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We propose an algorithmic framework for dataset normalization in data augmentation pipelines that preserves topological stability under non-uniform scaling transformations. Given a finite metric space \( X \subset \mathbb{R}^n \) with Euclidean distance \( d_X \), we consider scaling transformations defined by scaling factors \( s_1, s_2, \ldots, s_n > 0 \). Specifically, we define a scaling function \( S \) that maps each point \( x = (x_1, x_2, \ldots, x_n) \in X \) to \[ S(x) = (s_1 x_1, s_2 x_2, \ldots, s_n x_n). \] Our main result establishes that the bottleneck distance \( d_B(D, D_S) \) between the persistence diagrams \( D \) of \( X \) and \( D_S \) of \( S(X) \) satisfies: \[ d_B(D, D_S) \leq (s_{\max} - s_{\min}) \cdot \operatorname{diam}(X), \] where \( s_{\min} = \min_{1 \leq i \leq n} s_i \), \( s_{\max} = \max_{1 \leq i \leq n} s_i \), and \( \operatorname{diam}(X) \) is the diameter of \( X \). Based on this theoretical guarantee, we formulate an optimization problem to minimize the scaling variability \( \Delta_s = s_{\max} - s_{\min} \) under the constraint \( d_B(D, D_S) \leq \epsilon \), where \( \epsilon > 0 \) is a user-defined tolerance. We develop an algorithmic solution to this problem, ensuring that data augmentation via scaling transformations preserves essential topological features. We further extend our analysis to higher-dimensional homological features, alternative metrics such as the Wasserstein distance, and iterative or probabilistic scaling scenarios. Our contributions provide a rigorous mathematical framework for dataset normalization in data augmentation pipelines, ensuring that essential topological characteristics are maintained despite scaling transformations., Comment: 20 pages

We investigate the stability of persistence diagrams \( D \) under non-uniform scaling transformations \( S \) in \( \mathbb{R}^n \). Given a finite metric space \( X \subset \mathbb{R}^n \) with Euclidean distance \( d_X \), and scaling factors \( s_1, s_2, \ldots, s_n > 0 \) applied to each coordinate, we derive explicit bounds on the bottleneck distance \( d_B(D, D_S) \) between the persistence diagrams of \( X \) and its scaled version \( S(X) \). Specifically, we show that \[ d_B(D, D_S) \leq \frac{1}{2} (s_{\max} - s_{\min}) \cdot \operatorname{diam}(X), \] where \( s_{\min} \) and \( s_{\max} \) are the smallest and largest scaling factors, respectively, and \( \operatorname{diam}(X) \) is the diameter of \( X \). We extend this analysis to higher-dimensional homological features, alternative metrics such as the Wasserstein distance, and iterative or probabilistic scaling scenarios. Our results provide a framework for quantifying the effects of non-uniform scaling on persistence diagrams., Comment: 14 pages

Monitored Natural Attenuation (MNA) is gaining prominence as an effective method for managing soil and groundwater contamination due to its cost-efficiency and minimal environmental disruption. Despite its benefits, MNA necessitates extensive groundwater monitoring to ensure that contaminant levels decrease to meet safety standards. This study expands the capabilities of PyLEnM, a Python package designed for long-term environmental monitoring, by incorporating new algorithms to enhance its predictive and analytical functionalities. We introduce methods to estimate the timeframe required for contaminants like Sr-90 and I-129 to reach regulatory safety standards using linear regression and to forecast future contaminant levels with the Bidirectional Long Short-Term Memory (Bi-LSTM) networks. Additionally, Random Forest regression is employed to identify factors influencing the time to reach safety standards. Our methods are illustrated using data from the Savannah River Site (SRS) F-Area, where preliminary findings reveal a notable downward trend in contaminant levels, with variability linked to initial concentrations and groundwater flow dynamics. The Bi-LSTM model effectively predicts contaminant concentrations for the next four years, demonstrating the potential of advanced time series analysis to improve MNA strategies and reduce reliance on manual groundwater sampling. The code, along with its usage instructions, validation, and requirements, is available at: https://github.com/csplevuanh/pylenm_extension., Comment: The paper will be withdrawn to fix some work issues with the sections on Bi-LSTM models

