Word embedding models are typically able to capture the semantics of words via the distributional hypothesis, but fail to capture the numerical properties of numbers that appear in the text. This leads to problems with numerical reasoning involving tasks such as question answering. We propose a new methodology to assign and learn embeddings for numbers. Our approach creates Deterministic, Independent-of-Corpus Embeddings (the model is referred to as DICE) for numbers, such that their cosine similarity reflects the actual distance on the number line. DICE outperforms a wide range of pre-trained word embedding models across multiple examples of two tasks: (i) evaluating the ability to capture numeration and magnitude; and (ii) to perform list maximum, decoding, and addition. We further explore the utility of these embeddings in downstream tasks, by initializing numbers with our approach for the task of magnitude prediction. We also introduce a regularization approach to learn model-based embeddings of numbers in a contextual setting.

Pretrained Language Models (PLMs) have improved the performance of natural language understanding in recent years. Such models are pretrained on large corpora, which encode the general prior knowledge of natural languages but are agnostic to information characteristic of downstream tasks. This often results in overfitting when fine-tuned with low resource datasets where task-specific information is limited. In this paper, we integrate label information as a task-specific prior into the self-attention component of pretrained BERT models. Experiments on several benchmarks and real-word datasets suggest that the proposed approach can largely improve the performance of pretrained models when fine-tuning with small datasets.