Spectrum of non-Hermitian deep-Hebbian neural networks

Neural networks with recurrent asymmetric couplings are important to understand how episodic memories are encoded in the brain. Here, we integrate the experimental observation of wide synaptic integration window into our model of sequence retrieval in the continuous time dynamics. The model with non-normal neuron-interactions is theoretically studied by deriving a random matrix theory of the Jacobian matrix in neural dynamics. The spectra bears several distinct features, such as breaking rotational symmetry about the origin, and the emergence of nested voids within the spectrum boundary. The spectral density is thus highly non-uniformly distributed in the complex plane. The random matrix theory also predicts a transition to chaos. In particular, the edge of chaos provides computational benefits for the sequential retrieval of memories. Our work provides a systematic study of time-lagged correlations with arbitrary time delays, and thus can inspire future studies of a broad class of memory models, and even big data analysis of biological time series.

A comparative study of deep learning methods for building footprints detection using high spatial resolution aerial images

Building footprints data is of importance in several urban applications and natural disaster management. In contrast to traditional surveying and mapping, using high spatial resolution aerial images, deep learning-based building footprints extraction methods can extract building footprints accurately and efficiently. With rapidly development of deep learning methods, it is hard for novice to harness the powerful tools in building footprints extraction. The paper aims at providing the whole process of building footprints extraction from high spatial resolution images using deep learning-based methods. In addition, we also compare the commonly used methods, including Fully Convolutional Networks (FCN)-8s, U-Net and DeepLabv3+. At the end of the work, we change the data size used in models training to explore the influence of data size to the performance of the algorithms. The experiments show that, in different data size, DeepLabv3+ is the best algorithm among them with the highest accuracy and moderate efficiency; FCN-8s has the worst accuracy and highest efficiency; U-Net shows the moderate accuracy and lowest efficiency. In addition, with more training data, algorithms converged faster with higher accuracy in extraction results.

Relationship between manifold smoothness and adversarial vulnerability in deep learning with local errors

Artificial neural networks can achieve impressive performances, and even outperform humans in some specific tasks. Nevertheless, unlike biological brains, the artificial neural networks suffer from tiny perturbations in sensory input, under various kinds of adversarial attacks. It is therefore necessary to study the origin of the adversarial vulnerability. Here, we establish a fundamental relationship between geometry of hidden representations (manifold perspective) and the generalization capability of the deep networks. For this purpose, we choose a deep neural network trained by local errors, and then analyze emergent properties of trained networks through the manifold dimensionality, manifold smoothness, and the generalization capability. To explore effects of adversarial examples, we consider independent Gaussian noise attacks and fast-gradient-sign-method (FGSM) attacks. Our study reveals that a high generalization accuracy requires a relatively fast power-law decay of the eigen-spectrum of hidden representations. Under Gaussian attacks, the relationship between generalization accuracy and power-law exponent is monotonic, while a non-monotonic behavior is observed for FGSM attacks. Our empirical study provides a route towards a final mechanistic interpretation of adversarial vulnerability under adversarial attacks.