I am looking for a program that would allow me to fine-tune pre-trained word embeddings on my data set. Ideally, open source and working on Linux or Windows.
While I am not aware of software specifically for tuning trained word embeddings, perhaps the following open source software might be helpful, if you can figure out what parts can be modified for the fine-tuning part (just an idea off the top of my head - I'm not too familiar with the details):
GloVe: Global Vectors for Word Representation (part of Stanford NLP Group software);
Code on GitHub for Deep Learning-based word embeddings training;
Neural Probabilistic Language Model Toolkit, mentioned above (also Deep Learning-based).
If you use SGNS or CBOW, https://radimrehurek.com/gensim/ will let you continue continue training a pre-trained model on a different corpus if that is what you mean by fine tuning.