Quantum computing has emerged as a powerful tool for solving complex computational problems, but access to real quantum hardware remains limited due to high costs and increasing demand for efficient quantum simulations. Unfortunately, software simulators on CPUs/GPUs such as Qiskit, ProjectQ, and Qsun offer flexibility and support for a large number of qubits, they struggle with high power consumption and limited processing speed, especially as qubit counts scale. Accordingly, quantum emulators implemented on dedicated hardware, such as FPGAs and analog circuits, offer a promising path for addressing energy efficiency concerns. However, existing studies on hardware-based emulators still face challenges in terms of limited flexibility, lack of fidelity evaluation, and power consumption. To overcome these gaps, we propose FQsun, a quantum emulator that enhances performance by integrating four key innovations: efficient memory organization, a configurable Quantum Gate Unit (QGU), optimized scheduling, and multiple number precisions. Five FQsun versions with different number precisions, including 16-bit floating point, 32-bit floating point, 16-bit fixed point, 24-bit fixed point, and 32-bit fixed point, are implemented on the Xilinx ZCU102 FPGA, utilizing between 9,226 and 18,093 LUTs, 1,440 and 7,031 FFs, 344 and 464 BRAMs, and 14 and 88 DSPs and consuming a maximum power of 2.41W. Experimental results demonstrate high accuracy in normalized gate speed, fidelity, and mean square error, particularly with 32-bit fixed-point and floating-point versions, establishing FQsun's capability as a precise quantum emulator. Benchmarking on quantum algorithms such as Quantum Fourier Transform, Parameter-Shift Rule, and Random Quantum Circuits reveals that FQsun achieves superior power-delay product, outperforming traditional software simulators on powerful CPUs by up to 9,870 times., Comment: 17 pages, 14 figures, submitted to the IEEE Transaction on Quantum Engineering

This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to enhance the stability, convergence, generalization, and computational efficiency of neural operators. We revisit key theoretical insights, including stability in high dimensions, exponential convergence, and universality of neural operators. Based on these insights, we provide detailed design recommendations, each supported by mathematical proofs and citations. Our contributions offer a systematic methodology for developing next-gen neural operators with improved performance and reliability., Comment: 22 pages

Neural operators have emerged as transformative tools for learning mappings between infinite-dimensional function spaces, offering useful applications in solving complex partial differential equations (PDEs). This paper presents a rigorous mathematical framework for analyzing the behaviors of neural operators, with a focus on their stability, convergence, clustering dynamics, universality, and generalization error. By proposing a list of novel theorems, we provide stability bounds in Sobolev spaces and demonstrate clustering in function space via gradient flow interpretation, guiding neural operator design and optimization. Based on these theoretical gurantees, we aim to offer clear and unified guidance in a single setting for the future design of neural operator-based methods., Comment: 24 pages

Quantum emulators play an important role in the development and testing of quantum algorithms, especially given the limitations of the current FTQC era. Developing high-speed, memory-optimized quantum emulators is a growing research trend, with gate fusion being a promising technique. However, existing gate fusion implementations often struggle to efficiently support large-scale quantum systems with a high number of qubits due to a lack of optimizations for the exponential growth in memory requirements. Therefore, this study proposes the EMMS (Efficient-Memory Matrix Storage) method for storing quantum operators and states, along with an EMMS-based Quantum Emulator Accelerator (QEA) architecture that incorporates multiple processing elements (PEs) to accelerate tensor product and matrix multiplication computations in quantum emulation with gate fusion. The theoretical analysis of the QEA on the Xilinx ZCU102 FPGA, using varying numbers of PEs and different depths of unitary and local data memory, reveals a linear increase in memory depth with the number of qubits. This scaling highlights the potential of the EMMS-based QEA to accommodate larger quantum circuits, providing insights into selecting appropriate memory sizes and FPGA devices. Furthermore, the estimated performance of the QEA with PE counts ranging from $2^2$ to $2^5$ on the Xilinx ZCU102 FPGA demonstrates that increasing the number of PEs significantly reduces the computation cycle count for circuits with fewer than 18 qubits, making it significantly faster than previous works.

LLMs-as-a-judge is a recently popularized method which replaces human judgements in task evaluation (Zheng et al. 2024) with automatic evaluation using LLMs. Due to widespread use of RLHF (Reinforcement Learning from Human Feedback), state-of-the-art LLMs like GPT4 and Llama3 are expected to have strong alignment with human preferences when prompted for a quality judgement, such as the coherence of a text. While this seems beneficial, it is not clear whether the assessments by an LLM-as-a-judge constitute only an evaluation based on the instructions in the prompts, or reflect its preference for high-quality data similar to its fine-tune data. To investigate how much influence prompting the LLMs-as-a-judge has on the alignment of AI judgements to human judgements, we analyze prompts with increasing levels of instructions about the target quality of an evaluation, for several LLMs-as-a-judge. Further, we compare to a prompt-free method using model perplexity as a quality measure instead. We aggregate a taxonomy of quality criteria commonly used across state-of-the-art evaluations with LLMs and provide this as a rigorous benchmark of models as judges. Overall, we show that the LLMs-as-a-judge benefit only little from highly detailed instructions in prompts and that perplexity can sometimes align better with human judgements than prompting, especially on textual quality.

