Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules

Probabilistic logical models are a core component of neurosymbolic AI and are important models in their own right for tasks that require high explainability. Unlike neural networks, logical models are often handcrafted using domain expertise, making their development costly and prone to errors. While there are algorithms that learn logical models from data, they are generally prohibitively expensive, limiting their applicability in real-world settings. In this work, we introduce precision and recall for logical rules and define their composition as rule utility -- a cost-effective measure to evaluate the predictive power of logical models. Further, we introduce SPECTRUM, a scalable framework for learning logical models from relational data. Its scalability derives from a linear-time algorithm that mines recurrent structures in the data along with a second algorithm that, using the cheap utility measure, efficiently ranks rules built from these structures. Moreover, we derive theoretical guarantees on the utility of the learnt logical model. As a result, SPECTRUM learns more accurate logical models orders of magnitude faster than previous methods on real-world datasets.

MetaGFN: Exploring Distant Modes with Adapted Metadynamics for Continuous GFlowNets

Generative Flow Networks (GFlowNets) are a class of generative models that sample objects in proportion to a specified reward function through a learned policy. They can be trained either on-policy or off-policy, needing a balance between exploration and exploitation for fast convergence to a target distribution. While exploration strategies for discrete GFlowNets have been studied, exploration in the continuous case remains to be investigated, despite the potential for novel exploration algorithms due to the local connectedness of continuous domains. Here, we introduce Adapted Metadynamics, a variant of metadynamics that can be applied to arbitrary black-box reward functions on continuous domains. We use Adapted Metadynamics as an exploration strategy for continuous GFlowNets. We show three continuous domains where the resulting algorithm, MetaGFN, accelerates convergence to the target distribution and discovers more distant reward modes than previous off-policy exploration strategies used for GFlowNets.

Principled and Efficient Motif Finding for Structure Learning in Lifted Graphical Models

Structure learning is a core problem in AI central to the fields of neuro-symbolic AI and statistical relational learning. It consists in automatically learning a logical theory from data. The basis for structure learning is mining repeating patterns in the data, known as structural motifs. Finding these patterns reduces the exponential search space and therefore guides the learning of formulas. Despite the importance of motif learning, it is still not well understood. We present the first principled approach for mining structural motifs in lifted graphical models, languages that blend first-order logic with probabilistic models, which uses a stochastic process to measure the similarity of entities in the data. Our first contribution is an algorithm, which depends on two intuitive hyperparameters: one controlling the uncertainty in the entity similarity measure, and one controlling the softness of the resulting rules. Our second contribution is a preprocessing step where we perform hierarchical clustering on the data to reduce the search space to the most relevant data. Our third contribution is to introduce an O(n ln n) (in the size of the entities in the data) algorithm for clustering structurally-related data. We evaluate our approach using standard benchmarks and show that we outperform state-of-the-art structure learning approaches by up to 6% in terms of accuracy and up to 80% in terms of runtime.