Serial Order Codes for Dimensionality Reduction in the Learning of Higher-Order Rules and Compositionality in Planning

Rapid extraction of higher-order rules from sequences of items and their immediate application to construction of novel sequences is a challenging task for neural networks. One of the mechanisms that allows to capture hierarchical dependencies between items within sequences is ordinal coding. Ordinal patterns create a grammar, or a set of rules, that reduces the dimensionality of the search space and that can be used in a generative manner to compose new sequences. Using this framework, we propose a sample-efficient and lightweight neuro-symbolic architecture that uses ordinal codes in a generative manner, adhering to the principle of compositionality. The higher-order rules are extracted and learned in a one-shot manner, and allow to extrapolate sequences of items from the given repertoire. We demonstrate how this framework can be used to make the solver robust to exponentially growing complexity of the given task by reducing its dimensionality.