In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward this goal often suffered from a lack of interpretability and tractability. In particular, the high-dimensional latent spaces often required for a faithful embedding, even when the underlying dynamics lives on a lower-dimensional manifold, can hamper theoretical analysis. Motivated by the emerging principles of dendritic computation, we augment a dynamically interpretable and mathematically tractable piecewise-linear (PL) recurrent neural network (RNN) by a linear spline basis expansion. We show that this approach retains all the theoretically appealing properties of the simple PLRNN, yet boosts its capacity for approximating arbitrary nonlinear dynamical systems in comparatively low dimensions. We employ two frameworks for training the system, one combining BPTT with teacher forcing, and another based on fast and scalable variational inference. We show that the dendritically expanded PLRNN achieves better reconstructions with fewer parameters and dimensions on various dynamical systems benchmarks and compares favorably to other methods, while retaining a tractable and interpretable structure.

Large intra-class variation is the result of changes in multiple object characteristics. Images, however, only show the superposition of different variable factors such as appearance or shape. Therefore, learning to disentangle and represent these different characteristics poses a great challenge, especially in the unsupervised case. Moreover, large object articulation calls for a flexible part-based model. We present an unsupervised approach for disentangling appearance and shape by learning parts consistently over all instances of a category. Our model for learning an object representation is trained by simultaneously exploiting invariance and equivariance constraints between synthetically transformed images. Since no part annotation or prior information on an object class is required, the approach is applicable to arbitrary classes. We evaluate our approach on a wide range of object categories and diverse tasks including pose prediction, disentangled image synthesis, and video-to-video translation. The approach outperforms the state-of-the-art on unsupervised keypoint prediction and compares favorably even against supervised approaches on the task of shape and appearance transfer.