  We propose an unsupervised technique for implicit parameterization of data
manifolds. In our approach, the data is assumed to belong to a lower
dimensional manifold in a higher dimensional space, and the data points are
viewed as the endpoints of the trajectories originating outside the manifold.
Under this assumption, the data manifold is an attractive manifold of a
dynamical system to be estimated. We parameterize such a dynamical system with
a residual neural network and propose a spectral localization technique to
ensure it is locally attractive in the vicinity of data. We also present
initialization and additional regularization of the proposed residual layers. %
that we call dissipative bottlenecks. We mention the importance of the
considered problem for the tasks of reinforcement learning and support our
discussion with examples demonstrating the performance of the proposed layers
in denoising and generative tasks.
