Transformers have advanced the field of natural language processing (NLP) on a variety of important tasks. At the cornerstone of the Transformer architecture is the multi-head attention (MHA) mechanism which models pairwise interactions between the elements of the sequence. Despite its massive success, the current framework ignores interactions among different heads, leading to the problem that many of the heads are redundant in practice, which greatly wastes the capacity of the model. To improve parameter efficiency, we re-formulate the MHA as a latent variable model from a probabilistic perspective. We present cascaded head-colliding attention (CODA) which explicitly models the interactions between attention heads through a hierarchical variational distribution. We conduct extensive experiments and demonstrate that CODA outperforms the transformer baseline, by 0.6 perplexity on Wikitext-103 in language modeling, and by 0.6 BLEU on WMT14 EN-DE in machine translation, due to its improvements on the parameter efficiency.

Generative semantic hashing is a promising technique for large-scale information retrieval thanks to its fast retrieval speed and small memory footprint. For the tractability of training, existing generative-hashing methods mostly assume a factorized form for the posterior distribution, enforcing independence among the bits of hash codes. From the perspectives of both model representation and code space size, independence is always not the best assumption. In this paper, to introduce correlations among the bits of hash codes, we propose to employ the distribution of Boltzmann machine as the variational posterior. To address the intractability issue of training, we first develop an approximate method to reparameterize the distribution of a Boltzmann machine by augmenting it as a hierarchical concatenation of a Gaussian-like distribution and a Bernoulli distribution. Based on that, an asymptotically-exact lower bound is further derived for the evidence lower bound (ELBO). With these novel techniques, the entire model can be optimized efficiently. Extensive experimental results demonstrate that by effectively modeling correlations among different bits within a hash code, our model can achieve significant performance gains.