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Passed Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Models [article]

Stefano Sarao Mannelli, Florent Krzakala, Pierfrancesco Urbani, and Lenka Zdeborová
2020 arXiv   pre-print
to perform well even in the part of the region of parameters where spurious local minima are present.  ...  We analyze the performance of an approximate message passing algorithm estimating the maximum likelihood configuration via its state evolution.  ...  the sense that all spurious local minima disappear.  ... 
arXiv:1902.00139v4 fatcat:jzmm4vlbu5cqffqce226be5q7m

Chaincode contour processing for handwritten word recognition

S. Madhvanath, G. Kim, V. Govindaraju
1999 IEEE Transactions on Pattern Analysis and Machine Intelligence  
Our experiments indicate that significant gains are to be realized in both speed and recognition accuracy by using a contour representation in handwriting applications.  ...  AbstractÐContour representations of binary images of handwritten words afford considerable reduction in storage requirements while providing lossless representation.  ...  The system remains in the reject state until the stack is completely empty, at which point it returns to the accept state.  ... 
doi:10.1109/34.790433 fatcat:i63uywfaljfcxbbofkfdvyqgg4

Global and Local Analyses of Nonlinear Low-Rank Matrix Recovery Problems [article]

Yingjie Bi, Javad Lavaei
2020 arXiv   pre-print
The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements.  ...  Using RIP and BDP jointly, we first focus on the rank-1 matrix recovery problem, for which we propose a new criterion to certify the nonexistence of spurious local minima over the entire space.  ...  It also appears in engineering problems, such as power system state estimation (Zhang et al., 2018b) .  ... 
arXiv:2010.04349v3 fatcat:qlaooa4ahfffdbkiockxxegbp4

Blind analysis of molecular dynamics [article]

Sergei Krivov
2021 arXiv   pre-print
In particular, it does not require a functional form with many parameters to closely approximate eigenvectors, e.g., a neural network, and thus no extensive expertise with the system.  ...  The power of the approach is illustrated on long atomistic protein folding trajectories.  ...  F (ũ 1 ) shows two minima with an intermediate state in agreement with other studies [23, 24] .  ... 
arXiv:2005.02782v2 fatcat:bwhi7ao42rglhbtbh5d6q2nhua

On the Landscape of Synchronization Networks: A Perspective from Nonconvex Optimization [article]

Shuyang Ling, Ruitu Xu, Afonso S. Bandeira
2019 arXiv   pre-print
underlying network and exploring the relationship between the existence of local minima and network topology.  ...  Consequently, the stable equilibrium of the corresponding homogeneous Kuramoto model is unique and the basin of attraction for the synchronous state of these coupled oscillators is the whole phase space  ...  Does (1.3) have spurious local minima? How does the existence of spurious local minima depend on the topology of the network?  ... 
arXiv:1809.11083v2 fatcat:v247knsqprcptm6qergvlt74ka

Portable Ultrasound-Based Device for Detecting Older Adults' Sit-to-Stand Transitions in Unsupervised 30-Second Chair-Stand Tests

Antonio Cobo, Elena Villalba-Mora, Dieter Hayn, Xavier Ferre, Rodrigo Pérez-Rodríguez, Alberto Sánchez-Sánchez, Raquel Bernabé-Espiga, Juan-Luis Sánchez-Sánchez, Andrea López-Diez-Picazo, Cristian Moral, Leocadio Rodriguez-Mañas
2020 Sensors  
Lower-limb strength is a marker of functional decline in elders.  ...  The funding organisms had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  ...  The authors would like to specially thank the volunteers in the study, in particular the older people, for their unselfish collaboration, enthusiasm, and dedication.  ... 
doi:10.3390/s20071975 pmid:32244761 pmcid:PMC7180983 fatcat:kicsp7rbnjdm5jcqsahxquk2aa

Improved unfolding by detrending of statistical fluctuations in quantum spectra

Irving O. Morales, E. Landa, P. Stránský, A. Frank
2011 Physical Review E  
This relationship has been addressed previously as a signature of chaos in quantum dynamical systems.  ...  Unfortunately this process, called unfolding, is not trivial and can lead to erroneous conclusions about the chaoticity of a system.  ...  envelope defined by the local maxima and the envelope defined by the local minima is zero.  ... 
doi:10.1103/physreve.84.016203 pmid:21867269 fatcat:2fyqm7rvrfet3pjwr2xbadnhym

Energy landscape of silicon systems and its description by force fields, tight binding schemes, density functional methods, and quantum Monte Carlo methods

