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Combinatorial alphabet-dependent bounds for insdel codes

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arXiv 2024年

作者： Kong, Xiangliang Tamo, Itzhak Wei, Hengjia The Department of Electrical Engineering-Systems Tel Aviv University Tel Aviv-Yafo6997801 Israel The Peng Cheng Laboratory Shenzhen518000 China The School of Mathematics and Statistics Xi’an Jiaotong University Xi’an710049 China Guangzhou510555 China

Error-correcting codes resilient to synchronization errors such as insertions and deletions are known as insdel codes. Due to their important applications in DNA storage and computational biology, insdel codes have recently become a focal point of research in coding theory. In this paper, we present several new combinatorial upper and lower bounds on the maximum size of q-ary insdel codes. Our main upper bound is a sphere-packing bound obtained by solving a linear programming (LP) problem. It improves upon previous results for cases when the distance d or the alphabet size q is large. Our first lower bound is derived from a connection between insdel codes and matchings in special hypergraphs. This lower bound, together with our upper bound, shows that for fixed block length n and edit distance d, when q is sufficiently large, the maximum size of insdel codes is (Formula Presented). The second lower bound refines Alon et al.’s recent logarithmic improvement on Levenshtein’s GV-type bound and extends its applicability to large q and *** Codes 05B40, 68P30 Copyright © 2024, The Authors. All rights reserved.

关键词： coding errors

NoteContrast: Contrastive Language-Diagnostic Pretraining for Medical Text

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arXiv 2024年

作者： Kailas, Prajwal Homilius, Max Deo, Rahul C. MacRae, Calum A. Brigham and Women’s Hospital Harvard Medical School United States

Accurate diagnostic coding of medical notes is crucial for enhancing patient care, medical research, and error-free billing in healthcare organizations. Manual coding is a time-consuming task for providers, and diagnostic codes often exhibit low sensitivity and specificity, whereas the free text in medical notes can be a more precise description of a patient’s status. Thus, accurate automated diagnostic coding of medical notes has become critical for a learning healthcare system. Recent developments in long-document transformer architectures have enabled attention-based deep-learning models to adjudicate medical notes. In addition, contrastive loss functions have been used to jointly pre-train large language and image models with noisy labels. To further improve the automated adjudication of medical notes, we developed an approach based on i) models for ICD-10 diagnostic code sequences using a large real-world data set, ii) large language models for medical notes, and iii) contrastive pre-training to build an integrated model of both ICD-10 diagnostic codes and corresponding medical text. We demonstrate that a contrastive approach for pre-training improves performance over prior state-of-the-art models for the MIMIC-III-50, MIMIC-III-rare50, and MIMIC-III-full diagnostic coding tasks. © 2024, CC BY.

关键词： coding errors

The Method of Manufactured Solutions in 3D for the verification of computational electromagnetics.

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The Method of Manufactured Solutions in 3D for the verificat...

IEEE International Symposium on Antennas and Propagation

作者： Renier Marchand David B Davidson Department of Electrical and Electronic Engineering University of Stellenbosch Stellenbosch South Africa

ISBN: (纸本)9781467304610

The Method of Manufactured Solutions is introduced for Computational Electromagnetics in three-dimensions. It is shown by way of Mutation Testing that the method is effective in detecting numerous coding errors. The application of the method to three-dimensions is discussed and meshing relevant to showing theoretical convergence is explained. It is found that certain meshing strategies are more appropriate at initial error assessment and that typical meshing strategies are more appropriate when testing different versions of a code.

