How to Leverage Digit Embeddings to Represent Numbers?

Apart from performing arithmetic operations, understanding numbers themselves is still a challenge for existing language models. Simple generalisations, such as solving 100+200 instead of 1+2, can substantially affect model performance (Sivakumar and Moosavi, 2023). Among various techniques, character-level embeddings of numbers have emerged as a promising approach to improve number representation. However, this method has limitations as it leaves the task of aggregating digit representations to the model, which lacks direct supervision for this process. In this paper, we explore the use of mathematical priors to compute aggregated digit embeddings and explicitly incorporate these aggregates into transformer models. This can be achieved either by adding a special token to the input embeddings or by introducing an additional loss function to enhance correct predictions. We evaluate the effectiveness of incorporating this explicit aggregation, analysing its strengths and shortcomings, and discuss future directions to better benefit from this approach. Our methods, while simple, are compatible with any pretrained model and require only a few lines of code, which we have made publicly available.

FERMAT: An Alternative to Accuracy for Numerical Reasoning

While pre-trained language models achieve impressive performance on various NLP benchmarks, they still struggle with tasks that require numerical reasoning. Recent advances in improving numerical reasoning are mostly achieved using very large language models that contain billions of parameters and are not accessible to everyone. In addition, numerical reasoning is measured using a single score on existing datasets. As a result, we do not have a clear understanding of the strengths and shortcomings of existing models on different numerical reasoning aspects and therefore, potential ways to improve them apart from scaling them up. Inspired by CheckList (Ribeiro et al., 2020), we introduce a multi-view evaluation set for numerical reasoning in English, called FERMAT. Instead of reporting a single score on a whole dataset, FERMAT evaluates models on various key numerical reasoning aspects such as number understanding, mathematical operations, and training dependency. Apart from providing a comprehensive evaluation of models on different numerical reasoning aspects, FERMAT enables a systematic and automated generation of an arbitrarily large training or evaluation set for each aspect.The datasets and codes are publicly available to generate further multi-view data for ulterior tasks and languages.