dot product
Recently Published Documents





Kang He ◽  
Roberto Barrio ◽  
Lin Chen ◽  
Hao Jiang ◽  
Jie Liu ◽  

2021 ◽  
Yuanyue Li ◽  
Tobias Kind ◽  
Jacob Folz ◽  
Arpana Vaniya ◽  
Sajjan Singh Mehta ◽  

2021 ◽  
Vol 10 (1) ◽  
Shaofu Xu ◽  
Jing Wang ◽  
Haowen Shu ◽  
Zhike Zhang ◽  
Sicheng Yi ◽  

AbstractOptical implementations of neural networks (ONNs) herald the next-generation high-speed and energy-efficient deep learning computing by harnessing the technical advantages of large bandwidth and high parallelism of optics. However, due to the problems of the incomplete numerical domain, limited hardware scale, or inadequate numerical accuracy, the majority of existing ONNs were studied for basic classification tasks. Given that regression is a fundamental form of deep learning and accounts for a large part of current artificial intelligence applications, it is necessary to master deep learning regression for further development and deployment of ONNs. Here, we demonstrate a silicon-based optical coherent dot-product chip (OCDC) capable of completing deep learning regression tasks. The OCDC adopts optical fields to carry out operations in the complete real-value domain instead of in only the positive domain. Via reusing, a single chip conducts matrix multiplications and convolutions in neural networks of any complexity. Also, hardware deviations are compensated via in-situ backpropagation control provided the simplicity of chip architecture. Therefore, the OCDC meets the requirements for sophisticated regression tasks and we successfully demonstrate a representative neural network, the AUTOMAP (a cutting-edge neural network model for image reconstruction). The quality of reconstructed images by the OCDC and a 32-bit digital computer is comparable. To the best of our knowledge, there is no precedent of performing such state-of-the-art regression tasks on ONN chips. It is anticipated that the OCDC can promote the novel accomplishment of ONNs in modern AI applications including autonomous driving, natural language processing, and scientific study.

Peng Zhang ◽  
Menglan Duan ◽  
Qiang gao ◽  
Jianmin Ma ◽  
Jinxin Wang ◽  

2021 ◽  
Peter Kochunov ◽  
Yizhou Ma ◽  
Kathryn S Hatch ◽  
Lianne Schmaal ◽  
Neda Jahanshad ◽  

Big Data neuroimaging collaborations including Enhancing Neuro Imaging Genetics through Meta-Analysis (ENIGMA) integrated worldwide data to identify regional brain deficits in major depressive disorder (MDD). We evaluated the sensitivity of translating ENIGMA-defined MDD deficit patterns to the individual level. We treated ENIGMA MDD deficit patterns as a vector to gauge the similarity between individual and MDD patterns by calculating ENIGMA dot product (EDP). We analyzed the sensitivity and specificity of EDP in separating subjects with (1) subclinical depressive symptoms without a diagnosis of MDD, (2) single episode MDD, (3) recurrent MDD, and (4) controls free of neuropsychiatric disorders. We compared EDP to the Quantile Regression Index (QRI; a linear alternative to the brain age metric) and the global gray matter thickness and subcortical volumes and fractional anisotropy (FA) of water diffusion. We performed this analysis in a large epidemiological sample of UK Biobank (UKBB) participants (N=17,053/19,265 M/F). Group-average increases in depressive symptoms from controls to recurrent MDD was mirrored by EDP (r2=0.85), followed by FA (r2=0.81) and QRI (r2=0.56). Subjects with MDD showed worse performance on cognitive tests than controls with deficits observed for 3 out of 9 cognitive tests administered by the UKBB. We calculated correlations of EDP and other brain indices with measures of cognitive performance in controls. The correlation pattern between EDP and cognition in controls was similar (r2=0.75) to the pattern of cognitive differences in MDD. This suggests that the elevation in EDP, even in controls, is associated with cognitive performance - specifically in the MDD-affected domains. That specificity was missing for QRI, FA or other brain imaging indices. In summary, translating anatomically informed meta-analytic indices of similarity using a linear vector approach led to better sensitivity to depressive symptoms and cognitive patterns than whole-brain imaging measurements or an index of accelerated aging.

Karthik Viswanath S ◽  
Naveen L ◽  
Ananda Raj ◽  
Rajalakshmi S ◽  
Angel Deborah S

Matthew Johnson ◽  
Daniël Paulusma ◽  
Erik Jan van Leeuwen

Let [Formula: see text] be an integer. From a set of [Formula: see text]-dimensional vectors, we obtain a [Formula: see text]-dot by letting each vector [Formula: see text] correspond to a vertex [Formula: see text] and by adding an edge between two vertices [Formula: see text] and [Formula: see text] if and only if their dot product [Formula: see text], for some fixed, positive threshold [Formula: see text]. Dot product graphs can be used to model social networks. Recognizing a [Formula: see text]-dot product graph is known to be NP -hard for all fixed [Formula: see text]. To understand the position of [Formula: see text]-dot product graphs in the landscape of graph classes, we consider the case [Formula: see text], and investigate how [Formula: see text]-dot product graphs relate to a number of other known graph classes including a number of well-known classes of intersection graphs.

Sign in / Sign up

Export Citation Format

Share Document