Jonathan Laurent

We propose a new approach to automated theorem proving where an AlphaZero- style agent is self-training to refine a generic high-level expert strategy expressed as a nondeterministic program. An analogous teacher agent is self-training to generate tasks of suitable relevance and difficulty for the learner. This allows leveraging minimal amounts of domain knowledge to tackle problems for which training data is unavailable or hard to synthesize. As a specific illustration, we consider loop invariant synthesis for imperative programs and use neural networks to refine both the teacher and solver strategies.

Models based on rules that express local and heterogeneous mechanisms of stochastic interactions between structured agents are an important tool for investigating the dynamical behavior of complex systems, especially in molecular biology. Given a simulated trace of events, the challenge is to construct a causal diagram that explains how a phenomenon of interest occurred. Counterfactual analysis can provide distinctive insights, but its standard definition is not applicable in rule-based models because they are not readily expressible in terms of structural equations. We provide a semantics of counterfactual statements that addresses this challenge by sampling counterfactual trajectories that are probabilistically as close to the factual trace as a given intervention permits them to be. We then show how counterfactual dependencies give rise to explanations in terms of relations of enablement and prevention between events.