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 Q]: Neural network training depends on the structure of the underlying loss landscape, i.e. local minima, saddle points, flat plateaus, and loss barriers. In relation to the structure of the landscape, we study the permutation symmetry of neurons in each layer of a deep neural network, which gives rise not only to multiple equivalent global minima of the loss function but also to critical points in between partner minima. In a network of $d-1$ hidden layers with $n_k$ neurons in layers $k = 1, \ldots, d$, we construct continuous paths between equivalent global minima that lead through a `permutation point' where the input and output weight vectors of two neurons in the same hidden layer $k$ collide and interchange. We show that such permutation points are critical points which lie inside high-dimensional subspaces of equal loss, contributing to the global flatness of the landscape. We also find that a permutation point for the exchange of neurons $i$ and $j$ transits into a flat high-dimensional plateau that enables all $n_k!$ permutations of neurons in a given layer $k$ at the same loss value. Moreover , we introduce higher-order permutation points by exploiting the hierarchical structure in the loss landscapes of neural networks, and find that the number of $K$-th order permutation points is much larger than the (already huge) number of equivalent global minima -- at least by a polynomial factor of order $K$. In two tasks, we demonstrate numerically with our path finding method that continuous paths between partner minima exist: first, in a toy network with a single hidden layer on a function approximation task and, second, in a multilayer network on the MNIST task. Our geometric approach yields a lower bound on the number of critical points generated by weight-space symmetries and provides a simple intuitive link between previous theoretical results and numerical observations.
[EX A]: Weight-space symmetry in neural network landscapes gives rise to numerous number of saddles and flat high-dimensional subspaces.

[EX Q]: To understand how object vision develops in infancy and childhood, it will be necessary to develop testable computational models. Deep neural networks (DNNs) have proven valuable as models of adult vision, but it is not yet clear if they have any value as models of development. As a first model, we measured learning in a DNN designed to mimic the architecture and representational geometry of the visual system (CORnet). We quantified the development of explicit object representations at each level of this network through training by freezing the convolutional layers and training an additional linear decoding layer. We evaluate decoding accuracy on the whole ImageNet validation set, and also for individual visual classes. CORnet, however, uses supervised training and because infants have only extremely impoverished access to labels they must instead learn in an unsupervised manner. We therefore also measured learning in a state-of-the-art unsupervised network (DeepCluster). CORnet and DeepCluster differ in both supervision and in the convolutional networks at their heart, thus to isolate the effect of supervision, we ran a control experiment in which we trained the convolutional network from DeepCluster (an AlexNet variant) in a supervised manner. We make predictions on how learning should develop across brain regions in infants. In all three networks, we also tested for a relationship in the order in which infants and machines acquire visual classes, and found only evidence for a counter-intuitive relationship. We discuss the potential reasons for this.
[EX A]: Unsupervised networks learn from bottom up; machines and infants acquire visual classes in different orders

[EX Q]: Using higher order knowledge to reduce training data has become a popular research topic. However, the ability for available methods to draw effective decision boundaries is still limited: when training set is small, neural networks will be biased to certain labels. Based on this observation, we consider constraining output probability distribution as higher order domain knowledge. We design a novel algorithm that jointly optimizes output probability distribution on a clustered embedding space to make neural networks draw effective decision boundaries.   While directly applying probability constraint is not effective, users need to provide additional very weak supervisions: mark some batches that have output distribution greatly differ from target probability distribution. We use experiments to empirically prove that our model can converge to an accuracy higher than other state-of-art semi-supervised learning models with less high quality labeled training examples.
[EX A]:
We introduce an embedding space approach to constrain neural network output probability distribution.