Kolmogorov-Arnold Networks (KANs), a novel type of neural network, have recently gained popularity and attention due to the ability to substitute multi-layer perceptions (MLPs) in artificial intelligence (AI) with higher accuracy and interoperability. However, KAN assessment is still limited and cannot provide an in-depth analysis of a specific domain. Furthermore, no study has been conducted on the implementation of KANs in hardware design, which would directly demonstrate whether KANs are truly superior to MLPs in practical applications. As a result, in this paper, we focus on verifying KANs for classification issues, which are a common but significant topic in AI using four different types of datasets. Furthermore, the corresponding hardware implementation is considered using the Vitis high-level synthesis (HLS) tool. To the best of our knowledge, this is the first article to implement hardware for KAN. The results indicate that KANs cannot achieve more accuracy than MLPs in high complex datasets while utilizing substantially higher hardware resources. Therefore, MLP remains an effective approach for achieving accuracy and efficiency in software and hardware implementation., Comment: 6 pages, 3 figures, 2 tables

Large language models (LLMs) can be leveraged to help with writing formulas in spreadsheets, but resources on these formulas are scarce, impacting both the base performance of pre-trained models and limiting the ability to fine-tune them. Given a corpus of formulas, we can use a(nother) model to generate synthetic natural language utterances for fine-tuning. However, it is important to validate whether the NL generated by the LLM is indeed accurate to be beneficial for fine-tuning. In this paper, we provide empirical results on the impact of validating these synthetic training examples with surrogate objectives that evaluate the accuracy of the synthetic annotations. We demonstrate that validation improves performance over raw data across four models (2 open and 2 closed weight). Interestingly, we show that although validation tends to prune more challenging examples, it increases the complexity of problems that models can solve after being fine-tuned on validated data.

In this paper, we study the connectedness of the commuting graph of a general Lie algebra and provide a process to determine whether the commuting graph is connected or not, as well as to compute an upper bound for its diameter. In addition, we will examine the connectedness and diameter of the commuting graphs of some remarkable classes of Lie algebras, including: (1) a class of Lie algebras with one- or two-dimensional derived algebras; and (2) a class of solvable Lie algebras over the real field of dimension up to $4$., Comment: 21 pages

Automated insight generation is a common tactic for helping knowledge workers, such as data scientists, to quickly understand the potential value of new and unfamiliar data. Unfortunately, automated insights produced by large-language models can generate code that does not correctly correspond (or align) to the insight. In this paper, we leverage the semantic knowledge of large language models to generate targeted and insightful questions about data and the corresponding code to answer those questions. Then through an empirical study on data from Open-WikiTable, we show that embeddings can be effectively used for filtering out semantically unaligned pairs of question and code. Additionally, we found that generating questions and code together yields more diverse questions.

Large language models (LLMs) are rapidly replacing help forums like StackOverflow, and are especially helpful for non-professional programmers and end users. These users are often interested in data-centric tasks, such as spreadsheet manipulation and data wrangling, which are hard to solve if the intent is only communicated using a natural-language description, without including the data. But how do we decide how much data and which data to include in the prompt? This paper makes two contributions towards answering this question. First, we create a dataset of real-world NL-to-code tasks manipulating tabular data, mined from StackOverflow posts. Second, we introduce a cluster-then-select prompting technique, which adds the most representative rows from the input data to the LLM prompt. Our experiments show that LLM performance is indeed sensitive to the amount of data passed in the prompt, and that for tasks with a lot of syntactic variation in the input table, our cluster-then-select technique outperforms a random selection baseline., Comment: Paper accepted to NAACL 2024 (Findings)

Multi-modality promises to unlock further uses for large language models. Recently, the state-of-the-art language model GPT-4 was enhanced with vision capabilities. We carry out a prompting evaluation of GPT-4V and five other baselines on structured reasoning tasks, such as mathematical reasoning, visual data analysis, and code generation. We show that visual Chain-of-Thought, an extension of Chain-of-Thought to multi-modal LLMs, yields significant improvements over the vanilla model. We also present a categorized analysis of scenarios where these models perform well and where they struggle, highlighting challenges associated with coherent multimodal reasoning., Comment: 9 pages, 9 figures

Most face identification approaches employ a Siamese neural network to compare two images at the image embedding level. Yet, this technique can be subject to occlusion (e.g. faces with masks or sunglasses) and out-of-distribution data. DeepFace-EMD (Phan et al. 2022) reaches state-of-the-art accuracy on out-of-distribution data by first comparing two images at the image level, and then at the patch level. Yet, its later patch-wise re-ranking stage admits a large $O(n^3 \log n)$ time complexity (for $n$ patches in an image) due to the optimal transport optimization. In this paper, we propose a novel, 2-image Vision Transformers (ViTs) that compares two images at the patch level using cross-attention. After training on 2M pairs of images on CASIA Webface (Yi et al. 2014), our model performs at a comparable accuracy as DeepFace-EMD on out-of-distribution data, yet at an inference speed more than twice as fast as DeepFace-EMD (Phan et al. 2022). In addition, via a human study, our model shows promising explainability through the visualization of cross-attention. We believe our work can inspire more explorations in using ViTs for face identification., Comment: 20 pages, 15 Figures

