Protein functions can be described by the Gene Ontology (GO) terms, allowing us to compare the functions of two proteins by measuring the similarity of the terms assigned to them. Recent works have applied neural network models to derive the vector representations for GO terms and compute similarity scores for these terms by comparing their vector embeddings. There are two typical ways to embed GO terms into vectors; a model can either embed the definitions of the terms or the topology of the terms in the ontology. In this paper, we design three tasks to critically evaluate the GO embeddings of two recent neural network models, and further introduce additional models for embedding GO terms, adapted from three popular neural network frameworks: Graph Convolution Network (GCN), Embeddings from Language Models (ELMo), and Bidirectional Encoder Representations from Transformers (BERT), which have not yet been explored in previous works. Task 1 studies edge cases where the GO embeddings may not provide meaningful similarity scores for GO terms. We find that all neural network based methods fail to produce high similarity scores for related terms when these terms have low Information Content values. Task 2 is a canonical task which estimates how well GO embeddings can compare functions of two orthologous genes or two interacting proteins. The best neural network methods for this task are those that embed GO terms using their definitions, and the differences among such methods are small. Task 3 evaluates how GO embeddings affect the performance of GO annotation methods, which predict whether a protein should be labeled by certain GO terms. When the annotation datasets contain many samples for each GO label, GO embeddings do not improve the classification accuracy. Machine learning GO annotation methods often remove rare GO labels from the training datasets so that the model parameters can be efficiently trained. We evaluate whether GO embeddings can improve prediction of rare labels unseen in the training datasets, and find that GO embeddings based on the BERT framework achieve the best results in this setting. We present our embedding methods and three evaluation tasks as the basis for future research on this topic.

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