Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving

A BSTRACT We incorporate Tensor-Product Representations within the Transformer in order to better support the explicit representation of relation structure. Our Tensor-Product Transformer (TP-Transformer) sets a new state of the art on the recently-introduced Mathematics Dataset containing 56 categories of free-form math word-problems. The essential component of the model is a novel attention mechanism, called TP-Attention, which explicitly encodes the relations between each Transformer cell and the other cells from which values have been retrieved by attention. TP-Attention goes beyond linear combination of retrieved values, strengthening representation-building and resolving ambiguities introduced by multiple layers of standard attention. The TP-Transformer's attention maps give better insights into how it is capable of solving the Mathematics Dataset's challenging problems. Pretrained models and code will be made available after publication. 1 I NTRODUCTION In this paper we propose a variation of the Transformer (V aswani et al., 2017) that is designed to allow it to better incorporate structure into its representations. We test the proposal on a task where structured representations are expected to be particularly helpful: math word-problem solving, where, among other things, correctly parsing expressions and compositionally evaluating them is crucial.