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.

[Q]: We introduce our Distribution Regression Network (DRN) which performs regression from input probability distributions to output probability distributions. Compared to existing methods, DRN learns with fewer model parameters and easily extends to multiple input and multiple output distributions. On synthetic and real-world datasets, DRN performs similarly or better than the state-of-the-art. Furthermore, DRN generalizes the conventional multilayer perceptron (MLP). In the framework of MLP, each node encodes a real number, whereas in DRN, each node encodes a probability distribution.
[A]: A learning network which generalizes the MLP framework to perform distribution-to-distribution regression


[Q]: Energy  based  models  outputs  unmormalized  log-probability  values  given  datasamples.   Such a estimation is essential in a variety of application problems suchas sample generation, denoising, sample restoration, outlier detection, Bayesianreasoning, and many more.   However, standard maximum likelihood training iscomputationally expensive due to the requirement of sampling model distribution. Score matching potentially alleviates this problem, and denoising score matching(Vincent, 2011) is a particular convenient version.   However,  previous attemptsfailed to produce models capable of high quality sample synthesis.   We believethat  it  is  because  they  only  performed  denoising  score  matching  over  a  singlenoise scale. To overcome this limitation, here we instead learn an energy functionusing all noise scales.    When sampled using Annealed Langevin dynamics andsingle step denoising jump, our model produced high-quality samples comparableto state-of-the-art techniques such as GANs, in addition to assigning likelihood totest data comparable to previous likelihood models.   Our model set a new sam-ple quality baseline in likelihood-based models.   We further demonstrate that our model learns sample distribution and generalize well on an image inpainting tasks.
[A]: Learned energy based model with score matching


[Q]: The Tensor-Train factorization (TTF) is an efficient way to compress large weight matrices of fully-connected layers and recurrent layers in recurrent neural networks (RNNs). However, high Tensor-Train ranks for all the core tensors of parameters need to be element-wise fixed, which results in an unnecessary redundancy of model parameters. This work applies Riemannian stochastic gradient descent (RSGD) to train core tensors of parameters in the Riemannian Manifold before finding vectors of lower Tensor-Train ranks for parameters. The paper first presents the RSGD algorithm with a convergence analysis and then tests it on more advanced Tensor-Train RNNs such as bi-directional GRU/LSTM and Encoder-Decoder RNNs with a Tensor-Train attention model. The experiments on digit recognition and machine translation tasks suggest the effectiveness of the RSGD algorithm for Tensor-Train RNNs.
[A]:
Applying the Riemannian SGD (RSGD) algorithm for training Tensor-Train RNNs to further reduce model parameters.