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Large Language Models (LLMs) like GPT-4 and LLaMA have shown incredible proficiency at natural language processing tasks and have even begun to excel at tasks across other modalities such as vision and audio. Despite their success, LLMs often struggle to perform well on low-resource languages because there is so little training data available. This shortcoming is especially prevalent with open source models. In this work, we explore training LLaMA-2 to speak Amharic, a language which is spoken by over 50 million people world wide, but has orders of magnitude less data available than languages like English. We employ methods previously used for training LLMs on other languages with data scarcity, and use open source translation models to perform data augmentation and grow our dataset from millions of tokens to billions. We further enhance the capabilities of our model by connecting an image encoder and training on a translated visual instruction tuning dataset in the same manner as LLaVA, resulting in a multimodal Amharic LLM that can understand images along with text. We introduce an Amharic version of a popular benchmarking dataset to evaluate our work. Our models and dataset are open sourced and available on GitHub.

The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been proposed. Exploring the maximum entropy provides a possible way of understanding the physical meaning of RPS. In this paper, a new concept, the envelope of entropy function, is defined. In addition, the limit of the envelope of RPS entropy is derived and proved. Compared with the existing method, the computational complexity of the proposed method to calculate the envelope of RPS entropy decreases greatly. The result shows that when $N \to \infty$, the limit form of the envelope of the entropy of RPS converges to $e \times (N!)^2$, which is highly connected to the constant $e$ and factorial. Finally, numerical examples validate the efficiency and conciseness of the proposed envelope, which provides a new insight into the maximum entropy function.

Prognostics and Health Management (PHM) is a discipline focused on predicting the point at which systems or components will cease to perform as intended, typically measured as Remaining Useful Life (RUL). RUL serves as a vital decision-making tool for contingency planning, guiding the timing and nature of system maintenance. Historically, PHM has primarily been applied to hardware systems, with its application to software only recently explored. In a recent study we introduced a methodology and demonstrated how changes in software can impact the RUL of software. However, in practical software development, real-time performance is also influenced by various environmental attributes, including operating systems, clock speed, processor performance, RAM, machine core count and others. This research extends the analysis to assess how changes in environmental attributes, such as operating system and clock speed, affect RUL estimation in software. Findings are rigorously validated using real performance data from controlled test beds and compared with predictive model-generated data. Statistical validation, including regression analysis, supports the credibility of the results. The controlled test bed environment replicates and validates faults from real applications, ensuring a standardized assessment platform. This exploration yields actionable knowledge for software maintenance and optimization strategies, addressing a significant gap in the field of software health management.

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}.

While large language models have achieved remarkable performance on various code generation benchmarks, there have been growing concerns regarding potential contamination of these benchmarks as they may be leaked into pretraining and finetuning data. While recent work has investigated contamination in natural language generation and understanding tasks, there has been less extensive research into how data contamination impacts the evaluation of code generation, which is critical for understanding the robustness and reliability of LLMs in programming contexts. In this work, we perform a comprehensive study of data contamination of popular code generation benchmarks, and precisely quantify their overlap with pretraining corpus through both surface-level and semantic-level matching. In our experiments, we show that there are substantial overlap between popular code generation benchmarks and open training corpus, and models perform significantly better on the subset of the benchmarks where similar solutions are seen during training. We also conduct extensive analysis on the factors that affects model memorization and generalization, such as model size, problem difficulty, and question length. We release all resulting files from our matching pipeline for future research.