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: 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.

SOLUTION: A synaptic neural network with synapse graph and learning that has the feature of topological conjugation and Bose-Einstein distribution in surprisal space.  

PROBLEM: We consider new variants of optimization algorithms. Our algorithms are based on the observation that mini-batch of stochastic gradients in consecutive iterations do not change drastically and consequently may be predictable. Inspired by the similar setting in online learning literature called Optimistic Online learning, we propose two new optimistic algorithms for AMSGrad and Adam, respectively, by  exploiting the predictability of gradients.   The new algorithms combine the idea of momentum method, adaptive gradient method, and algorithms in Optimistic Online learning, which leads to speed up in training deep neural nets in practice.

SOLUTION: We consider new variants of optimization algorithms for training deep nets.

PROBLEM: DeePa is a deep learning framework that explores parallelism in all parallelizable dimensions to accelerate the training process of convolutional neural networks. DeePa optimizes parallelism at the granularity of each individual layer in the network. We present an elimination-based algorithm that finds an optimal parallelism configuration for every layer. Our evaluation shows that DeePa achieves up to 6.5× speedup compared to state-of-the-art deep learning frameworks and reduces data transfers by up to 23×.

SOLUTION:
To the best of our knowledge, DeePa is the first deep learning framework that controls and optimizes the parallelism of CNNs in all parallelizable dimensions at the granularity of each layer.