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Large language models (LLMs) achieve impressive performance on complex mathematical benchmarks yet sometimes fail on basic math reasoning while generating unnecessarily verbose responses. In this paper, we present LLMThinkBench, a…
The ubiquity of neural networks (NNs) in real-world applications, from healthcare to natural language processing, underscores their immense utility in capturing complex relationships within high-dimensional data. However, NNs come with…
Recently, deep Convolutional Neural Networks (CNNs) have proven to be successful when employed in areas such as reduced order modeling of parametrized PDEs. Despite their accuracy and efficiency, the approaches available in the literature…
The programming capabilities of large language models (LLMs) have revolutionized automatic code generation and opened new avenues for automatic statistical analysis. However, the validity and quality of these generated codes need to be…
Scientific software relies on high-precision computation, yet finite floating-point representations can introduce precision errors that propagate in safety-critical domains. Despite the growing use of large language models (LLMs) in…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
Systematic reviews and meta-analyses rely on converting narrative articles into structured, numerically grounded study records. Despite rapid advances in large language models (LLMs), it remains unclear whether they can meet the structural…
Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by…
Existing anomaly detection (AD) methods for tabular data usually rely on some assumptions about anomaly patterns, leading to inconsistent performance in real-world scenarios. While Large Language Models (LLMs) show remarkable reasoning…
Multivariate time-series forecasting is vital in various domains, e.g., economic planning and weather prediction. Deep train-from-scratch models have exhibited effective performance yet require large amounts of data, which limits real-world…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
Linear algebra expressions, which play a central role in countless scientific computations, are often computed via a sequence of calls to existing libraries of building blocks (such as those provided by BLAS and LAPACK). A sequence…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Logically constrained rewrite systems (LCTRSs) are a versatile and efficient rewriting formalism that can be used to model programs from various programming paradigms, as well as simplification systems in compilers and SMT solvers. In this…
Function approximation has been an indispensable component in modern reinforcement learning algorithms designed to tackle problems with large state spaces in high dimensions. This paper reviews recent results on error analysis for these…
New Large Language Models (LLMs) become available every few weeks, and modern application developers confronted with the unenviable task of having to decide if they should switch to a new model. While human evaluation remains the gold…
Large Language Models (LLMs) are increasingly utilized in AI-driven educational instruction and assessment, particularly within mathematics education. The capability of LLMs to generate accurate answers and detailed solutions for math…
Recent advances in convolutional neural networks have considered model complexity and hardware efficiency to enable deployment onto embedded systems and mobile devices. For example, it is now well-known that the arithmetic operations of…