Related papers: From Euler to AI: Unifying Formulas for Mathematic…
Visuals are valuable tools for teaching math word problems (MWPs), helping young learners interpret textual descriptions into mathematical expressions before solving them. However, creating such visuals is labor-intensive and there is a…
Mathematical reasoning is essential for problem-solving in education, science, and industry, serving as a crucial benchmark for evaluating artificial intelligence systems. As Large Language Models (LLMs) improve their reasoning…
We show that the discrete complex, and numerous hypercomplex, Fourier transforms defined and used so far by a number of researchers can be unified into a single framework based on a matrix exponential version of Euler's formula…
Artificial intelligence (AI) is transforming the practice of science. Machine learning and large language models (LLMs) can generate hypotheses at a scale and speed far exceeding traditional methods, offering the potential to accelerate…
A fundamental problem in robotic perception is matching identical objects or data, with applications such as loop closure detection, place recognition, object tracking, and map fusion. While the problem becomes considerably more challenging…
Unlabeled data are increasingly prevalent in contemporary economic studies, yet their effective use for improving prediction remains challenging because the outcomes are often costly or even infeasible to observe. Machine learning methods…
With the availability of virtually infinite number text documents in digital format, automatic comparison of textual data is essential for extracting meaningful insights that are difficult to identify manually. Many existing tools,…
An applied problem facing all areas of data science is harmonizing data sources. Joining data from multiple origins with unmapped and only partially overlapping features is a prerequisite to developing and testing robust, generalizable…
Two linear recurrences exhibit mirror symmetry connecting the constants $e$ and $\pi$. When parametrized, their asymptotic connection constants extend to meromorphic functions satisfying additive functional equations with rational…
Interactive theorem provers (ITPs) require manual formalization, which is labor-intensive and demands expert knowledge. While automated formalization offers a potential solution, it faces two major challenges: model hallucination (e.g.,…
Large-enrollment university courses face persistent challenges in providing timely and scalable instructional support. While generative AI holds promise, its effective use depends on reliability and pedagogical alignment. We present a…
Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the…
Let $T$ be the triangle with vertices (1,0), (0,1), (1,1). We study certain integrals over $T$, one of which was computed by Euler. We give expressions for them both as a linear combination of multiple zeta values, and as a polynomial in…
Scientists have developed hundreds of techniques to measure the interactions between pairs of processes in complex systems. But these computational methods, from correlation coefficients to causal inference, rely on distinct quantitative…
Large language models have shown impressive capabilities in code generation, yet they often produce functionally incorrect code. Uncertainty quantification (UQ) methods have emerged as a promising approach for detecting hallucinations in…
Large language models (LLMs) often produce confident yet incorrect responses, and uncertainty quantification is one potential solution to more robust usage. Recent works routinely rely on self-consistency to estimate aleatoric uncertainty…
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundamental computations in this field are persistent homology and…
We present results for some infinite series appearing in Feynman diagram calculations, many of which are similar to the Euler series. These include both one-dimensional and two-dimensional series. Most of these series can be expressed in…
Unified multimodal models aim to jointly enable visual understanding and generation, yet current benchmarks rarely examine their true integration. Existing evaluations either treat the two abilities in isolation or overlook tasks that…
Autoformalization, the task of automatically translating natural language descriptions into a formal language, poses a significant challenge across various domains, especially in mathematics. Recent advancements in large language models…