instruction:
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.
question:
A Synaptic Neural Network (SynaNN) consists of synapses and neurons. Inspired by the synapse research of neuroscience, we built a synapse model with a nonlinear synapse function of excitatory and inhibitory channel probabilities. Introduced the concept of surprisal space and constructed a commutative diagram, we proved that the inhibitory probability function -log(1-exp(-x)) in surprisal space is the topologically conjugate function of the inhibitory complementary probability 1-x in probability space. Furthermore, we found that the derivative of the synapse over the parameter in the surprisal space is equal to the negative Bose-Einstein distribution. In addition, we constructed a fully connected synapse graph (tensor) as a synapse block of a synaptic neural network. Moreover, we proved the gradient formula of a cross-entropy loss function over parameters, so synapse learning can work with the gradient descent and backpropagation algorithms. In the proof-of-concept experiment, we performed an MNIST training and testing on the MLP model with synapse network as hidden layers.
answer:
A synaptic neural network with synapse graph and learning that has the feature of topological conjugation and Bose-Einstein distribution in surprisal space.  


question:
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.
answer:
A learning network which generalizes the MLP framework to perform distribution-to-distribution regression


question:
Meta learning has been making impressive progress for fast model adaptation. However, limited work has been done on learning fast uncertainty adaption for Bayesian modeling. In this paper, we propose to achieve the goal by placing meta learning on the space of probability measures, inducing the concept of meta sampling for fast uncertainty adaption. Specifically, we propose a Bayesian meta sampling framework consisting of two main components: a meta sampler and a sample adapter. The meta sampler is constructed by adopting a neural-inverse-autoregressive-flow (NIAF) structure, a variant of the recently proposed neural autoregressive flows, to efficiently generate meta samples to be adapted. The sample adapter moves meta samples to task-specific samples, based on a newly proposed and general Bayesian sampling technique, called optimal-transport Bayesian sampling. The combination of the two components allows a simple learning procedure for the
 meta sampler to be developed, which can be efficiently optimized via standard back-propagation. Extensive experimental results demonstrate the efficiency and effectiveness of the proposed framework, obtaining better sample quality and faster
 uncertainty adaption compared to related methods.
answer:

We proposed a Bayesian meta sampling method for adapting the model uncertainty in meta learning