  Learning interpretable dialog structure from human-human dialogs yields basic
insights into the structure of conversation, and also provides background
knowledge to facilitate dialog generation. In this paper, we conduct
unsupervised discovery of dialog structure from chitchat corpora, and then
leverage it to facilitate dialog generation in downstream systems. To this end,
we present a Discrete Variational Auto-Encoder with Graph Neural Network
(DVAE-GNN), to discover a unified human-readable dialog structure. The
structure is a two-layer directed graph that contains session-level semantics
in the upper-layer vertices, utterance-level semantics in the lower-layer
vertices, and edges among these semantic vertices. In particular, we integrate
GNN into DVAE to fine-tune utterance-level semantics for more effective
recognition of session-level semantic vertex. Furthermore, to alleviate the
difficulty of discovering a large number of utterance-level semantics, we
design a coupling mechanism that binds each utterance-level semantic vertex
with a distinct phrase to provide prior semantics. Experimental results on two
benchmark corpora confirm that DVAE-GNN can discover meaningful dialog
structure, and the use of dialog structure graph as background knowledge can
facilitate a graph grounded conversational system to conduct coherent
multi-turn dialog generation.
