Dissipative residual layers for unsupervised implicit parameterization of data manifolds
This addresses data manifold learning for reinforcement learning and related applications, but appears incremental as it builds on existing dynamical system and residual network frameworks.
The paper tackles the problem of unsupervised implicit parameterization of data manifolds by modeling them as attractive manifolds of a dynamical system estimated with residual neural networks, achieving performance in denoising and generative tasks.
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.