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The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster and more robust than previous algorithms for such problems…
We propose Automatic Curricula via Expert Demonstrations (ACED), a reinforcement learning (RL) approach that combines the ideas of imitation learning and curriculum learning in order to solve challenging robotic manipulation tasks with…
The proofs first generated by automated theorem provers are far from optimal by any measure of simplicity. In this paper I describe a technique for simplifying automated proofs. Hopefully this discussion will stimulate interest in the…
Self-evolving agents should not train on examples they cannot justify. Data-free self-evolving search agents offer a scalable route to systems that generate their own questions, answer them, and improve from their own feedback without human…
Pretrained contextualized embeddings are powerful word representations for structured prediction tasks. Recent work found that better word representations can be obtained by concatenating different types of embeddings. However, the…
Annually, research teams spend large amounts of money to evaluate the quality of machine translation systems (WMT, inter alia). This is expensive because it requires a lot of expert human labor. In the recently adopted annotation protocol,…
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 --…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Accurate auto-formalization of theorem statements is essential for advancing automated discovery and verification of research-level mathematics, yet remains a major bottleneck for LLMs due to hallucinations, semantic mismatches, and their…
The `mathematical language' Automath, conceived by N.G. de Bruijn in 1968, was the first theorem prover actually working and was used for checking many specimina of mathematical content. Its goals and syntactic ideas inspired Th. Coquand…
Entity alignment (EA) for knowledge graphs (KGs) plays a critical role in knowledge engineering. Existing EA methods mostly focus on utilizing the graph structures and entity attributes (including literals), but ignore images that are…
Deep learning and deep architectures are emerging as the best machine learning methods so far in many practical applications such as reducing the dimensionality of data, image classification, speech recognition or object segmentation. In…
This paper describes a general framework for automatic termination analysis of logic programs, where we understand by ``termination'' the finitenes s of the LD-tree constructed for the program and a given query. A general property of…
Diproche ("Didactical Proof Checking") is an automatic system for supporting the acquistion of elementary proving skills in the initial phase of university education in mathematics. A key feature of Diproche - which is designed by the…
Recently, it is often said that the data used for the pre-training of large language models (LLMs) have been exhausted. This paper proposes a solution to the problem: Automated generation of massive reasonable empirical theorems by forward…
Automatic essay grading (AEG) has attracted the the attention of the NLP community because of its applications to several educational applications, such as scoring essays, short answers, etc. AEG systems can save significant time and money…
AI agents increasingly excel at generating, testing, and refining code. However, they fall short on tasks requiring formal guarantees of full coverage that testing alone cannot provide. Distributed systems are a prime example: properties…
Noting that lemmas are a key feature of mathematics, we engage in an investigation of the role of lemmas in automated theorem proving. The paper describes experiments with a combined system involving learning technology that generates…
Machine learning, the foundation of modern artificial intelligence, has driven innovations that have fundamentally transformed the world. Yet, behind advancements lies a complex and often tedious process requiring labor and compute…
Context. In less than a year practitioners and researchers witnessed a rapid and wide implementation of Generative Artificial Intelligence. The daily availability of new models proposed by practitioners and researchers has enabled quick…