In Latent Dirichlet Allocation (LDA), is it reasonable to reconstruct the original bag-of-words using the document and word representations?
It is possible to produce a corpus from the learned LDA parameters ($\theta$ and $\phi$) according to the generative model of LDA but it is not realistic to expect that you would recreate the original documents (in bag-of-words form). To be more specific, it is possible - but highly improbable - that you would generate the bag-of-words documents corresponding to the input corpus.