Imagine a developer who can only change their last line of code, how often would they have to start writing a function from scratch before it is correct? Auto-regressive models for code generation from natural language have a similar limitation: they do not easily allow reconsidering earlier tokens generated. We introduce CodeFusion, a pre-trained diffusion code generation model that addresses this limitation by iteratively denoising a complete program conditioned on the encoded natural language. We evaluate CodeFusion on the task of natural language to code generation for Bash, Python, and Microsoft Excel conditional formatting (CF) rules. Experiments show that CodeFusion (75M parameters) performs on par with state-of-the-art auto-regressive systems (350M-175B parameters) in top-1 accuracy and outperforms them in top-3 and top-5 accuracy due to its better balance in diversity versus quality., Comment: Contains inappropriately sourced conjecture of OpenAI's ChatGPT parameter count from www.forbes.com/sites/forbestechcouncil/2023/02/17/is-bigger-better-why-the-chatgpt-vs-gpt-3-vs-gpt-4-battle-is-just-a-family-chat, a citation which was omitted. The authors do not have direct knowledge or verification of this information, and relied solely on this article, which may lead to public confusion

Formatting is an important property in tables for visualization, presentation, and analysis. Spreadsheet software allows users to automatically format their tables by writing data-dependent conditional formatting (CF) rules. Writing such rules is often challenging for users as it requires them to understand and implement the underlying logic. We present FormaT5, a transformer-based model that can generate a CF rule given the target table and a natural language description of the desired formatting logic. We find that user descriptions for these tasks are often under-specified or ambiguous, making it harder for code generation systems to accurately learn the desired rule in a single step. To tackle this problem of under-specification and minimise argument errors, FormaT5 learns to predict placeholders though an abstention objective. These placeholders can then be filled by a second model or, when examples of rows that should be formatted are available, by a programming-by-example system. To evaluate FormaT5 on diverse and real scenarios, we create an extensive benchmark of 1053 CF tasks, containing real-world descriptions collected from four different sources. We release our benchmarks to encourage research in this area. Abstention and filling allow FormaT5 to outperform 8 different neural approaches on our benchmarks, both with and without examples. Our results illustrate the value of building domain-specific learning systems., Comment: Contains inappropriately sourced conjecture of OpenAI's ChatGPT parameter count from www.forbes.com/sites/forbestechcouncil/2023/02/17/is-bigger-better-why-the-chatgpt-vs-gpt-3-vs-gpt-4-battle-is-just-a-family-chat, a citation which was omitted. The authors do not have direct knowledge or verification of this information, and relied solely on this article, which may lead to public confusion

Target similarity tuning (TST) is a method of selecting relevant examples in natural language (NL) to code generation through large language models (LLMs) to improve performance. Its goal is to adapt a sentence embedding model to have the similarity between two NL inputs match the similarity between their associated code outputs. In this paper, we propose different methods to apply and improve TST in the real world. First, we replace the sentence transformer with embeddings from a larger model, which reduces sensitivity to the language distribution and thus provides more flexibility in synthetic generation of examples, and we train a tiny model that transforms these embeddings to a space where embedding similarity matches code similarity, which allows the model to remain a black box and only requires a few matrix multiplications at inference time. Second, we show how to efficiently select a smaller number of training examples to train the TST model. Third, we introduce a ranking-based evaluation for TST that does not require end-to-end code generation experiments, which can be expensive to perform., Comment: Accepted for EMNLP-Findings, 2023

Large language models (LLMs) are increasingly applied for tabular tasks using in-context learning. The prompt representation for a table may play a role in the LLMs ability to process the table. Inspired by prior work, we generate a collection of self-supervised structural tasks (e.g. navigate to a cell and row; transpose the table) and evaluate the performance differences when using 8 formats. In contrast to past work, we introduce 8 noise operations inspired by real-world messy data and adversarial inputs, and show that such operations can impact LLM performance across formats for different structural understanding tasks.

String data is common in real-world datasets: 67.6% of values in a sample of 1.8 million real Excel spreadsheets from the web were represented as text. Systems that successfully clean such string data can have a significant impact on real users. While prior work has explored errors in string data, proposed approaches have often been limited to error detection or require that the user provide annotations, examples, or constraints to fix the errors. Furthermore, these systems have focused independently on syntactic errors or semantic errors in strings, but ignore that strings often contain both syntactic and semantic substrings. We introduce DataVinci, a fully unsupervised string data error detection and repair system. DataVinci learns regular-expression-based patterns that cover a majority of values in a column and reports values that do not satisfy such patterns as data errors. DataVinci can automatically derive edits to the data error based on the majority patterns and constraints learned over other columns without the need for further user interaction. To handle strings with both syntactic and semantic substrings, DataVinci uses an LLM to abstract (and re-concretize) portions of strings that are semantic prior to learning majority patterns and deriving edits. Because not all data can result in majority patterns, DataVinci leverages execution information from an existing program (which reads the target data) to identify and correct data repairs that would not otherwise be identified. DataVinci outperforms 7 baselines on both error detection and repair when evaluated on 4 existing and new benchmarks., Comment: 13 pages

