Rules over a knowledge graph (KG) capture interpretable patterns in data and can be used for KG cleaning and completion. Inspired by the TensorLog differentiable logic framework, which compiles rule inference into a sequence of differentiable operations, recently a method called Neural LP has been proposed for learning the parameters as well as the structure of rules. However, it is limited with respect to the treatment of numerical features like age, weight or scientific measurements. We address this limitation by extending Neural LP to learn rules with numerical values, e.g., "People younger than 18 typically live with their parents". We demonstrate how dynamic programming and cumulative sum operations can be exploited to ensure efficiency of such extension. Our novel approach allows us to extract more expressive rules with aggregates, which are of higher quality and yield more accurate predictions compared to rules learned by the state-of-the-art methods, as shown by our experiments on synthetic and real-world datasets.
This paper proposes an extension of NeuralLP that is able to learn a very restricted (in terms of expressiveness) set of logic rules involving numeric properties. The basic idea behind NeuralLP is quite simple: traversing relationships in a knowledge graph can be done by multiplicating adjacency matrices, and which rules hold and which ones don't can be discovered by learning an attention distribution over rules from data.
The idea is quite clever: relationships between numeric data properties of entities, such as age and heigh, can also be linked by relationships such as \leq and \geq, and those relations can be treated in the same way as standard knowledge graph relationship by the NeuralLP framework.
A major drawback in applying this idea is that the corresponding relational matrix is expensive to both materialise, and use within the NeuralLP framework (where matrices are mostly sparse). To this end, authors make this process tractable by using dynamic programming and by defining such a matrix as a dynamic computation graph by means of the cumsum operator.  Furthermore, authors also introduce negated operators, also by defining the corresponding adjacency matrices by means of computation graphs.
Authors evaluate on several datasets - two real world and two synthetic - often showing more accurate results than the considered baselines.
One thing that puts me off is that, in Table 2, AnyBurl (the single one baseline authors considered other than the original NeuralLP) yields better Hits@10 values than Neural-LP-N, but the corresponding bold in the results is conveniently omitted.
Another concern I have is that the expressiveness of the learned rules can be somehow limited, but this paper seems like a good star towards learning interpretable rules involving multiple modalities.
Missing references - authors may want to consider citing https://arxiv.org/abs/1906.06187 as well in Sec. 2 - it seems very related to this work.