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Intelligent Matrix Exponentiation [article]

Thomas Fischbacher and Iulia M. Comsa and Krzysztof Potempa and Moritz Firsching and Luca Versari and Jyrki Alakuijala
2020 arXiv   pre-print
We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity.  ...  Despite its simplicity, a single matrix exponential layer already provides universal approximation properties and can learn fundamental functions of the input, such as periodic functions or multivariate  ...  Matrix Exponentiation The exponential of a square matrix M is defined as: exp(M ) = ∞ k=0 1 k!  ... 
arXiv:2008.03936v1 fatcat:dj63wv43kzbfvcwphjxarxbymu

The Vision of the Trigonometry in the Monitoring of the Dynamics Concerning the Artificial Intelligence Phenomenons, through Matrix Analysis

Gabriela Opait
2020 Annals of Dunarea de Jos University. Fascicle I : Economics and Applied Informatics  
REVENUES FROM THE ARTIFICIAL INTELLIGENCE SOFTWARES ($ billions) The matrix of the statistical indexesThe matrix of the angles expressed in degreesThe matrix of the angles expressed in radiansThe  ...  Chips, if the "profile" has as hypothesis an exponential tendency YEARS WORLDWIDE REVENUES FROM THE ARTIFICIAL INTELLIGENCE CHIPS ($ billions) (  i) EXPONENTIAL TENDENCY i  lg  ...  The configuration of the model concerning the values for the worldwide Artificial Intelligence funding start-up companies Conclusions In 2020, the worldwide revenues from the Artificial Intelligence  ... 
doi:10.35219/eai15840409149 fatcat:zccas2irpzekhmep6seuzvkowe

The "Statistical Planet" of the Robots

Gabriela OPAIT
2018 Annals of Dunarea de Jos University. Fascicle I : Economics and Applied Informatics  
The "statistical planet" of the robots knows continuous new sizes, owing to the permanent development of the robots world, especially as effect of the robots with artificial intelligence which impress  ...  The sensation is created by the robots with artificial intelligence which conquer the hearts of the public, through a lot of quantitative and qualitative variables: size, aerodynamics motion, voice stamp  ...  describes an exponential tendency YEARS ROBOTS WITH ARTIFICIAL INTELLIGENCE (billions USD) Table 9 9 The "intelligence matrix" for the data of the i  characteristic regarding the worldwide  ... 
doaj:3eff4b8faa9a403195093c3a1de71419 fatcat:guvkmf27jrbkpdsh4qll4mnb3e

Design of Group Precoding for MU-MIMO Systems with Exponential Spatial Correlation Channel

Van-Khoi Dinh, Thanh-Binh Chu, Minh-Tuan Le, Vu-Duc Ngo
2021 EAI Endorsed Transactions on Industrial Networks and Intelligent Systems  
Simulation results also show that the performance of the proposed algorithms is significantly improved compared to the BD algorithm in an exponential spatial correlation channel.  ...  In this paper, a low-complexity precoding algorithm is proposed to reduce the computational complexity and improve the performance for MU-MIMO systems under exponential spatial correlation channel conditions  ...  EAI Endorsed Transactions on Industrial Networks and Intelligent Systems Online First 7 Design of Group Precoding for MU-MIMO Systems with Exponential Spatial Correlation Channel EAI Endorsed  ... 
doi:10.4108/eai.26-1-2021.168228 fatcat:orrupuz4vjawzjx2t5tyg6jqxa

A New Criterion for Exponential Stability of a Class of Hopfield Neural Network with Time-Varying Delay Based on Gronwall's Inequality

Faming Guo, Ricai Luo, Xiaolan Qin, Yunfei Yi, Wei Xiang
2021 Computational Intelligence and Neuroscience  
In this paper, we study the problem of exponential stability for the Hopfield neural network with time-varying delays.  ...  Computational Intelligence and Neuroscience Example 2.  ...  According to the criterion of exponential stability obtained in paper [30] , it is necessary to find some symmetric matrices that meet the specified matrix inequalities.  ... 
doi:10.1155/2021/4713450 pmid:34552626 pmcid:PMC8452427 fatcat:s3imr2nreratbp5dfft4fv6ibq

Stability Coefficients in Longitudinal Studies

Joseph Levin
1993 Applied Psychological Measurement  
Longitudinal studies of personality traits and intelligence have used an exponential function to relate the magnitudes of the correlations between occasions to the time interval.  ...  This exponential function is shown to be equivalent to a quasisimplex model of a stationary process with constant reliability.  ...  Stability Coefficients in Longitudinal Studies Joseph Levin Tel-Aviv University Longitudinal studies of personality traits and intelligence have used an exponential function to relate the magnitudes of  ... 
doi:10.1177/014662169301700104 fatcat:jv5diewjbfarrejzrktekdsfva

Aircraft Combat Survivability Calculation Based on Combination Weighting and Multiattribute Intelligent Grey Target Decision Model

Lintong Jia, Zhongxiang Tong, Chaozhe Wang, Shenbo Li
2016 Mathematical Problems in Engineering  
Then a multiattribute intelligent grey target decision model is introduced.  ...  Finally, utilize the multiattribute intelligent grey target decision model to assess the aircraft combat survivability of aircraft, verified by a practical case of five aircraft.  ...  The exponential scale is shown in Table 3 .  ... 
doi:10.1155/2016/8934749 fatcat:7d5pf2dwpbhvhoqj7zb2udm7ya

Page 2193 of Mathematical Reviews Vol. , Issue 2000c [page]

2000 Mathematical Reviews  
2193 68T Artificial intelligence of noise).  ...  (English summary) Artificial intelligence and mathematics, VIII (Fort Lauderdale, FL, 1998). Ann. Math. Artificial Intelligence 24 (1998), no. 1-4, 129-153 (1999).  ... 