Data management and analysis tasks are often carried out using spreadsheet software. A popular feature in most spreadsheet platforms is the ability to define data-dependent formatting rules. These rules can express actions such as "color red all entries in a column that are negative" or "bold all rows not containing error or failure." Unfortunately, users who want to exercise this functionality need to manually write these conditional formatting (CF) rules. We introduce CORNET, a system that automatically learns such conditional formatting rules from user examples. CORNET takes inspiration from inductive program synthesis and combines symbolic rule enumeration, based on semi-supervised clustering and iterative decision tree learning, with a neural ranker to produce accurate conditional formatting rules. In this demonstration, we show CORNET in action as a simple add-in to Microsoft Excel. After the user provides one or two formatted cells as examples, CORNET generates formatting rule suggestions for the user to apply to the spreadsheet., Comment: 4 Pages, VLDB 2023 Demonstration Track

We advance the Cohn-Umans framework for developing fast matrix multiplication algorithms. We introduce, analyze, and search for a new subclass of strong uniquely solvable puzzles (SUSP), which we call simplifiable SUSPs. We show that these puzzles are efficiently verifiable, which remains an open question for general SUSPs. We also show that individual simplifiable SUSPs can achieve the same strength of bounds on the matrix multiplication exponent $\omega$ that infinite families of SUSPs can. We report on the construction, by computer search, of larger SUSPs than previously known for small width. This, combined with our tighter analysis, strengthens the upper bound on the matrix multiplication exponent from $2.66$ to $2.505$ obtainable via this computational approach, and nears the results of the handcrafted constructions of Cohn et al., Comment: 21 pages, 1 figure, 1 table

Automation platforms aim to automate repetitive tasks using workflows, which start with a trigger and then perform a series of actions. However, with many possible actions, the user has to search for the desired action at each step, which hinders the speed of flow development. We propose a personalized transformer model that recommends the next item at each step. This personalization is learned end-to-end from user statistics that are available at inference time. We evaluated our model on workflows from Power Automate users and show that personalization improves top-1 accuracy by 22%. For new users, our model performs similar to a model trained without personalization., Comment: 4 pages, Accepted at ICSE 2023

Creating programs to correctly manipulate data is a difficult task, as the underlying programming languages and APIs can be challenging to learn for many users who are not skilled programmers. Large language models (LLMs) demonstrate remarkable potential for generating code from natural language, but in the data manipulation domain, apart from the natural language (NL) description of the intended task, we also have the dataset on which the task is to be performed, or the "data context". Existing approaches have utilized data context in a limited way by simply adding relevant information from the input data into the prompts sent to the LLM. In this work, we utilize the available input data to execute the candidate programs generated by the LLMs and gather their outputs. We introduce semantic reranking, a technique to rerank the programs generated by LLMs based on three signals coming the program outputs: (a) semantic filtering and well-formedness based score tuning: do programs even generate well-formed outputs, (b) semantic interleaving: how do the outputs from different candidates compare to each other, and (c) output-based score tuning: how do the outputs compare to outputs predicted for the same task. We provide theoretical justification for semantic interleaving. We also introduce temperature mixing, where we combine samples generated by LLMs using both high and low temperatures. We extensively evaluate our approach in three domains, namely databases (SQL), data science (Pandas) and business intelligence (Excel's Power Query M) on a variety of new and existing benchmarks. We observe substantial gains across domains, with improvements of up to 45% in top-1 accuracy and 34% in top-3 accuracy., Comment: 14 pages

Spreadsheets are a vital tool for end-user data management. Using large language models for formula authoring assistance in these environments can be difficult, as these models are expensive to train and challenging to deploy due to their size (up to billions of parameters). We present FLAME, a transformer-based model trained exclusively on Excel formulas that leverages domain insights to achieve competitive performance while being substantially smaller (60M parameters) and training on two orders of magnitude less data. We curate a training dataset using sketch deduplication, introduce an Excel-specific formula tokenizer, and use domain-specific versions of masked span prediction and noisy auto-encoding as pre-training objectives. We evaluate FLAME on formula repair, formula completion, and similarity-based formula retrieval. FLAME can outperform much larger models, such as the Davinci (175B) and Cushman (12B) variants of Codex and CodeT5 (220M), in 10 of 14 evaluation settings for the repair and completion tasks. For formula retrieval, FLAME outperforms CodeT5, CodeBERT, and GraphCodeBERT., Comment: Accepted to AAAI 2024

