Related papers: Mathematics and Coding are Universal AI Benchmarks
In [1], K\"otter and Kschischang presented a new model for error correcting codes in network coding. The alphabet in this model is the subspace lattice of a given vector space, a code is a subset of this lattice and the used metric on this…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
We introduce CODS (Computational Optimization in Design Space), a theoretical model that frames computational design as a constrained optimization problem over a structured, multi-dimensional design space. Unlike existing methods that rely…
Generative AI is gaining increasing attention in software engineering, where testing remains an indispensable reliability mechanism. According to the widely adopted testing pyramid, unit tests constitute the majority of test cases and are…
Logic Artificial Intelligence (AI) is a subfield of AI where variables can take two defined arguments, True or False, and are arranged in clauses that follow the rules of formal logic. Several problems that span from physical systems to…
The increasing deployment of AI is shaping the future landscape of the internet, which is set to become an integrated ecosystem of AI agents. Orchestrating the interaction among AI agents necessitates decentralized, self-sustaining…
Artificial intelligence (AI)-driven fault diagnosis in motor drives often requires significant computational efforts and time for re-training, in addition to the limited knowledge behind the model and suitability of training and learning…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular,…
We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and…
Recent failures such as Google Gemini generating people of color in Nazi-era uniforms illustrate how AI outputs can be factually plausible yet socially harmful. AI models are increasingly evaluated for "fairness," yet existing benchmarks…
For decades, neuroscientists and computer scientists have pursued a shared ambition: to understand intelligence and build it. Modern artificial neural networks now rival humans in language, perception, and reasoning, yet it is still largely…
We consider the matrix composite materials (CM) of either random (statistically homogeneous or inhomogeneous), periodic, or deterministic (neither random nor periodic) structures. CMs exhibit linear or nonlinear behavior, coupled or…
Advances in manufacturing and characterization of complex molecular systems have created a need for new methods for design at molecular length scales. Emerging approaches are increasingly relying on the use of Artificial Intelligence (AI),…
The remarkable performance of modern AI systems has been driven by unprecedented scales of data, computation, and energy -- far exceeding the resources required by human intelligence. This disparity highlights the need for new guiding…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Creating fair AI systems is a complex problem that involves the assessment of context-dependent bias concerns. Existing research and programming libraries express specific concerns as measures of bias that they aim to constrain or mitigate.…
In this study, we conducted a comparative analysis of the automated coding provided by three Artificial Intelligence functionalities (At-las.ti, ChatGPT and Google Bard) in relation to the manual coding of 12 research interviews focused on…