Related papers: AlephZero and Mathematical Experience
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
Generative AI systems such as ChatGPT have a disruptive effect on learning and assessment. Computer science requires practice to develop skills in problem solving and programming that are traditionally developed using assignments.…
Mathematical research is often motivated by the desire to reach a beautiful result or to prove it in an elegant way. Mathematician's work is thus strongly influenced by his aesthetic judgments. However, the criteria these judgments are…
Defeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computer-aided design models enables faster…
Algorithmic fairness is an expanding field that addresses a range of discrimination issues associated with algorithmic processes. However, most works in the literature focus on analyzing it only from an ethical perspective, focusing on…
The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with…
Research on reasoning in language models (LMs) predominantly focuses on improving the correctness of their outputs. But some important applications require modeling reasoning patterns that are incorrect. For example, automated systems that…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
We investigate the degree to which human plausibility judgments of multiple-choice commonsense benchmark answers are subject to influence by (im)plausibility arguments for or against an answer, in particular, using rationales generated by…
Machine-generated proofs are poised to reach large-scale, human-unreadable artifacts. They foreshadow what we call the Fourth Mathematical Crisis. This crisis crystallizes around three fundamental tensions: trusting proofs that no human can…
Algorithmic fairness has attracted increasing attention in the machine learning community. Various definitions are proposed in the literature, but the differences and connections among them are not clearly addressed. In this paper, we…
The rise of machine learning has brought closer scrutiny to intelligent systems, leading to calls for greater transparency and explainable algorithms. We explore the effects of transparency on user perceptions of a working intelligent…
Multi-round incomplete information tasks are crucial for evaluating the lateral thinking capabilities of large language models (LLMs). Currently, research primarily relies on multiple benchmarks and automated evaluation metrics to assess…
Assisting LLMs with code generation improved their performance on mathematical reasoning tasks. However, the evaluation of code-assisted LLMs is generally restricted to execution correctness, lacking a rigorous evaluation of their generated…
We describe a case of an interplay between human and computer proving which played a role in the discovery of an interesting mathematical result. The unusual feature of the use of computers here was that a computer generated but human…
Mechanical reasoning is a key area of research that lies at the crossroads of mathematical logic and artificial intelligence. The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians…
In this paper, we discuss different models for human logic systems and describe a game with nature. G\"odel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry…
Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…
Artificial intelligence (AI) technology enables a range of enhancements in computer-aided instruction, from accelerating the creation of teaching materials to customizing learning paths based on learner outcomes. However, ensuring the…
AI and ML models have already found many applications in critical domains, such as healthcare and criminal justice. However, fully automating such high-stakes applications can raise ethical or fairness concerns. Instead, in such cases,…