Lifted Relational Neural Networks: Efficient Learning of Latent Relational Structures

By Gustav Sourek, Vojtech Aschenbrenner, Filip Zelezný, Steven Schockaert, Ondřej Kuželka. 2018

98 citations recorded by the source corpus.

We propose a method to combine the interpretability and expressive power of firstorder logic with the effectiveness of neural network learning. In particular, we introduce a lifted framework in which first-order rules are used to describe the structure of a given problem setting. These rules are then used as a template for constructing a number of neural networks, one for each training and testing example. As the different networks corresponding to different examples share their weights, these weights can be efficiently learned using stochastic gradient descent. Our framework provides a flexible way for implementing and combining a wide variety of modelling constructs. In particular, the use of first-order logic allows for a declarative specification of latent relational structures, which can then be efficiently discovered in a given data set using neural network learning. Experiments on 78 relational learning benchmarks clearly demonstrate the effectiveness of the framework.

Subfields: Artificial Intelligence

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Citations in the corpus

DeepProbLog: Neural Probabilistic Logic Programming (2018, background): “These successes have inspired a number of works developing (probabilistic) logic formulations of basic deep learning primitives [ˇSourek et al., 2018, Duman ˇ ci ´ c and Blockeel, 2017, Kazemi and Poole, 2018].”
Unsupervised Grounding of Plannable First-Order Logic Representation from Images (2019, background): “Neural theorem proving systems (Rocktäschel and Riedel 2017; Sourek et al. 2018; Manhaeve et al. 2018) learn to reason about logical relations.”
SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver (2019, background): “…focused on creating differentiable modules from an existing set of known relationships , so that a deep network can learn the parameters of these relationships (Dai et al., 2018; Manhaeve et al., 2018; Sourek et al., 2018; Xu et al., 2018; Hu et al., 2016; Yang et al., 2017; Selsam et al., 2018).”
Logic Tensor Networks (2020, methodology): “Modify the predictions of a neural network using logical knowledge [46, 14] Encode the satisfiability of logical knowledge in the loss function: LTN and [22, 48] Use of logical knowledge in addition to neural predictions [42, 13] Logical specification of neural networks [26, 68, 23, 58]”
Representation Learning for Dynamic Graphs: A Survey (2019, background): “Sourek et al. (2018) and Kazemi and Poole (2018b) propose other variants for Equation (17) where (roughly) the transformations are done using soft first-order logic rules.”
Relational Representation Learning for Dynamic (Knowledge) Graphs: A Survey (2019, background): “Sourek et al. [207] and Kazemi and Poole [114] propose other variants for Equation (28) where (roughly) the transformations are done using soft ﬁrst-order logic rules.”