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Despite the advancements in learning governing differential equations from observations of dynamical systems, data-driven methods are often unaware of fundamental physical laws, such as frame invariance. As a result, these algorithms may…
Despite recent advances in modern machine learning algorithms, the opaqueness of their underlying mechanisms continues to be an obstacle in adoption. To instill confidence and trust in artificial intelligence systems, Explainable Artificial…
Maximum Inner Product Search (MIPS) for high-dimensional vectors is pivotal across databases, information retrieval, and artificial intelligence. Existing methods either reduce MIPS to Nearest Neighbor Search (NNS) while suffering from…
We introduce a benchmark to evaluate the capability of AI to solve problems in theoretical physics, focusing on high-energy theory and cosmology. The first iteration of our benchmark consists of 57 problems of varying difficulty, from…
Evaluating the mathematical capability of Large Language Models (LLMs) is a critical yet challenging frontier. Existing benchmarks fall short, particularly for proof-centric problems, as manual creation is unscalable and costly, leaving the…
Using AI to write formal proofs for mathematical problems is a challenging task that has seen some advancements in recent years. Automated systems such as Lean can verify the correctness of proofs written in formal language, yet writing the…
In this paper, we introduce a combination of novel and exciting tasks: the solution and generation of linguistic puzzles. We focus on puzzles used in Linguistic Olympiads for high school students. We first extend the existing benchmark for…
Modern large language models (LLMs) show promising progress in formalizing informal mathematics into machine-verifiable theorems. However, these methods still face bottlenecks due to the limited quantity and quality of multilingual parallel…
As artificial intelligence (AI) increasingly becomes an integral part of our societal and individual activities, there is a growing imperative to develop responsible AI solutions. Despite a diverse assortment of machine learning fairness…
Humans detect real-world object anomalies by perceiving, interacting, and reasoning based on object-conditioned physical knowledge. The long-term goal of Industrial Anomaly Detection (IAD) is to enable machines to autonomously replicate…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
Large Language Models (LLMs) challenge the validity of traditional open-ended assessments by blurring the lines of authorship. While recent research has focused on the accuracy of automated scoring (AES), these static approaches fail to…
Large language models (LLMs) have recently achieved remarkable success in generating rigorous mathematical proofs, with "AI for Math" emerging as a vibrant field of research (Ju et al., 2026). While these models have mastered…
As the complexity of modern workloads and hardware increasingly outpaces human research and engineering capacity, existing methods for database performance optimization struggle to keep pace. To address this gap, a new class of techniques,…
As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier.…
Training large language models for complex reasoning is bottlenecked by the scarcity of verifiable, high-quality data. In domains like physics, standard text augmentation often introduces hallucinations, while static benchmarks lack the…
Olympiad-level physics problem-solving significantly challenges both humans and artificial intelligence (AI), as it requires integrating appropriate modeling, application of physical principles, and precise calculation within long reasoning…
This work presents a generalized implementation of the infeasible primal-dual Interior Point Method (IPM) achieved by the use of non-Archimedean values, i.e., infinite and infinitesimal numbers. The extended version, called here…
We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…