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.

Ex Input:
The Lottery Ticket Hypothesis from Frankle & Carbin (2019) conjectures that, for typically-sized neural networks, it is possible to find small sub-networks which train faster and yield superior performance than their original counterparts. The proposed algorithm to search for such sub-networks (winning tickets), Iterative Magnitude Pruning (IMP), consistently finds sub-networks with 90-95% less parameters which indeed train faster and better than the overparameterized models they were extracted from, creating potential applications to problems such as transfer learning.

 In this paper, we propose a new algorithm to search for winning tickets, Continuous Sparsification, which continuously removes parameters from a network during training, and learns the sub-network's structure with gradient-based methods instead of relying on pruning strategies. We show empirically that our method is capable of finding tickets that outperforms the ones learned by Iterative Magnitude Pruning, and at the same time providing up to 5 times faster search, when measured in number of training epochs.

Ex Output:
We propose a new algorithm that quickly finds winning tickets in neural networks.


Ex Input:
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.

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


Ex Input:
Biological neural networks face homeostatic and resource constraints that restrict the allowed configurations of connection weights. If a constraint is tight it defines a very small solution space, and the size of these constraint spaces determines their potential overlap with the solutions for computational tasks. We study the geometry of the solution spaces for constraints on neurons' total synaptic weight and on individual synaptic weights, characterizing the connection degrees (numbers of partners) that maximize the size of these solution spaces. We then hypothesize that the size of constraints' solution spaces could serve as a cost function governing neural circuit development. We develop analytical approximations and bounds for the model evidence of the maximum entropy degree distributions under these cost functions. We test these on a published electron microscopic connectome of an associative learning center in the fly brain, finding evidence for a developmental progression in circuit structure.

Ex Output:

We examine the hypothesis that the entropy of solution spaces for constraints on synaptic weights (the "flexibility" of the constraint) could serve as a cost function for neural circuit development.