My task deals with multi-language like (english and hindi). For that I need a common embedding to represent both languages.
I know there are methods for learning multilingual embedding like 'MUSE', but this represents those two embeddings in a common vector space, obviously they are similar, but not the same.
So I wanted to know if there is any method or approach that can learn to represent both embedding in form of a single embedding that represents the both the language.
Any lead is strongly appreciated!!!</div
I think a good lead would be to look at past work that has been done in the field. A good overview to start with is Sebastian Ruder's talk, which gives you a multitude of approaches, depending on the level of information you have about your source/target language. This is basically what MUSE is doing, and I'm relatively sure that it is considered state-of-the-art.
The basic idea in most approaches is to map embedding spaces such that you minimize some (usually Euclidean) distance between the both (see p. 16 of the link). This obviously works best if you have a known dictionary and can precisely map the different translations, and works even better if the two languages have similar linguistic properties (not so sure about Hindi and English, to be honest).
Another recent approach is the one by Multilingual-BERT (mBERT), or similarly, XLM-RoBERTa, but those learn embeddings based on a shared vocabulary. This might again be less desirable if you have morphologically dissimilar languages, and also has the drawback that they incorporate a bunch of other, unrelated, languages.
Otherwise, I'm unclear on what exactly you are expecting from a "common embedding", but happy to extend the answer once clarified.</div