With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions. We have presented a neural network architecture capable, in principle, of supporting predicate logic's powers of abstraction without compromising the ideal of end-to-end learning, where the network itself discovers objects and relations in the raw data and thus avoids the symbol grounding problem entailed by symbolic AI's practice of hand-crafting representations (Harnad, 1990) . Our empirical results support the view that a network architecturally constrained to learn explicitly propositional, relational representations will have beneficial data efficiency, generalisation, and transfer properties. Although, the present experiments don't use the fully propositional version of the PrediNet output, the concatenated vector form inherits many of its beneficial properties, notably a degree of compositionality. In particular, one important respect in which the PrediNet differs from other network architectures is the extent to which it canalises information flow; at the core of the network, information is organised into small chunks which are processed in parallel channels that limit the ways the chunks can interact. We believe this pressures the network to learn representations where each separate chunk of information (such as a single value in the vector R * ) has independent meaning and utility. (We see evidence of this in the relational disentanglement of Fig. 6 .) The result is a representation whose component parts are amenable to recombination, and therefore re-use in a novel task. But the findings reported here are just the first foray into unexplored architectural territory, and much work needs to be done to gauge the architecture's full potential. The focus of the present paper is the acquisition of propositional representations rather than their use. But thanks to the structural priors of its architecture, representations generated by a PrediNet module have a natural semantics compatible with predicate calculus (Equation 1), which makes them an ideal medium for logic-like downstream processes such as rule-based deduction, causal or counterfactual reasoning, and inference to the best explanation (abduction). One approach here would be to stack PrediNet modules and / or make them recurrent, enabling them to carry out the sort of iterated, sequential computations required for such processes (Palm et al., 2018; Dehghani et al., 2019) . Another worthwhile direction for further research would be to develop reinforcement learning (RL) agents using the PrediNet architecture. One form of inference of particular interest in this context is model-based prediction, which can be used to endow an RL agent with look-ahead and planning abilities (Racanière et al., 2017; Zambaldi et al., 2019) . Our expectation is that RL agents in which explicitly propositional, relational representations underpin these capacities will manifest more of the beneficial data efficiency, generalisation, and transfer properties suggested by the present results. As a stepping stone to such RL agents, the Relations Game family of datasets could be extended into the temporal domain, and multi-task curricula developed to encourage the acquisition of temporal, as well as spatial, abstractions. Table S2 shows the default hyperparameters used for the experiments reported in the main text.
We present an end-to-end differentiable architecture that learns to map pixels to predicates, and evaluate it on a suite of simple relational reasoning tasks A network architecture based on the multi-head self-attention module to learn a new form of relational representations, which improves data efficiency and generalization ability on curriculum learning.