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Polyhedrons and Perceptrons Are Functionally Equivalent [article]

Daniel Crespin
2013 arXiv   pre-print
The main theme is that single output perceptron neural networks and characteristic functions of polyhedrons are one and the same class of functions.  ...  Mathematical definitions of polyhedrons and perceptron networks are discussed. The formalization of polyhedrons is done in a rather traditional way.  ...  Polyhedrons and Perceptrons Are Functionally Equivalent Theorem 1.  ... 
arXiv:1311.1090v1 fatcat:tmpbamvfl5gkhb4cqd32s3gywa

Playing Billiard in Version Space [article]

Pal Rujan
1995 arXiv   pre-print
While the Bayes-optimum requires a majority decision over all Perceptrons separating the example set, the problem considered here corresponds to finding the single Perceptron with best average generalization  ...  In real-life classification problems the generalization error is consistently reduced compared to the maximal stability Perceptron.  ...  Acknowledgments I thank Manfred Opper for the analytic Bayes data and Bruno Eckhardt for discussions.  ... 
arXiv:cond-mat/9508130v1 fatcat:oe5d6qurw5cr7mjt7oroyhuy7y

An Algorithm for Building Regularized Piecewise Linear Discrimination Surfaces: The Perceptron Membrane

Guillaume Deffuant
1995 Neural Computation  
Starting from only one convex polyhedron, new facets and new polyhedrons are added dur- ing learning.  ...  It is well known that such functions are equivalent to 2-hidden layered feedforward networks (Bochereau et al. 1990; Sethi 1990), in which the weights of the hidden layers are fixed according to the logical  ... 
doi:10.1162/neco.1995.7.2.380 fatcat:v6yepuqbyjddvb2qxycpp2usnq

Page 383 of Neural Computation Vol. 7, Issue 2 [page]

1995 Neural Computation  
It is well known that such functions are equivalent to 2-hidden layered feedforward networks (Bochereau et al. 1990; Sethi 1990), in which the weights of the hidden layers are fixed according to the logical  ...  [(M) is defined by three convex polyhedrons. in the active part of perceptron k iff the following conditions are verified: i. x belongs to hyperplane k: w -x+bk=0 ii. x belongs to facet k of CP j: Aj|kEC  ... 

An Analysis of the Anti-learning Phenomenon for the Class Symmetric Polyhedron [chapter]

Adam Kowalczyk, Olivier Chapelle
2005 Lecture Notes in Computer Science  
Moreover, the analysis leads to a specification of some machine learning procedures which can overcome anti-learning and generate machines able to classify training and test data consistently.  ...  The initial analysis presented in this paper shows that anti-learning is a property of data sets and is quite distinct from over-fitting of a training data.  ...  Acknowlegements Many thanks to Cheng Soon Ong, Alex Smola and Grant Baldwin for help in preparation of this paper and to Manfred Warmuth and S.V.N. Vishwanathan for clarifying discussions.  ... 
doi:10.1007/11564089_8 fatcat:v32mzx4xxffyzp3sz6kcvfmdn4

Page 5306 of Psychological Abstracts Vol. 82, Issue 11 [page]

1995 Psychological Abstracts  
The discrimination surfaces of PMs are defined by the union of convex polyhedrons. Starting from only one convex polyhedron, new facets and new polyhedrons are added during learning.  ...  —This article describes a neural network model of speech motor skill acquisition and speech production that explains a wide range of data on variability, motor equivalence, coarticulation, and rate effects  ... 

Page 437 of Mathematical Reviews Vol. 49, Issue 2 [page]

1975 Mathematical Reviews  
The author characterizes graphs and functions as they appear in perceptron networks and their infinite extensions by means of topological set theory.  ...  Several theorems char- acterizing the output functions are given, which are too involved to be reproduced here.  ... 

Warped-Linear Models for Time Series Classification [article]

Brijnesh J. Jain
2017 arXiv   pre-print
This article proposes and studies warped-linear models for time series classification. The proposed models are time-warp invariant analogues of linear models.  ...  Empirical results on time series classification suggest that warped-linear functions better trade solution quality against computation time than nearest-neighbor and prototype-based methods.  ...  Examples of loss functions and their derivatives are summarized in Table 1 . Unless otherwise stated, we assume that is the perceptron loss and px, yq P D is a training example.  ... 
arXiv:1711.09156v1 fatcat:pb722xhg4feoto3gmkbimztmpa

Page 1754 of Mathematical Reviews Vol. 48, Issue 5 [page]

1974 Mathematical Reviews  
It is analogous to simple homotopy equivalence, and corre- sponding results are proved, including the facts that (a) reducible polyhedra are homotopically equivalent, and thus have isomorphic homotopy,  ...  The properties of this functional relation are explored and it is shown that a reasonable model results if this functional relation is identified in the Boolean algebra as non-implication.  ... 

