相关论文: Can A Neural Network Hear the Shape of A Drum?

Neural population activity in sensory cortex is organized on low-dimensional manifolds, but why such manifolds arise and what determines their geometry remain unclear. We model cortical populations as recurrent circuits driven by…

The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by…

We consider a family of deep neural networks consisting of two groups of convolutional layers, a downsampling operator, and a fully connected layer. The network structure depends on two structural parameters which determine the numbers of…

We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is…

This paper describes how realistic neuromorphic networks can have their connectivity fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional…

Shape learning, or the ability to leverage shape information, could be a desirable property of convolutional neural networks (CNNs) when target objects have specific shapes. While some research on the topic is emerging, there is no…

Classical deep networks are effective because depth enables adaptive geometric deformation of data representations. In quantum neural networks (QNNs), however, depth or state reachability alone does not guarantee this feature-learning…

Mark Kac asked a famous question in 1966 entitled Can one hear the shape of a drum?, a spectral geometry problem that has intrigued mathematicians for the last six decades and is important to many other fields, such as architectural…

Even though Deep Neural Networks (DNNs) are widely celebrated for their practical performance, they possess many intriguing properties related to depth that are difficult to explain both theoretically and intuitively. Understanding how…

Graph neural networks trained to predict observable dynamics can be used to decompose the temporal activity of complex heterogeneous systems into simple, interpretable representations. Here we apply this framework to simulated neural…

Establishing accurate morphological measurements of galaxies in a reasonable amount of time for future big-data surveys such as EUCLID, the Large Synoptic Survey Telescope or the Wide Field Infrared Survey Telescope is a challenge. Because…

Domain adaptation, adapting models from domains rich in labeled training data to domains poor in such data, is a fundamental NLP challenge. We introduce a neural network model that marries together ideas from two prominent strands of…

Deep convolutional neural networks (CNNs) have demonstrated impressive performance on visual object classification tasks. In addition, it is a useful model for predication of neuronal responses recorded in visual system. However, there is…

Deep convolutional neural networks (CNN) brought revolution without any doubt to various challenging tasks, mainly in computer vision. However, their model designing still requires attention to reduce number of learnable parameters, with no…

Improving the interpretability of deep neural networks has recently gained increased attention, especially when the power of deep learning is leveraged to solve problems in physics. Interpretability helps us understand a model's ability to…

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based…

The ability to design complex neural network architectures which enable effective training by stochastic gradient descent has been the key for many achievements in the field of deep learning. However, developing such architectures remains a…

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…

In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples. More specifically we…

This paper proposed a novel approach for the detection and reconstruction of dysarthric speech. The encoder-decoder model factorizes speech into a low-dimensional latent space and encoding of the input text. We showed that the latent space…