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A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small neighborhood of the minimum, it cannot explain many…

This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear),…

A well-trained deep neural network is shown to gain capability of simultaneously restoring two kinds of images, which are completely destroyed by two distinct scattering medias respectively. The network, based on the U-net architecture, can…

A novel framework of optical image hiding based on deep learning (DL) is proposed in this paper, and hidden information can be reconstructed from an interferogram by using an end to end network with high-quality. By using the prior data…

We present a global algorithm for training multilayer neural networks in this Letter. The algorithm is focused on controlling the local fields of neurons induced by the input of samples by random adaptations of the synaptic weights. Unlike…

Score-based models have achieved remarkable results in the generative modeling of many domains. By learning the gradient of smoothed data distribution, they can iteratively generate samples from complex distribution e.g. natural images.…

Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…

In this paper, we advocate for two stages in a neural network's decision making process. The first is the existing feed-forward inference framework where patterns in given data are sensed and associated with previously learned patterns. The…

We propose a learning-based approach for estimating the spectrum of a multisinusoidal signal from a finite number of samples. A neural-network is trained to approximate the spectra of such signals on simulated data. The proposed methodology…

There is strong interest in developing mathematical methods that can be used to understand complex neural networks used in image analysis. In this paper, we introduce techniques from Linear Algebra to model neural network layers as maps…

We investigate the problem of estimating the structure of a weighted network from repeated measurements of a Gaussian Graphical Model (GGM) on the network. In this vein, we consider GGMs whose covariance structures align with the geometry…

Linear layers in neural networks (NNs) trained by gradient descent can be expressed as a key-value memory system which stores all training datapoints and the initial weights, and produces outputs using unnormalised dot attention over the…

We devise a universal adaptive neural layer to "learn" optimal frequency filter for each image together with the weights of the base neural network that performs some computer vision task. The proposed approach takes the source image in the…

In order to design haptic icons or build a haptic vocabulary, we require a set of easily distinguishable haptic signals to avoid perceptual ambiguity, which in turn requires a way to accurately estimate the perceptual (dis)similarity of…

The backpropagation algorithm is an invaluable tool for training artificial neural networks; however, because of a weight sharing requirement, it does not provide a plausible model of brain function. Here, in the context of a two-layer…

We present a novel convolutional neural network architecture for photometric stereo (Woodham, 1980), a problem of recovering 3D object surface normals from multiple images observed under varying illuminations. Despite its long history in…

For performing successful measurements within limited experimental time, efficient use of preliminary data plays a crucial role. This work shows that a simple feedforward type neural networks approach for learning preliminary experimental…

We give a new algorithm for learning a two-layer neural network under a general class of input distributions. Assuming there is a ground-truth two-layer network $$ y = A \sigma(Wx) + \xi, $$ where $A,W$ are weight matrices, $\xi$ represents…

Input space reconstruction is an attractive representation learning paradigm. Despite interpretability of the reconstruction and generation, we identify a misalignment between learning by reconstruction, and learning for perception. We show…

Back-propagation with gradient method is the most popular learning algorithm for feed-forward neural networks. However, it is critical to determine a proper fixed learning rate for the algorithm. In this paper, an optimized recursive…