关键词： Computational electromagnetics Three Dimensions engaging Verification initial error A CODES coding errors

A test-free semantic mistakes localization framework in Neural Code Translation

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arXiv 2024年

作者： Chen, Lei Zhang, Sai Xu, Fangzhou Zhang, Xiaowang Xing, Zhenchang Wan, Liang Feng, Zhiyong School of Computer Science and Technology Tianjin University Tianjin China CSIRO’s Data61 CSIRO Australia

In the task of code translation, neural network-based models have been shown to frequently produce semantically erroneous code that deviates from the original logic of the source code. This issue persists even with advanced large models. Although a recent approach proposed using test cases to identify these semantic errors, it relies heavily on the quality of the test cases and is not applicable to code snippets without test cases in real-world scenarios. Therefore, We present EISP, a static analysis framework based on the Large Language Model (LLM).First, the framework generates a semantic mapping between source code and translated code. Next, each sub-code fragment is identified by recursively traversing the abstract syntax tree of the source code, and its corresponding translated code fragment is found through the semantic mapping. Finally, EISP connects each pair of sub-code fragments with fine-grained knowledge hints through an AI chain to assist LLMs in discovering semantic mistakes in the translated code. In our benchmark evaluation, the EISP framework, based on GPT-4o mini, achieved an accuracy of 82.3%, representing a 20.3% improvement over baseline methods using the same base model, and a 7.4% improvement compared to dynamic analysis methods that require test cases and manual intervention. To our knowledge, EISP is the first tool to locate semantic errors in translated code without test cases or compilable code. This innovative tool provides the software engineering community with a new way to deal with code fragments without test cases. Copyright © 2024, The Authors. All rights reserved.

关键词： coding errors

Insights from Benchmarking Frontier Language Models on Web App Code Generation

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arXiv 2024年

作者： Cui, Yi ONEKQ Lab.

This paper presents insights from evaluating 16 frontier large language models (LLMs) on the WebApp1K benchmark, a test suite designed to assess the ability of LLMs to generate web application code. The results reveal that while all models possess similar underlying knowledge, their performance is differentiated by the frequency of mistakes they make. By analyzing lines of code (LOC) and failure distributions, we find that writing correct code is more complex than generating incorrect code. Furthermore, prompt engineering shows limited efficacy in reducing errors beyond specific cases. These findings suggest that further advancements in coding LLM should emphasize on model reliability and mistake minimization. © 2024, CC BY.

关键词： coding errors

Quantum LDPC codes from intersecting subsets

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arXiv 2023年

作者： Ostrev, Dimiter Institute of Communications and Navigation Wessling82234 Germany

This paper introduces a construction of quantum CSS codes from a tuple of component CSS codes and two collections of subsets. The resulting codes have parallelizable encoding and syndrome measurement circuits and built-in redundancy in the syndrome measurements. In a certain subfamily of the general construction, the resulting codes are related to a natural generalization of classical Reed-Muller codes, and this leads to formulas for the distance of the quantum code as well as for the distance of the associated classical code that protects against errors in the syndrome. The paper gives a number of examples of codes with block size 2m, m = 3, . . ., 9, and with syndrome measurements involving 2, 4 or 8 qubits. These include codes for which the distance exceeds the syndrome measurement weight, as well as codes which provide asymmetric protection against bit flip and phase flip errors. Copyright © 2023, The Authors. All rights reserved.

关键词： coding errors

Unbounded Error Correcting Codes

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arXiv 2024年

作者： Efremenko, Klim Zamir, Or Ben Gurion University Tel Aviv University

We introduce a variant of Error Correcting Codes with no predetermined length. An Unbounded ECC with rate R and distance Ε is an encoding of a possibly infinite message into a possibly infinite codeword, such that for every large enough k we may recover the first Rk symbols of the message from the first k symbols of the codeword - even when up to 1/2 Εk of these codeword symbols are adversarially corrupted. We study unbounded codes over a binary alphabet in the regime of small distance Ε, and obtain nearly-tight upper and lower bounds in several natural settings. We show that the optimal rate of such a code is between R 1 − O (√Ε log log (1/Ε)). Surprisingly, our construction is non-linear, and we show that the optimal rate of a linear unbounded code is the asymptotically worse R = 1 − Θ (√Ε log (1/Ε) ). In the setting of random noise, the optimal rate of unbounded codes improves and matches the rate of standard codes at R = 1 − Θ(Ε log (1/Ε)). © 2024, CC BY-NC-ND.

