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: System identification is the process of building a mathematical model of an unknown system from measurements of its inputs and outputs. It is a key step for model-based control, estimator design, and output prediction. This work presents an algorithm for non-linear offline system identification from partial observations, i.e. situations in which the system's full-state is not directly observable. The algorithm presented, called SISL, iteratively infers the system's full state through non-linear optimization and then updates the model parameters. We test our algorithm on a simulated system of coupled Lorenz attractors, showing our algorithm's ability to identify high-dimensional systems that prove intractable for particle-based approaches. We also use SISL to identify the dynamics of an aerobatic helicopter. By augmenting the state with unobserved fluid states, we learn a model that predicts the acceleration of the helicopter better than state-of-the-art approaches.

SOLUTION: This work presents a scalable algorithm for non-linear offline system identification from partial observations.

PROBLEM: Natural language is hierarchically structured: smaller units (e.g., phrases) are nested within larger units (e.g., clauses). When a larger constituent ends, all of the smaller constituents that are nested within it must also be closed. While the standard LSTM architecture allows different neurons to track information at different time scales, it does not have an explicit bias towards modeling a hierarchy of constituents. This paper proposes to add such inductive bias by ordering the neurons; a vector of master input and forget gates ensures that when a given neuron is updated, all the neurons that follow it in the ordering are also updated. Our novel recurrent architecture, ordered neurons LSTM (ON-LSTM), achieves good performance on four different tasks: language modeling, unsupervised parsing, targeted syntactic evaluation, and logical inference.

SOLUTION: We introduce a new inductive bias that integrates tree structures in recurrent neural networks.

PROBLEM: To provide principled ways of designing proper Deep Neural Network (DNN) models, it is essential to understand the loss surface of DNNs under realistic assumptions. We introduce interesting aspects for understanding the local minima and overall structure of the loss surface. The parameter domain of the loss surface can be decomposed into regions in which activation values (zero or one for rectified linear units) are consistent. We found that, in each region, the loss surface have properties similar to that of linear neural networks where every local minimum is a global minimum. This means that every differentiable local minimum is the global minimum of the corresponding region. We prove that for a neural network with one hidden layer using rectified linear units under realistic assumptions. There are poor regions that lead to poor local minima, and we explain why such regions exist even in the overparameterized DNNs.

SOLUTION:
The loss surface of neural networks is a disjoint union of regions where every local minimum is a global minimum of the corresponding region.