Matthew Morris

Matthew Morris, Thomas D. Barrett, Arnu Pretorius

Allowing agents to share information through communication is crucial for solving complex tasks in multi-agent reinforcement learning. In this work, we consider the question of whether a given communication protocol can express an arbitrary policy. By observing that many existing protocols can be viewed as instances of graph neural networks (GNNs), we demonstrate the equivalence of joint action selection to node labelling. With standard GNN approaches provably limited in their expressive capacity, we draw from existing GNN literature and consider augmenting agent observations with: (1) unique agent IDs and (2) random noise. We provide a theoretical analysis as to how these approaches yield universally expressive communication, and also prove them capable of targeting arbitrary sets of actions for identical agents. Empirically, these augmentations are found to improve performance on tasks where expressive communication is required, whilst, in general, the optimal communication protocol is found to be task-dependent.

Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau et al.

Graph neural networks (GNNs) are frequently used to predict missing facts in knowledge graphs (KGs). Motivated by the lack of explainability for the outputs of these models, recent work has aimed to explain their predictions using Datalog, a widely used logic-based formalism. However, such work has been restricted to certain subclasses of GNNs. In this paper, we consider one of the most popular GNN architectures for KGs, R-GCN, and we provide two methods to extract rules that explain its predictions and are sound, in the sense that each fact derived by the rules is also predicted by the GNN, for any input dataset. Furthermore, we provide a method that can verify that certain classes of Datalog rules are not sound for the R-GCN. In our experiments, we train R-GCNs on KG completion benchmarks, and we are able to verify that no Datalog rule is sound for these models, even though the models often obtain high to near-perfect accuracy. This raises some concerns about the ability of R-GCN models to generalise and about the explainability of their predictions. We further provide two variations to the training paradigm of R-GCN that encourage it to learn sound rules and find a trade-off between model accuracy and the number of learned sound rules.

Matthew Morris, Ian Horrocks

Graph neural networks (GNNs) are frequently used for knowledge graph completion. Their black-box nature has motivated work that uses sound logical rules to explain predictions and characterise their expressivity. However, despite the prevalence of GNNs that use mean as an aggregation function, explainability and expressivity results are lacking for them. We consider GNNs with mean aggregation and non-negative weights (MAGNNs), proving the precise class of monotonic rules that can be sound for them, as well as providing a restricted fragment of first-order logic to explain any MAGNN prediction. Our experiments show that restricting mean-aggregation GNNs to have non-negative weights yields comparable or improved performance on standard inductive benchmarks, that sound rules are obtained in practice, that insightful explanations can be generated in practice, and that the sound rules can expose issues in the trained models.

Matthew Morris, David J. Tena Cucala, Bernardo Cuenca Grau

Graph neural networks (GNNs) are often used for the task of link prediction: predicting missing binary facts in knowledge graphs (KGs). To address the lack of explainability of GNNs on KGs, recent works extract Datalog rules from GNNs with provable correspondence guarantees. The extracted rules can be used to explain the GNN's predictions; furthermore, they can help characterise the expressive power of various GNN models. However, these works address only a form of link prediction based on a restricted, low-expressivity graph encoding/decoding method. In this paper, we consider a more general and popular approach for link prediction where a scoring function is used to decode the GNN output into fact predictions. We show how GNNs and scoring functions can be adapted to be monotonic, use the monotonicity to extract sound rules for explaining predictions, and leverage existing results about the kind of rules that scoring functions can capture. We also define procedures for obtaining equivalent Datalog programs for certain classes of monotonic GNNs with scoring functions. Our experiments show that, on link prediction benchmarks, monotonic GNNs and scoring functions perform well in practice and yield many sound rules.

Miroslav Fil, Munib Mesinovic, Matthew Morris et al.

$β$-VAE is a follow-up technique to variational autoencoders that proposes special weighting of the KL divergence term in the VAE loss to obtain disentangled representations. Unsupervised learning is known to be brittle even on toy datasets and a meaningful, mathematically precise definition of disentanglement remains difficult to find. Here we investigate the original $β$-VAE paper and add evidence to the results previously obtained indicating its lack of reproducibility. We also further expand the experimentation of the models and include further more complex datasets in the analysis. We also implement an FID scoring metric for the $β$-VAE model and conclude a qualitative analysis of the results obtained. We end with a brief discussion on possible future investigations that can be conducted to add more robustness to the claims.