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: 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.

A: A synaptic neural network with synapse graph and learning that has the feature of topological conjugation and Bose-Einstein distribution in surprisal space.  
****
Q: In this paper we use the geometric properties of the optimal transport (OT) problem and the Wasserstein distances to define a prior distribution for the latent space of an auto-encoder. We introduce Sliced-Wasserstein Auto-Encoders (SWAE), that enable one to shape the distribution of the latent space into any samplable probability distribution without the need for training an adversarial network or having a likelihood function specified. In short, we regularize the auto-encoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a samplable prior distribution. We show that the proposed formulation has an efficient numerical solution that provides similar capabilities to Wasserstein Auto-Encoders (WAE) and Variational Auto-Encoders (VAE), while benefiting from an embarrassingly simple implementation. We provide extensive error analysis for our algorithm, and show its merits on three benchmark datasets.

A: In this paper we use the sliced-Wasserstein distance to shape the latent distribution of an auto-encoder into any samplable prior distribution. 
****
Q: Inductive and unsupervised graph learning is a critical technique for predictive or information retrieval tasks where label information is difficult to obtain. It is also challenging to make graph learning inductive and unsupervised at the same time, as learning processes guided by reconstruction error based loss functions inevitably demand graph similarity evaluation that is usually computationally intractable. In this paper, we propose a general framework SEED (Sampling, Encoding, and Embedding Distributions) for inductive and unsupervised representation learning on graph structured objects. Instead of directly dealing with the computational challenges raised by graph similarity evaluation, given an input graph, the SEED framework samples a number of subgraphs whose reconstruction errors could be efficiently evaluated, encodes the subgraph samples into a collection of subgraph vectors, and employs the embedding of the subgraph vector distribution as the output vector representation for the input graph. By theoretical analysis, we demonstrate the close connection between SEED and graph isomorphism. Using public benchmark datasets, our empirical study suggests the proposed SEED framework is able to achieve up to 10% improvement, compared with competitive baseline methods.

A:
This paper proposed a novel framework for graph similarity learning in inductive and unsupervised scenario.
****