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]: Federated learning allows edge devices to collaboratively learn a shared model while keeping the training data on device, decoupling the ability to do model training from the need to store the data in the cloud. We propose Federated matched averaging (FedMA) algorithm designed for federated learning of modern neural network architectures e.g. convolutional neural networks (CNNs) and LSTMs. FedMA constructs the shared global model in a layer-wise manner by matching and averaging hidden elements (i.e. channels for convolution layers; hidden states for LSTM; neurons for fully connected layers) with similar feature extraction signatures. Our experiments indicate that FedMA outperforms popular state-of-the-art federated learning algorithms on deep CNN and LSTM architectures trained on real world datasets, while improving the communication efficiency.
[EX A]: Communication efficient federated learning with layer-wise matching

[EX Q]: Human brain function as measured by functional magnetic resonance imaging
(fMRI), exhibits a rich diversity. In response, understanding the individual variability
of brain function and its association with behavior has become one of the
major concerns in modern cognitive neuroscience. Our work is motivated by the
view that generative models provide a useful tool for understanding this variability.
To this end, this manuscript presents two novel generative models trained
on real neuroimaging data which synthesize task-dependent functional brain images.
Brain images are high dimensional tensors which exhibit structured spatial
correlations. Thus, both models are 3D conditional Generative Adversarial networks
(GANs) which apply Convolutional Neural Networks (CNNs) to learn an
abstraction of brain image representations. Our results show that the generated
brain images are diverse, yet task dependent. In addition to qualitative evaluation,
we utilize the generated synthetic brain volumes as additional training data to improve
downstream fMRI classifiers (also known as decoding, or brain reading).
Our approach achieves significant improvements for a variety of datasets, classifi-
cation tasks and evaluation scores. Our classification results provide a quantitative
evaluation of the quality of the generated images, and also serve as an additional
contribution of this manuscript.
[EX A]:
Two novel GANs are constructed to generate high-quality 3D fMRI brain images and synthetic brain images greatly help to improve downstream classification tasks.