In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.

Ex Input:
Decades of research on the neural code underlying spatial navigation have revealed a diverse set of neural response properties. The Entorhinal Cortex (EC) of the mammalian brain contains a rich set of spatial correlates, including grid cells which encode space using tessellating patterns. However, the mechanisms and functional significance of these spatial representations remain largely mysterious. As a new way to understand these neural representations, we trained recurrent neural networks (RNNs) to perform navigation tasks in 2D arenas based on velocity inputs. Surprisingly, we find that grid-like spatial response patterns emerge in trained networks, along with units that exhibit other spatial correlates, including border cells and band-like cells. All these different functional types of neurons have been observed experimentally. The order of the emergence of grid-like and border cells is also consistent with observations from developmental studies. Together, our results suggest that grid cells, border cells and others as observed in EC may be a natural solution for representing space efficiently given the predominant recurrent connections in the neural circuits.

Ex Output:
To our knowledge, this is the first study to show how neural representations of space, including grid-like cells and border cells as observed in the brain, could emerge from training a recurrent neural network to perform navigation tasks.

Ex Input:
We propose a novel deep network architecture for lifelong learning which we refer to as Dynamically Expandable Network (DEN), that can dynamically decide its network capacity as it trains on a sequence of tasks, to learn a compact overlapping knowledge sharing structure among tasks. DEN is efficiently trained in an online manner by performing selective retraining, dynamically expands network capacity upon arrival of each task with only the necessary number of units, and effectively prevents semantic drift by splitting/duplicating units and timestamping them. We validate DEN on multiple public datasets in lifelong learning scenarios on multiple public datasets, on which it not only significantly outperforms existing lifelong learning methods for deep networks, but also achieves the same level of performance as the batch model with substantially fewer number of parameters.

Ex Output:
We propose a novel deep network architecture that can dynamically decide its network capacity as it trains on a lifelong learning scenario.

Ex Input:
This work studies the problem of modeling non-linear visual processes by leveraging deep generative architectures for learning linear, Gaussian models of observed sequences. We propose a joint learning framework, combining a multivariate autoregressive model and deep convolutional generative networks. After justification of theoretical assumptions of inearization, we propose an architecture that allows Variational Autoencoders and Generative Adversarial Networks to simultaneously learn the non-linear observation as well as the linear state-transition model from a sequence of observed frames. Finally, we demonstrate our approach on conceptual toy examples and dynamic textures.

Ex Output:
We model non-linear visual processes as autoregressive noise via generative deep learning.