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Information Geometry of Orthogonal Initializations and Training [article]

Piotr A. Sokol, Il Memming Park
2019 arXiv   pre-print
are near ℓ_2 isometries and as a consequence training is orders of magnitude faster.  ...  Here we show a novel connection between the maximum curvature of the optimization landscape (gradient smoothness) as measured by the Fisher information matrix (FIM) and the spectral radius of the input-output  ...  To test how enforcing strict orthogonality or near orthogonality affects convergence speed and the maximum eigenvalues of the Fisher information matrix, we trained Stiefel and Oblique constrained networks  ... 
arXiv:1810.03785v2 fatcat:tgwqcg3v25cqne5ctyruzzq54q

A Machine-Learning Framework for Design for Manufacturability [article]

Aditya Balu, Sambit Ghadai, Gavin Young, Soumik Sarkar, Adarsh Krishnamurthy
2017 arXiv   pre-print
We initially use the voxelized representation of the CAD geometry to train the DLDFM network.  ...  Later, we use the orthogonal distance field representation of the CAD geometry to train another DLDFM network.  ...  The heat map of (L 3DGradCAM ) is resampled using linear interpolation to match the input size, and then overlaid in 3D with the input to be able to spatially identify the source of nonmanufacturability  ... 
arXiv:1703.01499v2 fatcat:iswimkbw3ngohebe3avqrhmxbq

Modern Educational Instruments And Blended-Learning Technologies In Descriptive Geometry Teaching

Damaris Căuneac, Bogdan Chiliban, Marius Chiliban
2014 Balkan Region Conference on Engineering and Business Education  
The main concern of this paper is to demonstrate how using electronic methods young engineers learn about the descriptive geometry and improves the student's intellectual capability of space perception  ...  Using the modern educational instruments as DidaTech Platform, CAD or C++ program presentations in higher education for engineering the level of comprehending and interest in the profile subjects should  ...  ) of lifelong learning and training for higher education teachers.  ... 
doi:10.2478/cplbu-2014-0109 fatcat:l42zjwss4bg3lgat5wdzonnozy

Orthogonal Neighborhood Preserving Embedding for Face Recognition

Xiaoming Liu, Jianwei Yin, Zhilin Feng, Jinxiang Dong, Lu Wang
2007 Proceedings of IEEE international conference on image processing  
ONPE can preserve local geometry information and is based on the local linearity assumption that each data point and its k nearest neighbors lie on a linear manifold locally embedded in the image space  ...  ONPC is based on the natural assumption that the local neighborhood information is also preserved in reduced space, and the label of a data point can be obtained in the reduced space by the labels of its  ...  The original NPE utilize KNN (K-nearest neighbors) for classification, and is not optimal due to its ignoring of the local geometry information.  ... 
doi:10.1109/icip.2007.4378909 dblp:conf/icip/LiuYFDW07 fatcat:2zhsvwrvbvbk7pdxg4shda3e5y

Linear discriminant initialization for feed-forward neural networks [article]

Marissa Masden, Dev Sinha
2020 arXiv   pre-print
Networks initialized in this way take fewer training steps to reach the same level of training, and asymptotically have higher accuracy on training data.  ...  Informed by the basic geometry underlying feed forward neural networks, we initialize the weights of the first layer of a neural network using the linear discriminants which best distinguish individual  ...  and geometry of trained networks.  ... 
arXiv:2007.12782v2 fatcat:pdgxtzlhfzgzfeyyzfbzor2lni

Interactive Annotation of 3D Object Geometry using 2D Scribbles [article]

Tianchang Shen, Jun Gao, Amlan Kar, Sanja Fidler
2020 arXiv   pre-print
Inferring detailed 3D geometry of the scene is crucial for robotics applications, simulation, and 3D content creation.  ...  However, such information is hard to obtain, and thus very few datasets support it.  ...  We thank Louis Clergue for assistance with developing the web tool and extended discussion. This work was supported by NSERC. SF acknowledges the Canada CIFAR AI Chair award at the Vector Institute.  ... 
arXiv:2008.10719v2 fatcat:efmdbwwvq5akjbjrt2ivu7trju

Shared Representational Geometry Across Neural Networks [article]

Qihong Lu, Po-Hsuan Chen, Jonathan W. Pillow, Peter J. Ramadge, Kenneth A. Norman, Uri Hasson
2019 arXiv   pre-print
orthogonal transformations.  ...  Using a shared response model, we show that different neural networks encode the same input examples as different orthogonal transformations of an underlying shared representation.  ...  And their activity patterns are connected by orthogonal transformations (assuming the training data is structured hierarchically, small norm weight initialization, and small learning rate) [16, 17] .  ... 
arXiv:1811.11684v2 fatcat:cewhqgpww5gbrd2t75xizxm4ri

Charting the energy landscape of metal/organic interfaces via machine learning

Michael Scherbela, Lukas Hörmann, Andreas Jeindl, Veronika Obersteiner, Oliver T. Hofmann
2018 PHYSICAL REVIEW MATERIALS  
In this work we present a method to efficiently explore the potential energy surface and predict the formation energies of polymorphs and defects.  ...  This is achieved by training a machine learning model on a list of only 100 candidate structures that are evaluated via dispersion-corrected Density Functional Theory (DFT) calculations.  ...  Effect of the Methodology: Parallel vs Orthogonal Molecules To address the issue of orthogonal vs rotated molecules we calculated the energetic difference between both geometries for a polymorph with 2  ... 
doi:10.1103/physrevmaterials.2.043803 fatcat:r4534m3gzze43kdroonnuycpua

