In creating sentence embeddings for Natural Language Inference (NLI) tasks, using transformer-based models like BERT leads to high accuracy, but require hundreds of millions of parameters. These models take in sentences as a sequence of tokens, and learn to encode the meaning of the sequence into embeddings such that those embeddings can be used reliably for NLI tasks. Essentially, every word is considered against every other word in the sequence, and the transformer model is able to determine the relationships between them, entirely from scratch. However, a model that accepts explicit linguistic structures like dependency parse trees may be able to leverage prior encoded information about these relationships, without having to learn them from scratch, thus improving learning efficiency. To investigate this, we adapt Graph Matching Networks (GMN) to operate on dependency parse trees, creating Tree Matching Networks (TMN). We compare TMN to a BERT based model on the SNLI entailment task and on the SemEval similarity task. TMN is able to achieve significantly better results with a significantly reduced memory footprint and much less training time than the BERT based model on the SNLI task, while both models struggled to preform well on the SemEval. Explicit structural representations significantly outperform sequence-based models at comparable scales, but current aggregation methods limit scalability. We propose multi-headed attention aggregation to address this limitation.