Yanyang Xiao

Rubin Zhao, Yang Liu, Shiqi Zhang et al.

Neurons, with their elongated, tree-like dendritic and axonal structures, enable efficient signal integration and long-range communication across brain regions. By reconstructing individual neurons' morphology, we can gain valuable insights into brain connectivity, revealing the structure basis of cognition, movement, and perception. Despite the accumulation of extensive 3D microscopic imaging data, progress has been considerably hindered by the absence of automated tools to streamline this process. Here we introduce NeuroFly, a validated framework for large-scale automatic single neuron reconstruction. This framework breaks down the process into three distinct stages: segmentation, connection, and proofreading. In the segmentation stage, we perform automatic segmentation followed by skeletonization to generate over-segmented neuronal fragments without branches. During the connection stage, we use a 3D image-based path following approach to extend each fragment and connect it with other fragments of the same neuron. Finally, human annotators are required only to proofread the few unresolved positions. The first two stages of our process are clearly defined computer vision problems, and we have trained robust baseline models to solve them. We validated NeuroFly's efficiency using in-house datasets that include a variety of challenging scenarios, such as dense arborizations, weak axons, images with contamination. We will release the datasets along with a suite of visualization and annotation tools for better reproducibility. Our goal is to foster collaboration among researchers to address the neuron reconstruction challenge, ultimately accelerating advancements in neuroscience research. The dataset and code are available at https://github.com/beanli161514/neurofly

Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo et al.

We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often fit target functions from low to high frequencies -- on high-dimensional benchmark datasets such as MNIST/CIFAR10 and deep neural networks such as VGG16. This F-Principle of DNNs is opposite to the behavior of most conventional iterative numerical schemes (e.g., Jacobi method), which exhibit faster convergence for higher frequencies for various scientific computing problems. With a simple theory, we illustrate that this F-Principle results from the regularity of the commonly used activation functions. The F-Principle implies an implicit bias that DNNs tend to fit training data by a low-frequency function. This understanding provides an explanation of good generalization of DNNs on most real datasets and bad generalization of DNNs on parity function or randomized dataset.

Zhi-Qin John Xu, Yaoyu Zhang, Yanyang Xiao

Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding]. To find a potential mechanism, we focus on the study of implicit biases underlying the training process of DNNs. In this work, for both real and synthetic datasets, we empirically find that a DNN with common settings first quickly captures the dominant low-frequency components, and then relatively slowly captures the high-frequency ones. We call this phenomenon Frequency Principle (F-Principle). The F-Principle can be observed over DNNs of various structures, activation functions, and training algorithms in our experiments. We also illustrate how the F-Principle help understand the effect of early-stopping as well as the generalization of DNNs. This F-Principle potentially provides insights into a general principle underlying DNN optimization and generalization.