Related papers: Twitch: Learning Abstractions for Equational Theor…

Convex polyhedral abstractions of logic programs have been found very useful in deriving numeric relationships between program arguments in order to prove program properties and in other areas such as termination and complexity analysis. We…

The idea of assisting teachers with technological tools is not new. Mathematics in general, and geometry in particular, provide interesting challenges when developing educative softwares, both in the education and computer science aspects.…

Conventional closed-world information extraction (IE) approaches rely on human ontologies to define the scope for extraction. As a result, such approaches fall short when applied to new domains. This calls for systems that can automatically…

Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…

Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good…

We study the utility of incorporating entity type abstractions into pre-trained Transformers and test these methods on four NLP tasks requiring different forms of logical reasoning: (1) compositional language understanding with text-based…

Automated techniques for rigorous floating-point round-off error analysis are important in areas including formal verification of correctness and precision tuning. Existing tools and techniques, while providing tight bounds, fail to analyze…

General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might…

Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…

In many real-world problems, the learning agent needs to learn a problem's abstractions and solution simultaneously. However, most such abstractions need to be designed and refined by hand for different problems and domains of application.…

There has been a gap between artificial intelligence and human intelligence. In this paper, we identify three key elements forming human intelligence, and suggest that abstraction learning combines these elements and is thus a way to bridge…

Tracking developments in the highly dynamic data-technology landscape are vital to keeping up with novel technologies and tools, in the various areas of Artificial Intelligence (AI). However, It is difficult to keep track of all the…

We present an unsupervised approach for discovering semantic representations of mathematical equations. Equations are challenging to analyze because each is unique, or nearly unique. Our method, which we call equation embeddings, finds good…

Humans are capable of abstracting away irrelevant details when studying problems. This is especially noticeable for problems over grid-cells, as humans are able to disregard certain parts of the grid and focus on the key elements important…

Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…

While long, explicit chains-of-thought (CoT) have proven effective on complex reasoning tasks, they are costly to generate during inference. Non-verbal reasoning methods have emerged with shorter generation lengths by leveraging continuous…

We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…

Finding the best mathematical equation to deal with the different challenges found in complex scenarios requires a thorough understanding of the scenario and a trial and error process carried out by experts. In recent years, most…

Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training…

Large Language Models (LLMs) excel at reasoning and planning when trained on chainof-thought (CoT) data, where the step-by-step thought process is explicitly outlined by text tokens. However, this results in lengthy inputs where many words…