Formal Verification of Machine Learning Models: A Comprehensive Review

In this paper, we explore the concept of definition tasks in theorem proving, a process used to prove mathematical theorems using logical reasoning and argumentation. We delve into the nuances of definition tasks, explaining how they differ from other tasks in the proof hierarchy. Our analysis reveals that defining a task can be likened to naming a person – both are crucial for identification and organization, but they come with unique challenges.
To better understand these challenges, we examine the role of names in definition tasks. Just as names provide context and meaning to people, names in definition tasks help the model distinguish between different concepts and arguments. However, too much reliance on names can lead to an easy definition task for the model, similar to how a person might be given a name that defines their identity without any personal experience or effort.
To address these concerns, we explore alternative approaches to defining tasks, including ideas from self-supervised learning and contrastive learning. These techniques allow the model to learn from the entire graph of interconnected definitions, rather than just focusing on individual definition tasks. By leveraging the power of social networks, these methods can help the model better understand the relationships between different concepts and arguments, leading to more accurate predictions and a stronger foundation for theorem proving.
In conclusion, this paper offers valuable insights into the complex world of definition tasks in theorem proving. By demystifying these concepts and exploring alternative approaches, we can develop more effective methods for automating mathematical reasoning and advancing our understanding of mathematical theorems.