Quantum Divide-and-Conquer Anchoring for Separable Non-negative Matrix Factorization

Yuxuan Du, Tongliang Liu, Yinan Li, Runyao Duan, Dacheng Tao
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
In the divide step, the random projections in DCA is completed by a quantum algorithm for linear operations, which achieves the exponential speedup.  ...  It is NP-complete to find non-negative factors W and H with fixed rank r from a non-negative matrix X by minimizing ||X-WH^Τ ||^2.  ...  Joint Conference on Artificial Intelligence  ... 
doi:10.24963/ijcai.2018/289 dblp:conf/ijcai/DuLLDT18 fatcat:kxv7bknh5fhshcfcw3noh7lr7q

Causal Inference with Noisy and Missing Covariates via Matrix Factorization [article]

Nathan Kallus, Xiaojie Mao, Madeleine Udell
2018 arXiv   pre-print
We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing.  ...  We propose the use of matrix factorization to infer the confounders from noisy covariates, a flexible and principled framework that adapts to missing values, accommodates a wide variety of data types,  ...  Lemma 5 . 5 Suppose the resulting estimator from Exponential Family Matrix Completion (2) has singular value decompositionΘ =ÛΣV .  ... 
arXiv:1806.00811v1 fatcat:klh2usr3sfehfdx4ymg4jsicii

Tracking Controller Using Normalized Quasi-velocities

Przemysaw Herman
2006 Journal of Intelligent and Robotic Systems  
The presented controller in terms of NQV is exponentially convergent. Moreover, some geometrical interpretation of the normalized quasi-variables based on Riemannian geometry is given.  ...  We show that the proposed controller guarantees exponential convergence both quasi-velocities error and its time integral.  ...  all joint axes P ∈ R 6N ×6N articulated inertia matrix D = H PH T ∈ R N ×N articulated inertia about joint axes, a diagonal matrix D = D(θ) C ν (θ, ν) = m −1 (θ)C(θ,θ) −ṁ T (θ)θ ∈ R N vector of Coriolis  ... 
doi:10.1007/s10846-006-9073-1 fatcat:fhsl7wka5zfgfg443jhd6mao5a

The "Statistical Propulsions" Concerning the Businesses Focused on the Luxury Cars and the Light Vehicles

Gabriela OPAIT
2018 Annals of Dunarea de Jos University. Fascicle I : Economics and Applied Informatics  
8 The "intelligence matrix" for the data of the  variable, if the shopping of light vehicles in the United States describes an exponential trajectory YEARS LIGHT VEHICLES UNITED STATES (thousands  ...  matrix" for the data of the  variable, if the international businesses, concerning the luxury cars, exhibit an exponential trajectory YEARS THE GLOBAL INTERNATIONAL SIZE OF THE BUSINESSES CONCERNING  ...  Conclusions The values of the worldwide sales concerning the luxury cars, between 2010-2016, follow a trajectory which "sketchs" an exponential equation.  ... 
doaj:f241f53ab5324ad78cf704fc5800a11a fatcat:aoq4mrc2jffxhlx6sc7iug6sby

Active Controller Design for the Hybrid Synchronization of Hyperchaotic Zheng and Hyperchaotic Yu Systems

Sundarapandian Vaidyanathan
2013 International Journal on Soft Computing Artificial Intelligence and Applications  
method, we consider a candidate Lyapunov function ( ) , T V e e Pe = (6) where P is a positive definite matrix.  ...  Yu system (31) for all initial conditions 4 International Journal on Soft Computing, Artificial Intelligence and Applications (IJSCAI), Vol.2, No.2, April 2013  ... 
doi:10.5121/ijscai.2013.2202 fatcat:anc7edl66jhbfgie2ggjyh3maa

Interpolated Rigid-Body Motions and Robotics

J.M. Selig, Yuanqing Wu
2006 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems  
Exponential of a matrix is given by the standard formula, e S = I + S + 1 2! S 2 + 1 3! S 3 + · · · IROS Beijing 2006 -p.5/22 Product of Exponentials (cont.)  ...  IROS Beijing 2006 -p.4/22 Product of Exponentials Kinematics of serial robot can be written as product of exponentials.  ... 
doi:10.1109/iros.2006.281815 dblp:conf/iros/SeligW06 fatcat:dlybe7k6e5eatobu7ecghx7ikq

The Comparison Between Gumbel and Exponentiated Gumbel Distributions and Their Applications in Hydrological Process

2021 Advances in Machine Learning & Artificial Intelligence  
The results also confirmed the suitability of the Exponentiated Gumbel distribution for real data collection.  ...  In the end, two applications of the gumbel and exponentiated gumbel distribution have been discussed with two real lifetime data sets.  ...  information matrix i.e.  ... 
doi:10.33140/amlai.02.01.08 fatcat:opq7xycug5cv3hg6kzex5gjdci
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