S. Alireza Ghasemi, Maximilian Amsler, Richard G. Hennig, Shantanu Roy, Stefan Goedecker, Thomas J. Lenosky, C. J. Umrigar, Luigi Genovese, Tetsuya Morishita, Kengo Nishio
2010 Physical Review B  
On the other hand, force fields give a very poor description of the landscape that are in most cases too rough and contain many spurious local minima and saddle points or ones that have the wrong height  ...  states and thus a good overall description of the energy landscape of the silicon systems.  ...  at the National Center for Supercomputing Applications, which is supported by the National Science Foundation and by the Computational Center for Nanotechnology Innovations, which is supported by the state  ... 
doi:10.1103/physrevb.81.214107 fatcat:q4q5ssnfbfhjjlrmfjvkk34g7a

Page 445 of SMPTE Motion Imaging Journal Vol. 99, Issue 6 [page]

1990 SMPTE Motion Imaging Journal  
The default state for the EDRP system, after a channel switching or power-on, is the let- through mode, until the master algo- rithm verifies reliable operation and switches to a ghost-canceller mode of  ...  It also allows the use of large adaptation constants that yield a fast response while avoiding conver- gence to nonoptimal local minima on the performance surface.  ... 

Factorization Approach for Low-complexity Matrix Completion Problems: Exponential Number of Spurious Solutions and Failure of Gradient Methods [article]

Baturalp Yalcin, Haixiang Zhang, Javad Lavaei, Somayeh Sojoudi
2021 arXiv   pre-print
We construct an instance of polynomial-time solvable MC problems with exponentially many spurious local minima, which leads to the failure of most gradient-based methods.  ...  In this work, we provide a negative answer to the above question.  ...  Finally, we give an estimate on the largest lower bound for the number of spurious local minima. Corollary 3.  ... 
arXiv:2110.10279v1 fatcat:mginu4mnqncwpdecxijny5rxl4

Independent Component Analysis Based on Nonparametric Density Estimation

R. Boscolo, H. Pan, V.P. Roychowdhury
2004 IEEE Transactions on Neural Networks  
Using a nonparametric kernel density estimation technique, the algorithm performs simultaneously the estimation of the unknown probability density functions of the source signals and the estimation of  ...  The new algorithm not only consistently outperformed all state-of-the-art ICA methods, but also demonstrated the following properties: 1) Only a flexible model, capable of learning the source statistics  ...  Although the entropy function shows minima at the optimal points ( ), several spurious local minima appear in other locations.  ... 
doi:10.1109/tnn.2003.820667 pmid:15387247 fatcat:joqrgwzjkjbhjcssjpqf6dvu5a

Exponentially Many Local Minima in Quantum Neural Networks [article]

Xuchen You, Xiaodi Wu
2021 arXiv   pre-print
While local minima in classical neural networks are due to non-linear activations, in quantum neural networks local minima appear as a result of the quantum interference phenomenon.  ...  Specifically, we show for typical under-parameterized QNNs, there exists a dataset that induces a loss function with the number of spurious local minima depending exponentially on the number of parameters  ...  Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing and Quantum Algorithms Team programs, as well as the U.S.  ... 
arXiv:2110.02479v1 fatcat:z7nwdc2npzhdbi33l6vvx6bpi4

Equation of state in the inner crust of neutron stars: discusion of the unbound neutron states [article]

Jérôme Margueron
2007 arXiv   pre-print
A distinction is done between the shell effects due to the bound states and those induced by the unbound states, which are shown to be spurious.  ...  We then estimate the effects of the spurious shells on the total energy and decompose it into a smooth and a residual part.  ...  Spurious shell effects In order to estimate the spurious shell effects due to the unbound neutrons, we simulate an homogeneous gas of neutron matter in W-S cell by removing all the proton states.  ... 
arXiv:0711.0106v1 fatcat:7tymryyaonajvaol5q2uhrtsm4

Optical character recognition for cursive handwriting

N. Arica, F.T. Yarman-Vural
2002 IEEE Transactions on Pattern Analysis and Machine Intelligence  
The estimation of feature space parameters is embedded in HMM training stage together with the estimation of the HMM model parameters.  ...  The experiments in dicate higher recognition rates compared to the available methods reported in the literature.  ...  In memory of Cemile Zehra Turker-Yarman and Ifakat Arica.  ... 
doi:10.1109/tpami.2002.1008386 fatcat:zshtj353mfembe3xmb5akj5xjm

Nonlinear Least Absolute Value Estimator for Topology Error Detection and Robust State Estimation

SangWoo Park, Reza Mohammadi-Ghazi, Javad Lavaei
2021 IEEE Access  
In this paper, we propose a new methodology for robust power system state estimation (PSSE) modeled by AC power flow equations when there exists a small number of topological errors.  ...  Topology error, a modeling misrepresentation of the power system network configuration, can undermine the quality of state estimation.  ...  However, this does not exclude the existence of spurious local minima (local minima that are not globally optimal), which can be problematic when using local search algorithms.  ... 
doi:10.1109/access.2021.3118036 fatcat:gyadclmixrbhbe4g7tis6iibme
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