A no-go theorem for one-layer feedforward networks [article]

Chad Giusti, Vladimir Itskov
2013 arXiv   pre-print
An unexpected corollary of our main result is that any prescribed (finite) homotopy type can be realized by removing a polyhedron from the positive orthant of some Euclidean space.  ...  Our proofs use mathematical tools from classical combinatorial topology, such as the nerve lemma and the existence of an inverse nerve.  ...  in the input layer, and the transfer functions φ i : R → R ≥0 are monotone increasing.  ... 
arXiv:1310.3796v1 fatcat:aguv6bipcjeodlwg2fkfi4yvkm

THE DESIGN AND COMPLEXITY OF EXACT MULTILAYERED PERCEPTRONS

P.J. Zwietering, E.H.L. Aarts, J. Wessels
1991 International Journal of Neural Systems  
It is sufficient if both F( x) and c(yj x) are linear functions of x, where F( x) is said to be a linear function of x if all the constraints that define F(x) are linear in x.  ...  It is shown that a combinatorial optimization problem can be solved exactly by a three-layered perceptron if the cost function and feasibility constraints are piece-wise linear in the input data of the  ... 
doi:10.1142/s0129065791000170 fatcat:xdmpxh7jkrfjva7gfw2c5tamwi

A No-Go Theorem for One-Layer Feedforward Networks

Chad Giusti, Vladimir Itskov
2014 Neural Computation  
An unexpected corollary of our main result is that any prescribed (finite) homotopy type can be realized by a subset of the form R n ≥0 \P, where P is a polyhedron.  ...  Our proofs use mathematical tools from classical combinatorial topology, such as the nerve lemma and the existence of an inverse nerve.  ...  V.I. is thankful to Carly Klivans for pointing to the reference (Grünbaum, 1970) ; the authors are also grateful to Carina Curto for comments on the manuscript.  ... 
doi:10.1162/neco_a_00657 pmid:25149704 fatcat:wsdcrxycjjholhlg35pz2n6k3u

Two ways of using artificial neural networks in knowledge discovery from chemical materials data

Martin Holena
2010 Conference on Theory and Practice of Information Technologies  
However, they are frequently used without awareness of the difference between the numeric nature of knowledge obtained from data by neural network regression, and the symbolic nature of knowledge obtained  ...  Both ways of using neural networks are illustrated on examples from this application area.  ...  In addition, also implications and equivalences of important kinds of fuzzy logic are frequently extracted [8, 15] . In general, extracted formulas of a formal logic are called rules.  ... 
dblp:conf/itat/Holena10 fatcat:eqma6dtygfcpnj3yje6le7qtbi

Learning convex polyhedra with margin [article]

Lee-Ad Gottlieb, Eran Kaufman, Aryeh Kontorovich, Gabriel Nivasch
2021 arXiv   pre-print
an optimal polyhedron).  ...  We also identify distinct generalizations of the notion of margin from hyperplanes to polyhedra and investigate how they relate geometrically; this result may have ramifications beyond the learning setting  ...  The 1st and 3rd authors were supported in part by the Israel Science Foundation (grant No. 1602/19), an Amazon Research Award, and the BGU Data Science Research Center.  ... 
arXiv:1805.09719v3 fatcat:45r3lo7zhvbllgfyo7wq4txgna

Cognitive Technologies in the Management and Formation of Directions of the Priority Development of Industrial Enterprises

Aleksy Kwilinski, Aleksandra Kuzior
2020 Management Systems in Production Engineering  
The possibility of introduction of the Perceptron model in the industrial enterprise management with the purpose of identification of "bottlenecks" in the functionality of business activity and improvement  ...  Strategic links are defined in the development of a system of stochastic models of enterprise management based on artificial intelligence.  ...  Suppose that in (3) the sets X and Уω(x) are convex polyhedrons specified by the systems of linear inequalities; functions φ(x), φ0(x, y (ω)) are linear, and the set of random situations Ω = {1,2,...N}  ... 
doi:10.2478/mspe-2020-0020 fatcat:5xczl3ilvzg77j54ve762lglry
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