Related papers: Mathematics and Coding are Universal AI Benchmarks
Deep models are dominating the artificial intelligence (AI) industry since the ImageNet challenge in 2012. The size of deep models is increasing ever since, which brings new challenges to this field with applications in cell phones,…
This paper demonstrates that artificial intelligence can accelerate mathematical discovery by autonomously solving an open problem in theoretical physics. We present a neuro-symbolic system, combining the Gemini Deep Think large language…
Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…
This study highlights the transparency and accuracy of GenAI's inductive thematic analysis, particularly using GPT-4 Turbo API integrated within a stepwise prompt-based Python script. This approach ensured a traceable and systematic coding…
Predictive coding has emerged as a prominent model of how the brain learns through predictions, anticipating the importance accorded to predictive learning in recent AI architectures such as transformers. Here we propose a new framework for…
Generative AI challenges traditional assessments by allowing students to produce correct answers without demonstrating understanding or reasoning. Rather than prohibiting AI, this work argues that one way to integrate AI into education is…
In the article the problems of the systems of computer mathematics use as a tool for the students learning and research activities support are investigated. The promising ways of providing access to the mathematical software in the…
Humans construct internal cognitive maps of their environment directly from sensory inputs without access to a system of explicit coordinates or distance measurements. While machine learning algorithms like SLAM utilize specialized visual…
Large language models can generate scientific simulation code, but the generated code silently fails on most non-textbook problems. We show that classical mathematical validation -- well-posedness, convergence, and error certification --…
Universal approximation theorems provide a mathematical explanation for the expressive power of neural networks. They assert that, under mild conditions on the activation function, feedforward neural networks are dense in broad function…
Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…
Drori et al. (2022) report that "A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level ... [It] automatically answers 81\% of university-level mathematics…
Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in…
AI co-scientists are emerging as a tool to assist human researchers in achieving their research goals. A crucial feature of these AI co-scientists is the ability to generate a research plan given a set of aims and constraints. The plan may…
This paper addresses the question of how able the current trends of Artificial Intelligence (AI) are in managing to take the responsibility of a full course of mathematics at a college level. The study evaluates this ability in four…
Behavioral analysis of tutoring dialogues is essential for understanding student learning, yet manual coding remains a bottleneck. We present a methodology where LLM coding agents autonomously improve the prompts used by LLM classifiers to…
Based on Alan Turing's proposition on AI and computing machinery, which shaped Computing as we know it today, the new AI computing machinery should comprise a universal computer and a universal learning machine. The later should understand…
We introduce \textbf{Schr\"{o}dinger AI}, a unified machine learning framework inspired by quantum mechanics. The system is defined by three tightly coupled components: (1) a {time-independent wave-energy solver} that treats perception and…
Large language models (LLMs) have seen considerable advancements in natural language understanding tasks, yet there remains a gap to bridge before attaining true artificial general intelligence, especially concerning shortcomings in…
In this paper, a lemma in algebraic coding theory is established, which is frequently appeared in the encoding and decoding for algebraic codes such as Reed-Solomon codes and algebraic geometry codes. This lemma states that two vector…