Join-Chain Network: A Logical Reasoning View of the Multi-head Attention in Transformer

Developing neural architectures that are capable of logical reasoning has become increasingly important for a wide range of applications (e.g., natural language processing). Towards this grand objective, we propose a symbolic reasoning architecture that chains many join operators together to model output logical expressions. In particular, we demonstrate that such an ensemble of join chains can express a broad subset of “tree-structured” first-order logical expressions, named $\mathcal{FOET}$ which is particularly useful for modeling natural languages. To endow it with differentiable learning capability, we closely examine various neural operators for approximating the symbolic join-chains. Interestingly, we find that the widely used multi-head self-attention module in transformer can be understood as a special neural operator that implements the union bound of the join operator in probabilistic predicate space. Our analysis not only provides a new perspective on the mechanism of the pretrained models such as BERT for natural language understanding, but also suggests several important future improvement directions.