Actually, I was really wrong on this one. My apologies.
Early instances of (denoising) AE use exactly the same (transposed) weights for each decoder/encoder layer (but different biases). Basically described in all DL textbooks, happy to send the references. Sharing the transposed weights allows you to reduce the number of parameters by 1/2 (training each decoder/ encoder one layer at a time).
My point of reference was an unsupervised clustering paper from facebook (that used denoising AEs as a start): https://arxiv.org/abs/1511.06335 9
Even though they trained the denoising (stacked) AE one layer at a time, they used separate parameters for the decoder and the encoder layers. So I was clearly wrong.
However, my question remains the same: where is the blog post, experiment, paper that shows that weight-sharing (b/ween encoding/decodin layers) in a stacked denoising AE gives absolutely no benefit? If you have a question about what is a stacked AE just read the referenced paper.