Enhancing the Transformer with Explicit Relational Encoding for Math Problem Solving
This work addresses the challenge of explicit relation representation in math problem-solving for AI systems, though it appears incremental as it builds on existing Transformer architectures.
The authors tackled the problem of solving free-form math word problems by enhancing the Transformer with explicit relational encoding, resulting in a new state-of-the-art model on the Mathematics Dataset with 56 categories.
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.