A neuro-symbolic framework for answering conjunctive queries

The problem of answering logical queries over incomplete knowledge graphs is receiving significant attention in the machine learning community. Neuro-symbolic models are a promising recent approach, showing good performance and allowing for good interpretability properties. These models rely on trained architectures to execute atomic queries, combining them with modules that simulate the symbolic operators in queries. Unfortunately, most neuro-symbolic query processors are limited to the so-called tree-like logical queries that admit a bottom-up execution, where the leaves are constant values or anchors, and the root is the target variable. Tree-like queries, while expressive, fail short to express properties in knowledge graphs that are important in practice, such as the existence of multiple edges between entities or the presence of triangles. We propose a framework for answering arbitrary conjunctive queries over incomplete knowledge graphs. The main idea of our method is to approximate a cyclic query by an infinite family of tree-like queries, and then leverage existing models for the latter. Our approximations achieve strong guarantees: they are complete, i.e. there are no false negatives, and optimal, i.e. they provide the best possible approximation using tree-like queries. Our method requires the approximations to be tree-like queries where the leaves are anchors or existentially quantified variables. Hence, we also show how some of the existing neuro-symbolic models can handle these queries, which is of independent interest. Experiments show that our approximation strategy achieves competitive results, and that including queries with existentially quantified variables tends to improve the general performance of these models, both on tree-like queries and on our approximation strategy.

Graph Neural Networks with Local Graph Parameters

Various recent proposals increase the distinguishing power of Graph Neural Networks GNNs by propagating features between $k$-tuples of vertices. The distinguishing power of these "higher-order'' GNNs is known to be bounded by the $k$-dimensional Weisfeiler-Leman (WL) test, yet their $\mathcal O(n^k)$ memory requirements limit their applicability. Other proposals infuse GNNs with local higher-order graph structural information from the start, hereby inheriting the desirable $\mathcal O(n)$ memory requirement from GNNs at the cost of a one-time, possibly non-linear, preprocessing step. We propose local graph parameter enabled GNNs as a framework for studying the latter kind of approaches and precisely characterize their distinguishing power, in terms of a variant of the WL test, and in terms of the graph structural properties that they can take into account. Local graph parameters can be added to any GNN architecture, and are cheap to compute. In terms of expressive power, our proposal lies in the middle of GNNs and their higher-order counterparts. Further, we propose several techniques to aide in choosing the right local graph parameters. Our results connect GNNs with deep results in finite model theory and finite variable logics. Our experimental evaluation shows that adding local graph parameters often has a positive effect for a variety of GNNs, datasets and graph learning tasks.