Automatic Mechanism Modeling from a Single Image with CNNs

Minmin Lin, Tianjia Shao, Youyi Zheng, Zhong Ren, Yanlin Weng, Yin Yang
2018 Computer graphics forum (Print)  
Abstract This paper presents a novel system that enables a fully automatic modeling of both 3D geometry and functionality of a mechanism assembly from a single RGB image.  ...  The resulting 3D mechanism model highly resembles the one in the input image with the geometry, mechanical attributes, connectivity, and functionality of all the mechanical parts prescribed in a physically  ...  The depth information of an instantiated part is largely based on an assumed initial value (i.e. 2.0, which is default camera depth for training data generation).  ... 
doi:10.1111/cgf.13572 fatcat:bxedssjfdfhcvethshhqvfij2e

Natural parameterized quantum circuit [article]

Tobias Haug, M. S. Kim
2021 arXiv   pre-print
The initial training of variational quantum algorithms is substantially sped up as the gradient is equivalent to the quantum natural gradient.  ...  However, the non-euclidean quantum geometry of parameterized quantum circuits is detrimental for these applications.  ...  Number of layers is p = 10 and data averaged over 50 random instances. c) Training NPQC with initial parameter θr and initial infidelity ∆Kt(θr) = 0.9.  ... 
arXiv:2107.14063v2 fatcat:kt2o6rk2jvcbbkbnf7s3giv7u4

Divergence Framework for EEG based Multiclass Motor Imagery Brain Computer Interface [article]

Satyam Kumar, Tharun Kumar Reddy, Laxmidhar Behera
2019 arXiv   pre-print
The performance of the proposed stationarity enforcing algorithm is compared to that of baseline One-Versus-Rest (OVR)-CSP and JAD on publicly available BCI competition IV dataset IIa.  ...  We determine the subspace for the proposed approach through optimization using gradient descent on an orthogonal manifold.  ...  the orthogonal matrix is randomly initialized.  ... 
arXiv:1901.07457v1 fatcat:jaaxmkqqwva4dku3qvsv2cdvme

Application of Self-Organizing Artificial Neural Networks on Simulated Diffusion Tensor Images

Dilek Göksel-Duru, Mehmed Özkan
2013 Mathematical Problems in Engineering  
Four different tract geometries with varying SNRs and fractional anisotropy are investigated.  ...  Diffusion tensor magnetic resonance imaging (DTMRI) as a noninvasive modality providing in vivo anatomical information allows determination of fiber connections which leads to brain mapping.  ...  Conflict of Interests The authors have no conflict of interests to disclose. Acknowledgment This work is supported in part by Bogazici University Scientific Research Project no. 07HX104D.  ... 
doi:10.1155/2013/690140 fatcat:57qzcug6wzcarc3ieeem5lbr6q

Generalized BackPropagation, Étude De Cas: Orthogonality [article]

Mehrtash Harandi, Basura Fernando
2016 arXiv   pre-print
In particular, we make use of the Riemannian geometry and optimization techniques on matrix manifolds to step outside of normal practice in training deep networks, equipping the network with structures  ...  Among various applications, Stiefel layers can be used to design orthogonal filter banks, perform dimensionality reduction and feature extraction.  ...  The Stiefel manifold, the geometry encompassing the set of orthogonal matrices, is named in honor of him.  ... 
arXiv:1611.05927v1 fatcat:6xqppqkcljc53eunalcf4sv4zi

Laplacian Support Vector Analysis for Subspace Discriminative Learning

Nikolaos Arvanitopoulos, Dimitrios Bouzas, Anastasios Tefas
2014 2014 22nd International Conference on Pattern Recognition  
In our analysis, we derive an explicit form for the deflation matrix of the mapped features in both the initial and the Hilbert space by using the kernel trick and thus, we can handle linear and non-linear  ...  The proposed method, called Laplacian Support Vector Analysis, produces projection vectors, which capture the discriminant information that lies in the subspace orthogonal to the standard Laplacian SVMs  ...  The resulting normal vectors of the trained hyperplanes are used to project the initial data points in lower dimension and therefore, they provide new discriminative information for feature extraction.  ... 
doi:10.1109/icpr.2014.285 dblp:conf/icpr/ArvanitopoulosBT14 fatcat:wehioetc7bfrbesl4fpvpnazdy

Discriminative Orthogonal Neighborhood-Preserving Projections for Classification

Tianhao Zhang, Kaiqi Huang, Xuelong Li, Jie Yang, Dacheng Tao
2010 IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)  
DONPP 1) takes into account both intraclass and interclass geometries; 2) considers the neighborhood information of interclass relationships; and 3) follows the orthogonality property of ONPP.  ...  This uses unlabeled samples to improve the classification accuracy of the original DONPP. Empirical studies demonstrate the effectiveness of both DONPP and SDONPP.  ...  ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their constructive comments on the first version of this paper.  ... 
doi:10.1109/tsmcb.2009.2027473 pmid:19744914 fatcat:3yprnadlgnebxji74jcoa3eeqq
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