关键词： coding errors

Physics simulation capabilities of LLMs

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arXiv 2023年

作者： Ali-Dib, Mohamad Menou, Kristen New York University Abu Dhabi PO Box 129188 United Arab Emirates Physics & Astrophysics Group DPES University of Toronto ScarboroughONM1C 1A4 Canada Department of Astronomy & Astrophysics University of Toronto ONM5S 3H4 Canada Department of Physics University of Toronto ONM5S 1A7 Canada Observatoire de la Cote d’Azur TOP team Laboratoire Lagrange - CNRS Nice France

Large Language Models (LLMs) can solve some undergraduate-level to graduate-level physics textbook problems and are proficient at coding. Combining these two capabilities could one day enable AI systems to simulate and predict the physical world. We present an evaluation of state-of-the-art (SOTA) LLMs on PhD-level to research-level computational physics problems. We condition LLM generation on the use of well-documented and widely-used packages to elicit coding capabilities in the physics and astrophysics domains. We contribute ∼ 50 original and challenging problems in celestial mechanics (with REBOUND), stellar physics (with MESA), 1D fluid dynamics (with Dedalus) and non-linear dynamics (with SciPy). Since our problems do not admit unique solutions, we evaluate LLM performance on several soft metrics: counts of lines that contain different types of errors (coding, physics, necessity and sufficiency) as well as a more ‘educational’ Pass-Fail metric focused on capturing the salient physical ingredients of the problem at hand. As expected, today’s SOTA LLM (GPT4) zero-shot fails most of our problems, although about 40% of the solutions could plausibly get a passing grade. About 70 − 90% of the code lines produced are necessary, sufficient and correct (coding & physics). Physics and coding errors are the most common, with some unnecessary or insufficient lines. We observe significant variations across problem class and difficulty. We identify several failure modes of GPT4 in the computational physics domain, such as poor physical units handling, poor code versioning, tendency to hallucinate plausible sub-modules, lack of physical justification for global run parameters (e.g., simulation time, or upper-lower bounds for parametric exploration) and inability to define steady-state or stopping conditions reliably. Our reconnaissance work provides a snapshot of current computational capabilities in classical physics and points to obvious improvement targets if AI systems

关键词： coding errors

Asymptotically Optimal Codes for (t,s)-Burst Error

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arXiv 2024年

作者： Sun, Yubo Lu, Ziyang Zhang, Yiwei Ge, Gennian School of Mathematical Sciences Capital Normal University Beijing100048 China Key Laboratory of Cryptologic Technology and Information Security Ministry of Education China School of Cyber Science and Technology Shandong University Shandong Qingdao266237 China

Recently, codes for correcting a burst of errors have attracted significant attention. One of the most important reasons is that bursts of errors occur in certain emerging techniques, such as DNA storage. In this paper, we investigate a type of error, called a (t, s)-burst, which deletes t consecutive symbols and inserts s arbitrary symbols at the same coordinate. Note that a (t, s)-burst error can be seen as a generalization of a burst of insertions (t = 0), a burst of deletions (s = 0), and a burst of substitutions (t = s). Our main contribution is to give explicit constructions of q-ary (t, s)-burst correcting codes with log n + O(1) bits of redundancy for any given constant non-negative integers t, s, and q ≥ 2. These codes have optimal redundancy up to an additive constant. Furthermore, we apply our (t, s)-burst correcting codes to combat other various types of errors and improve the corresponding results. In particular, one of our byproducts is a permutation code capable of correcting a burst of t stable deletions with log n + O(1) bits of redundancy, which is optimal up to an additive constant. Copyright © 2024, The Authors. All rights reserved.

关键词： coding errors