Related papers: Towards Machine Learning Induction
The fundamental challenge in causal induction is to infer the underlying graph structure given observational and/or interventional data. Most existing causal induction algorithms operate by generating candidate graphs and evaluating them…
Recent advances in automated theorem proving use Large Language Models (LLMs) to translate informal mathematical statements into formal proofs. However, informal cues are often ambiguous or lack strict logical structure, making it hard for…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
We study the effectiveness of neural sequence models for premise selection in automated theorem proving, one of the main bottlenecks in the formalization of mathematics. We propose a two stage approach for this task that yields good results…
Imitation learning aims to extract knowledge from human experts' demonstrations or artificially created agents in order to replicate their behaviors. Its success has been demonstrated in areas such as video games, autonomous driving,…
We review the history of the automation of mathematical induction
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
At present, artificial intelligence in the form of machine learning is making impressive progress, especially the field of deep learning (DL) [1]. Deep learning algorithms have been inspired from the beginning by nature, specifically by the…
The no-free-lunch theorems promote a skeptical conclusion that all possible machine learning algorithms equally lack justification. But how could this leave room for a learning theory, that shows that some algorithms are better than others?…
Automated machine learning (AutoML) aims to find optimal machine learning solutions automatically given a machine learning problem. It could release the burden of data scientists from the multifarious manual tuning process and enable the…
New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In…
The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…
Foundational verification considers the functional correctness of programming languages with formalized semantics and uses proof assistants (e.g., Coq, Isabelle) to certify proofs. The need for verifying complex programs compels it to…
Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment…
The development and deployment of systems using supervised machine learning (ML) remain challenging: mainly due to the limited reliability of prediction models and the lack of knowledge on how to effectively integrate human intelligence…
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…
Recent advances in computing have changed not only the nature of mathematical computation, but mathematical proof and inquiry itself. While artificial intelligence and formalized mathematics have been the major topics of this conversation,…
Language models (LMs) can solve tasks such as answering questions about tables or images by writing programs. However, using primitive functions often leads to verbose and error-prone programs, and higher-level functions require expert…
We present automated theorem provers for the first-order logic of here and there (HT). They are based on a native sequent calculus for the logic of HT and an axiomatic embedding of the logic of HT into intuitionistic logic. The analytic…
Learning useful representations with little or no supervision is a key challenge in artificial intelligence. We provide an in-depth review of recent advances in representation learning with a focus on autoencoder-based models. To organize…