at least some languages beyond their intended use. Most models are more accurate when they respond faithfully. However, differences across models are large, and there is a long tail of languages where models are neither accurate nor faithful. We explore differences in tokenization as a potential explanation for our findings, identifying possible correlations that warrant further investigation.

Unfair behaviors of Machine Learning (ML) software have garnered increasing attention and concern among software engineers. To tackle this issue, extensive research has been dedicated to conducting fairness testing of ML software, and this paper offers a comprehensive survey of existing studies in this field. We collect 100 papers and organize them based on the testing workflow (i.e., how to test) and testing components (i.e., what to test). Furthermore, we analyze the research focus, trends, and promising directions in the realm of fairness testing. We also identify widely-adopted datasets and open-source tools for fairness testing.

Large Language Models (LLMs) have emerged as a powerful tool in advancing the Text-to-SQL task, significantly outperforming traditional methods. Nevertheless, as a nascent research field, there is still no consensus on the optimal prompt templates and design frameworks. Additionally, existing benchmarks inadequately explore the performance of LLMs across the various sub-tasks of the Text-to-SQL process, which hinders the assessment of LLMs' cognitive capabilities and the optimization of LLM-based solutions. To address the aforementioned issues, we firstly construct a new dataset designed to mitigate the risk of overfitting in LLMs. Then we formulate five evaluation tasks to comprehensively assess the performance of diverse methods across various LLMs throughout the Text-to-SQL process.Our study highlights the performance disparities among LLMs and proposes optimal in-context learning solutions tailored to each task. These findings offer valuable insights for enhancing the development of LLM-based Text-to-SQL systems.

The significant advancements in large language models (LLMs) give rise to a promising research direction, i.e., leveraging LLMs as recommenders (LLMRec). The efficacy of LLMRec arises from the open-world knowledge and reasoning capabilities inherent in LLMs. LLMRec acquires the recommendation capabilities through instruction tuning based on user interaction data. However, in order to protect user privacy and optimize utility, it is also crucial for LLMRec to intentionally forget specific user data, which is generally referred to as recommendation unlearning. In the era of LLMs, recommendation unlearning poses new challenges for LLMRec in terms of \textit{inefficiency} and \textit{ineffectiveness}. Existing unlearning methods require updating billions of parameters in LLMRec, which is costly and time-consuming. Besides, they always impact the model utility during the unlearning process. To this end, we propose \textbf{E2URec}, the first \underline{E}fficient and \underline{E}ffective \underline{U}nlearning method for LLM\underline{Rec}. Our proposed E2URec enhances the unlearning efficiency by updating only a few additional LoRA parameters, and improves the unlearning effectiveness by employing a teacher-student framework, where we maintain multiple teacher networks to guide the unlearning process. Extensive experiments show that E2URec outperforms state-of-the-art baselines on two real-world datasets. Specifically, E2URec can efficiently forget specific data without affecting recommendation performance. The source code is at \url{//github.com/justarter/E2URec}.