Students often make mistakes on their introductory programming assignments as part of their learning process. Unfortunately, providing custom repairs for these mistakes can require a substantial amount of time and effort from class instructors. Automated program repair (APR) techniques can be used to synthesize such fixes. Prior work has explored the use of symbolic and neural techniques for APR in the education domain. Both types of approaches require either substantial engineering efforts or large amounts of data and training. We propose to use a large language model trained on code, such as Codex, to build an APR system -- MMAPR -- for introductory Python programming assignments. Our system can fix both syntactic and semantic mistakes by combining multi-modal prompts, iterative querying, test-case-based selection of few-shots, and program chunking. We evaluate MMAPR on 286 real student programs and compare to a baseline built by combining a state-of-the-art Python syntax repair engine, BIFI, and state-of-the-art Python semantic repair engine for student assignments, Refactory. We find that MMAPR can fix more programs and produce smaller patches on average.

Most programmers make mistakes when writing code. Some of these mistakes are small and require few edits to the original program -- a class of errors recently termed last mile mistakes. These errors break the flow for experienced developers and can stump novice programmers. Existing automated repair techniques targeting this class of errors are language-specific and do not easily carry over to new languages. Transferring symbolic approaches requires substantial engineering and neural approaches require data and retraining. We introduce RING, a multilingual repair engine powered by a large language model trained on code (LLMC) such as Codex. Such a multilingual engine enables a flipped model for programming assistance, one where the programmer writes code and the AI assistance suggests fixes, compared to traditional code suggestion technology. Taking inspiration from the way programmers manually fix bugs, we show that a prompt-based strategy that conceptualizes repair as localization, transformation, and candidate ranking, can successfully repair programs in multiple languages with minimal effort. We present the first results for such a multilingual repair engine by evaluating on 6 different languages and comparing performance to language-specific repair engines. We show that RING can outperform language-specific repair engines for three of these languages., Comment: 13 pages, Accepted at AAAI 2023

We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometric description of the maximal-dimensional orbits in the coadjoint representation of all considered Lie groups. Next, we prove that, for each considered group, the family of the generic coadjoint orbits forms a measurable foliation in the sense of Connes. Finally, the topological classification of all these foliations is also provided., Comment: 33 pages. arXiv admin note: text overlap with arXiv:2107.09956

Spreadsheets are widely used for table manipulation and presentation. Stylistic formatting of these tables is an important property for both presentation and analysis. As a result, popular spreadsheet software, such as Excel, supports automatically formatting tables based on rules. Unfortunately, writing such formatting rules can be challenging for users as it requires knowledge of the underlying rule language and data logic. We present CORNET, a system that tackles the novel problem of automatically learning such formatting rules from user examples in the form of formatted cells. CORNET takes inspiration from advances in inductive programming and combines symbolic rule enumeration with a neural ranker to learn conditional formatting rules. To motivate and evaluate our approach, we extracted tables with over 450K unique formatting rules from a corpus of over 1.8M real worksheets. Since we are the first to introduce conditional formatting, we compare CORNET to a wide range of symbolic and neural baselines adapted from related domains. Our results show that CORNET accurately learns rules across varying evaluation setups. Additionally, we show that CORNET finds shorter rules than those that a user has written and discovers rules in spreadsheets that users have manually formatted., Comment: 12 pages content, 2 pages references

We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of MD-algebras., Comment: 21 pages

Most users of low-code platforms, such as Excel and PowerApps, write programs in domain-specific formula languages to carry out nontrivial tasks. Often users can write most of the program they want, but introduce small mistakes that yield broken formulas. These mistakes, which can be both syntactic and semantic, are hard for low-code users to identify and fix, even though they can be resolved with just a few edits. We formalize the problem of producing such edits as the last-mile repair problem. To address this problem, we developed LaMirage, a LAst-MIle RepAir-engine GEnerator that combines symbolic and neural techniques to perform last-mile repair in low-code formula languages. LaMirage takes a grammar and a set of domain-specific constraints/rules, which jointly approximate the target language, and uses these to generate a repair engine that can fix formulas in that language. To tackle the challenges of localizing the errors and ranking the candidate repairs, LaMirage leverages neural techniques, whereas it relies on symbolic methods to generate candidate repairs. This combination allows LaMirage to find repairs that satisfy the provided grammar and constraints, and then pick the most natural repair. We compare LaMirage to state-of-the-art neural and symbolic approaches on 400 real Excel and PowerFx formulas, where LaMirage outperforms all baselines. We release these benchmarks to encourage subsequent work in low-code domains.

