TASK DEFINITION: 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.
PROBLEM: Claims from the fields of network neuroscience and connectomics suggest that topological models of the brain involving complex networks are of particular use and interest. The field of deep neural networks has mostly left inspiration from these claims out. In this paper, we propose three architectures and use each of them to explore the intersection of network neuroscience and deep learning in an attempt to bridge the gap between the two fields. Using the teachings from network neuroscience and connectomics, we show improvements over the ResNet architecture, we show a possible connection between early training and the spectral properties of the network, and we show the trainability of a DNN based on the neuronal network of C.Elegans.

SOLUTION: We explore the intersection of network neurosciences and deep learning. 

PROBLEM: Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm for finding abstract MDPs in environments with continuous state spaces. It is based on MDP homomorphisms, a structure-preserving mapping between MDPs. We demonstrate our algorithm's ability to learns abstractions from collected experience and show how to reuse the abstractions to guide exploration in new tasks the agent encounters. Our novel task transfer method beats a baseline based on a deep Q-network.

SOLUTION: We create abstract models of environments from experience and use them to learn new tasks faster.

PROBLEM: We study SGD and Adam for estimating a rank one signal planted in matrix or tensor noise. The extreme simplicity of the problem setup allows us to isolate the effects of various factors: signal to noise ratio, density of critical points, stochasticity and initialization. We observe a surprising phenomenon: Adam seems to get stuck in local minima as soon as polynomially many critical points appear (matrix case), while SGD escapes those. However, when the number of critical points degenerates to exponentials (tensor case), then both algorithms get trapped. Theory tells us that at fixed SNR the problem becomes intractable for large $d$ and in our experiments SGD does not escape this. We exhibit the benefits of warm starting in those situations. We conclude that in this class of problems, warm starting cannot be replaced by stochasticity in gradients to find the basin of attraction.

SOLUTION:
SGD and Adam under single spiked model for tensor PCA