Approach to semantic similarity between documents I was wondering what approach people would take, or point me in the right direction on this challenge I have set myself. I am pretty new at this, I have covered some area but want to expand my skillset. 

Say you have an abstract from a research paper, which is a summarised form of information of a larger document, can you calculate, from a list of papers, which research paper this abstract belongs to?

Please note: I am not asking how to summarise the research paper. Also, note that the abstract information doesn't necessarily take the same form as the research paper, but is semantically similar.  

Would you, encode both datasets with a something like doc2vec to try to get the semantic meaning of the texts and then use cosine similarity?

Would the semantics of the numbers used in these papers get lost in the vectorizing?

IN this case, would a custom encoder work the best, or do you think USE or doc2vec would fair better?

Forgive my basic questions, I just wanted to explore things before I started coding!
If I understand correctly, you're trying to map abstracts to their research papers.

Here is a simple starting point:

Compute a TF IDF model using the entire corpus (all abstracts + research papers). Use this model to transform your abstracts and research papers into a weighted vector representation. Under the TF IDF weighting scheme, these documents will be represented by vectors that point in the direction of the words that are most discriminating for them. Put another way, these vectors point towards the words that are the best at telling you what the document is about. So if two vectors are close to each other, then the two documents are likely to be about the same topic because they are using similar words.

This is where cosine similarity comes in. Take an abstract, and then iterate across all the research paper vectors, computing the cosine similarity between them. Then, map that abstract to whichever research paper has the highest cosine similarity. Repeat this for each abstract.

Once you have this simple baseline approach, you can start looking at more sophisticated models for capturing semantic similarity.