Large pre-trained language models have been used to generate code,providing a flexible interface for synthesizing programs from natural language specifications. However, they often violate syntactic and semantic rules of their output language, limiting their practical usability. In this paper, we propose Synchromesh: a framework for substantially improving the reliability of pre-trained models for code generation. Synchromesh comprises two components. First, it retrieves few-shot examples from a training bank using Target Similarity Tuning (TST), a novel method for semantic example selection. TST learns to recognize utterances that describe similar target programs despite differences in surface natural language features. Then, Synchromesh feeds the examples to a pre-trained language model and samples programs using Constrained Semantic Decoding (CSD): a general framework for constraining the output to a set of valid programs in the target language. CSD leverages constraints on partial outputs to sample complete correct programs, and needs neither re-training nor fine-tuning of the language model. We evaluate our methods by synthesizing code from natural language descriptions using GPT-3 and Codex in three real-world languages: SQL queries, Vega-Lite visualizations and SMCalFlow programs. These domains showcase rich constraints that CSD is able to enforce, including syntax, scope, typing rules, and contextual logic. We observe substantial complementary gains from CSD and TST in prediction accuracy and in effectively preventing run-time errors., Comment: 10 pages, 9 additional pages of Appendix

Multi-modal program synthesis refers to the task of synthesizing programs (code) from their specification given in different forms, such as a combination of natural language and examples. Examples provide a precise but incomplete specification, and natural language provides an ambiguous but more "complete" task description. Machine-learned pre-trained models (PTMs) are adept at handling ambiguous natural language, but struggle with generating syntactically and semantically precise code. Program synthesis techniques can generate correct code, often even from incomplete but precise specifications, such as examples, but they are unable to work with the ambiguity of natural languages. We present an approach that combines PTMs with component-based synthesis (CBS): PTMs are used to generate candidates programs from the natural language description of the task, which are then used to guide the CBS procedure to find the program that matches the precise examples-based specification. We use our combination approach to instantiate multi-modal synthesis systems for two programming domains: the domain of regular expressions and the domain of CSS selectors. Our evaluation demonstrates the effectiveness of our domain-agnostic approach in comparison to a state-of-the-art specialized system, and the generality of our approach in providing multi-modal program synthesis from natural language and examples in different programming domains., Comment: To be published in OOPSLA 2021

This paper presents a classification of 7-dimensional real and complex indecomposable solvable Lie algebras having some 5-dimensional nilradicals. Afterwards, we combine our results with those of Rubin and Winternitz (1993), Ndogmo and Winternitz (1994), Snobl and Winternitz (2005, 2009), Snobl and Kar\'asek (2010) to obtain a complete classification of 7-dimensional real and complex indecomposable solvable Lie algebras with 5-dimensional nilradicals. In association with Gong (1998), Parry (2007), Hindeleh and Thompson (2008), we achieve a classification of 7-dimensional real and complex indecomposable solvable Lie algebras., Comment: 24 pages, 3 talbles

Let {\Lnk} be the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideals. In 2020 the authors et al. gave a classification of all non 2-step nilpotent Lie algebras of {\Li}. We propose in this paper to study representations of these Lie algebras as well as their corresponding connected and simply connected Lie groups. That is, for each algebra, we give an upper bound of the minimal degree of a faithful representation. Then, we give a geometrical description of coadjoint orbits of corresponding groups. Moreover, we show that the characteristic property of the family of maximal dimensional coadjoint orbits of a MD-group studied by K. P. Shum and the second author et al. is still true for the Lie groups considered here. Namely, we prove that, for each considered group, the family of the maximal dimensional coadjoint orbits forms a measurable foliation in the sense of Connes. The topological classification of these foliations is also provided., Comment: 25 pages

Forking structure is widespread in the open-source repositories and that causes a significant number of merge conflicts. In this paper, we study the problem of textual merge conflicts from the perspective of Microsoft Edge, a large, highly collaborative fork off the main Chromium branch with significant merge conflicts. Broadly, this study is divided into two sections. First, we empirically evaluate textual merge conflicts in Microsoft Edge and classify them based on the type of files, location of conflicts in a file, and the size of conflicts. We found that ~28% of the merge conflicts are 1-2 line changes, and many resolutions have frequent patterns. Second, driven by these findings, we explore Program Synthesis (for the first time) to learn patterns and resolve structural merge conflicts. We propose a novel domain-specific language (DSL) that captures many of the repetitive merge conflict resolution patterns and learn resolution strategies as programs in this DSL from example resolutions. We found that the learned strategies can resolve 11.4% of the conflicts (~41% of 1-2 line changes) that arise in the C++ files with 93.2% accuracy., Comment: Accepted at ICSE 2021

In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic relations of parameters in order to decide whether two parameterized Lie algebras are isomorphic. All of the considered Lie algebras are considered over a field $\F$, where $\F=\C$ or $\F=\R$. Several illustrative examples are given to show the applicability and the effectiveness of the proposed algorithms., Comment: 14 pages, 1 figure

This paper concerns the problem of classifying finite-dimensional real solvable Lie algebras whose derived algebras are of codimension 1 or 2. On the one hand, we present an effective method to classify all $(n+1)$-dimensional real solvable Lie algebras having 1-codimensional derived algebras provided that a full classification of $n$-dimensional nilpotent Lie algebras is given. On the other hand, the problem of classifying all $(n+2)$-dimensional real solvable Lie algebras having 2-codimensional derived algebras is proved to be wild. In this case, we provide a method to classify a subclass of the considered Lie algebras which are extended from their derived algebras by a pair of derivations containing at least one inner derivation.

