Related papers: Computing with Residue Numbers in High-Dimensional…

Distributed computation is a framework used to break down a complex computational task into smaller tasks and distributing them among computational nodes. Erasure correction codes have recently been introduced and have become a popular…

Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions, leading to significant residual errors in geospatial applications. Here we propose a residual-based neural correction strategy, in…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

Residual units are wildly used for alleviating optimization difficulties when building deep neural networks. However, the performance gain does not well compensate the model size increase, indicating low parameter efficiency in these…

The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…

Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is…

The block-based coding structure in the hybrid video coding framework inevitably introduces compression artifacts such as blocking, ringing, etc. To compensate for those artifacts, extensive filtering techniques were proposed in the loop 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 introduces a framework for super-resolution of scalable video based on compressive sensing and sparse representation of residual frames in reconnaissance and surveillance applications. We exploit efficient compressive sampling…

Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…

We model human and animal learning by computing with high-dimensional vectors (H = 10,000 for example). The architecture resembles traditional (von Neumann) computing with numbers, but the instructions refer to vectors and operate on them…

In computation-intensive domains such as digital signal processing, encryption, and neural networks, the performance of arithmetic units, including adders and multipliers, is pivotal. Conventional numerical systems often fall short of…

Residual networks (ResNets) have been utilized for various computer vision and image processing applications. The residual connection improves the training of the network with better gradient flow. A residual block consists of few…

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

We introduce a new technique for the efficient management of large sequences of multidimensional data, which takes advantage of regularities that arise in real-world datasets and supports different types of aggregation queries. More…

Learning expressive low-dimensional representations of ultrahigh-dimensional data, e.g., data with thousands/millions of features, has been a major way to enable learning methods to address the curse of dimensionality. However, existing…

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…

As datasets grow it becomes infeasible to process them completely with a desired model. For giant datasets, we frame the order in which computation is performed as a decision problem. The order is designed so that partial computations are…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…