  In this work, we have proposed augmented KRnets including both discrete and
continuous models. One difficulty in flow-based generative modeling is to
maintain the invertibility of the transport map, which is often a trade-off
between effectiveness and robustness. The exact invertibility has been achieved
in the real NVP using a specific pattern to exchange information between two
separated groups of dimensions. KRnet has been developed to enhance the
information exchange among data dimensions by incorporating the
Knothe-Rosenblatt rearrangement into the structure of the transport map. Due to
the maintenance of exact invertibility, a full nonlinear update of all data
dimensions needs three iterations in KRnet. To alleviate this issue, we will
add augmented dimensions that act as a channel for communications among the
data dimensions. In the augmented KRnet, a fully nonlinear update is achieved
in two iterations. We also show that the augmented KRnet can be reformulated as
the discretization of a neural ODE, where the exact invertibility is kept such
that the adjoint method can be formulated with respect to the discretized ODE
to obtain the exact gradient. Numerical experiments have been implemented to
demonstrate the effectiveness of our models.

Machine Learning;Machine Learning