Let $\mathrm{Lie} \left(n, k\right)$ denote the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideal ($1 \leqslant k \leqslant n-1$). In 1993, the class $\mathrm{Lie} \left(n, 1\right)$ was completely classified by Sch\"obel \cite{Sch93}. In 2016, Vu A. Le et al. \cite{VHTHT16} considered the class $\mathrm{Lie} \left(n, n-1\right)$ and classified its subclass containing all the algebras having 1-codimensional commutative derived ideal. One subclass in {\Li} was firstly considered and incompletely classified by Sch\"obel \cite{Sch93} in 1993. Later, Janisse also gave an incomplete classification of {\Li} and published as a scientific report \cite{Jan10} in 2010. In this paper, we set up a new approach to study the classifying problem of classes {\Li} as well as {\li} and present the new complete classification of {\Li} in the combination with the well-known Eberlein's result of 2-step nilpotent Lie algebras from \cite[p.\,37--72]{Ebe03}. The paper will also classify a subclass of {\li} and will point out missings in Sch\"obel \cite{Sch93}, Janisse \cite{Jan10}, Mubarakzyanov \cite{Mub63a} as well as revise an error of Morozov \cite{Mor58}., Comment: 33 pages, 5 talbles

Program synthesis from incomplete specifications (e.g. input-output examples) has gained popularity and found real-world applications, primarily due to its ease-of-use. Since this technology is often used in an interactive setting, efficiency and correctness are often the key user expectations from a system based on such technologies. Ensuring efficiency is challenging since the highly combinatorial nature of program synthesis algorithms does not fit in a 1-2 second response expectation of a user-facing system. Meeting correctness expectations is also difficult, given that the specifications provided are incomplete, and that the users of such systems are typically non-programmers. In this paper, we describe how interactivity can be leveraged to develop efficient synthesis algorithms, as well as to decrease the cognitive burden that a user endures trying to ensure that the system produces the desired program. We build a formal model of user interaction along three dimensions: incremental algorithm, step-based problem formulation, and feedback-based intent refinement. We then illustrate the effectiveness of each of these forms of interactivity with respect to synthesis performance and correctness on a set of real-world case studies.

The tunability of an optical cavity is an essential requirement for many areas of research. Here, we use the Pound-Drever-Hall technique to lock a laser to a whispering gallery mode (WGM) of a microbubble resonator, to show that linear tuning of the WGM, and the corresponding locked laser, display almost zero hysteresis. By applying aerostatic pressure to the interior surface of the microbubble resonator, optical mode shift rates of around $58$ GHz/MPa are achieved. The microbubble can measure pressure with a detection limit of $2\times 10^{-4}$ MPa, which is an improvement made on pressure sensing using this device. The long-term frequency stability of this tuning method for different input pressures is measured. The frequency noise of the WGM measured over $10$ minutes for an input pressure of $0.5$ MPa, has a maximum standard deviation of $36$ MHz., Comment: 5 pages, 4 figures

Dissipative optomechanics has some advantages in cooling compared to the conventional dispersion dominated systems. Here, we study the optical response of a cantilever-like, silica, microsphere pendulum, evanescently coupled to a fiber taper. In a whispering gallery mode resonator the cavity mode and motion of the pendulum result in both dispersive and dissipative optomechanical interactions. This unique mechanism leads to an experimentally observable, asymmetric response function of the transduction spectrum which can be explained using coupled-mode theory. The optomechanical transduction, and its relationship to the external coupling gap, are investigated and we show that the experimental behavior is in good agreement with the theoretical predictions. A deep understanding of this mechanism is necessary to explore trapping and cooling in dissipative optomechanical systems., Comment: 5 pages

We review the method of producing adiabatic optical micro- and nanofibers using a hydrogen/oxygen flame brushing technique. The flame is scanned along the fiber, which is being simultaneously stretched by two translation stages. The tapered fiber fabrication is reproducible and yields highly adiabatic tapers with either exponential or linear profiles. Details regarding the setup of the flame brushing rig and the various parameters used are presented. Information available from the literature is compiled and further details that are necessary to have a functioning pulling rig are included. This should enable the reader to fabricate various taper profiles, while achieving adiabatic transmission of ~ 99% for fundamental mode propagation. Using this rig, transmissions ranging from 85-95% for higher order modes in an optical nanofiber have been obtained.