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: We give a new algorithm for learning a two-layer neural network under a very general class of input distributions. Assuming there is a ground-truth two-layer network 
 y = A \sigma(Wx) + \xi,
 where A, W are weight matrices, \xi represents noise, and the number of neurons in the hidden layer is no larger than the input or output,  our algorithm is guaranteed to recover the parameters A, W of the ground-truth network. The only requirement on the input x is that it is symmetric, which still allows highly complicated and structured input. 

 Our algorithm is based on the method-of-moments framework and extends several results in tensor decompositions. We use spectral algorithms to avoid the complicated non-convex optimization in learning neural networks. Experiments show that our algorithm can robustly learn the ground-truth neural network with a small number of samples for many symmetric input distributions.

SOLUTION: We give an algorithm for learning a two-layer neural network with symmetric input distribution. 

PROBLEM: Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with 100% accuracy. In this work we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased towards low frequency functions, meaning that they cannot have local fluctuations without affecting their global behavior. Intuitively, this property is in line with the observation that over-parameterized networks find simple patterns that generalize across data samples. We also investigate how the shape of the data manifold affects expressivity by showing evidence that learning high frequencies gets easier with increasing manifold complexity, and present a theoretical understanding of this behavior. Finally, we study the robustness of the frequency components with respect to parameter perturbation, to develop the intuition that the parameters must be finely tuned to express high frequency functions.

SOLUTION: We investigate ReLU networks in the Fourier domain and demonstrate peculiar behaviour.

PROBLEM: Despite much success in many large-scale language tasks, sequence-to-sequence (seq2seq) models have not been an ideal choice for conversational modeling as they tend to generate generic and repetitive responses. In this paper, we propose a Latent Topic Conversational Model (LTCM) that augments the seq2seq model with a neural topic component to better model human-human conversations. The neural topic component encodes information from the source sentence to build a global “topic” distribution over words, which is then consulted by the seq2seq model to improve generation at each time step. The experimental results show that the proposed LTCM can generate more diverse and interesting responses by sampling from its learnt latent representations. In a subjective human evaluation, the judges also confirm that LTCM is the preferred option comparing to competitive baseline models.


SOLUTION:
Latent Topic Conversational Model, a hybrid of seq2seq and neural topic model to generate more diverse and interesting responses.