It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to analyze the ALBERT family of language models. Specifically, we extract the learned embeddings these models use to represent tokens that correspond to numbers and ordinals, and subject these embeddings to Principal Component Analysis (PCA). PCA results reveal that ALBERT models of different sizes, trained and initialized separately, consistently learn to use the axes of greatest variation to represent the approximate ordering of various numerical concepts. Numerals and their textual counterparts are represented in separate clusters, but increase along the same direction in 2D space. Our findings illustrate that language models, trained purely to model text, can intuit basic mathematical concepts, opening avenues for NLP applications that intersect with quantitative reasoning.

Position embeddings have long been essential for sequence-order encoding in transformer models, yet their structure is underexplored. This study uses principal component analysis (PCA) to quantitatively compare the dimensionality of absolute position and word embeddings in BERT and ALBERT. We find that, unlike word embeddings, position embeddings occupy a low-dimensional subspace, typically utilizing under 10% of the dimensions available. Additionally, the principal vectors are dominated by a few low-frequency rotational components, a structure arising independently across models.

Mechanisms for encoding positional information are central for transformer-based language models. In this paper, we analyze the position embeddings of existing language models, finding strong evidence of translation invariance, both for the embeddings themselves and for their effect on self-attention. The degree of translation invariance increases during training and correlates positively with model performance. Our findings lead us to propose translation-invariant self-attention (TISA), which accounts for the relative position between tokens in an interpretable fashion without needing conventional position embeddings. Our proposal has several theoretical advantages over existing position-representation approaches. Proof-of-concept experiments show that it improves on regular ALBERT on GLUE tasks, while only adding orders of magnitude less positional parameters.

We examine the capabilities of a unified, multi-task framework for three information extraction tasks: named entity recognition, relation extraction, and event extraction. Our framework (called DyGIE++) accomplishes all tasks by enumerating, refining, and scoring text spans designed to capture local (within-sentence) and global (cross-sentence) context. Our framework achieves state-of-the-art results across all tasks, on four datasets from a variety of domains. We perform experiments comparing different techniques to construct span representations. Contextualized embeddings like BERT perform well at capturing relationships among entities in the same or adjacent sentences, while dynamic span graph updates model long-range cross-sentence relationships. For instance, propagating span representations via predicted coreference links can enable the model to disambiguate challenging entity mentions. Our code is publicly available at https://github.com/dwadden/dygiepp and can be easily adapted for new tasks or datasets.