Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of research in Bayesian network structure learning that focuses on weakening the assumption, such as exact search methods with well-defined score functions, they do not scale well to large graphs. In this work, we introduce several strategies to improve the scalability of exact score-based methods in the linear Gaussian setting. In particular, we develop a super-structure estimation method based on the support of inverse covariance matrix which requires assumptions that are strictly weaker than faithfulness, and apply it to restrict the search space of exact search. We also propose a local search strategy that performs exact search on the local clusters formed by each variable and its neighbors within two hops in the superstructure. Numerical experiments validate the efficacy of the proposed procedure, and demonstrate that it scales up to hundreds of nodes with a high accuracy.

We propose a novel approach to interactive theorem proving (ITP) using deep reinforcement learning. The proposed framework is able to learn proof search strategies as well as tactic and arguments prediction in an end-to-end manner. We formulate the process of ITP as a Markov decision process (MDP) in which each state represents a set of potential derivation paths. This structure allows us to introduce a search mechanism which enables the agent to efficiently discard (predicted) dead-end derivations and restart from promising alternatives. We implement the framework in the HOL4 theorem prover. Experimental results show that the framework using learned search strategies outperforms existing automated theorem provers (i.e.

We propose a new approach to automated theorem proving where an AlphaZerostyle 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.

Augmenting tactic-based interactive theorem provers with neural guidance has been the focus of increased attention in recent years [1, 2, 3, 4, 5]. The dominant approach uses imitation learning on corpora of formalized mathematics. However, despite recent efforts involving self-supervised pre-training [5] or data-augmentation [6], this approach is limited by the conspicuous scarcity of human-producedtrainingdata.

Neural architecture search (NAS) finds high performing networks for a given task. Y et the results of NAS are fairly prosaic; they did not e.g.

The discovery of neural architectures from simple building blocks is a long-standing goal of Neural Architecture Search (NAS). Hierarchical search spaces are a promising step towards this goal but lack a unifying search space design framework and typically only search over some limited aspect of architectures. In this work, we introduce a unifying search space design framework based on context-free grammars that can naturally and compactly generate expressive hierarchical search spaces that are 100s of orders of magnitude larger than common spaces from the literature. By enhancing and using their properties, we effectively enable search over the complete architecture and can foster regularity. Further, we propose an efficient hierarchical kernel design for a Bayesian Optimization search strategy to efficiently search over such huge spaces. We demonstrate the versatility of our search space design framework and show that our search strategy can be superior to existing NAS approaches.