Graph Sequence Learning for Premise Selection

Premise selection is crucial for large theory reasoning as the sheer size of the problems quickly leads to resource starvation. This paper proposes a premise selection approach inspired by the domain of image captioning, where language models automatically generate a suitable caption for a given image. Likewise, we attempt to generate the sequence of axioms required to construct the proof of a given problem. This is achieved by combining a pre-trained graph neural network with a language model. We evaluated different configurations of our method and experience a 17.7% improvement gain over the baseline.Comment: 17 page

LUNA: A Model-Based Universal Analysis Framework for Large Language Models

Over the past decade, Artificial Intelligence (AI) has had great success recently and is being used in a wide range of academic and industrial fields. More recently, LLMs have made rapid advancements that have propelled AI to a new level, enabling even more diverse applications and industrial domains with intelligence, particularly in areas like software engineering and natural language processing. Nevertheless, a number of emerging trustworthiness concerns and issues exhibited in LLMs have already recently received much attention, without properly solving which the widespread adoption of LLMs could be greatly hindered in practice. The distinctive characteristics of LLMs, such as the self-attention mechanism, extremely large model scale, and autoregressive generation schema, differ from classic AI software based on CNNs and RNNs and present new challenges for quality analysis. Up to the present, it still lacks universal and systematic analysis techniques for LLMs despite the urgent industrial demand. Towards bridging this gap, we initiate an early exploratory study and propose a universal analysis framework for LLMs, LUNA, designed to be general and extensible, to enable versatile analysis of LLMs from multiple quality perspectives in a human-interpretable manner. In particular, we first leverage the data from desired trustworthiness perspectives to construct an abstract model as an auxiliary analysis asset, which is empowered by various abstract model construction methods. To assess the quality of the abstract model, we collect and define a number of evaluation metrics, aiming at both abstract model level and the semantics level. Then, the semantics, which is the degree of satisfaction of the LLM w.r.t. the trustworthiness perspective, is bound to and enriches the abstract model with semantics, which enables more detailed analysis applications for diverse purposes.Comment: 44 pages, 9 figure

MizAR 60 for Mizar 50

As a present to Mizar on its 50th anniversary, we develop an AI/TP system that automatically proves about 60% of the Mizar theorems in the hammer setting. We also automatically prove 75% of the Mizar theorems when the automated provers are helped by using only the premises used in the human-written Mizar proofs. We describe the methods and large-scale experiments leading to these results. This includes in particular the E and Vampire provers, their ENIGMA and Deepire learning modifications, a number of learning-based premise selection methods, and the incremental loop that interleaves growing a corpus of millions of ATP proofs with training increasingly strong AI/TP systems on them. We also present a selection of Mizar problems that were proved automatically