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Polyhedrons and Perceptrons Are Functionally Equivalent
[article]

2013
*
arXiv
*
pre-print

The main theme is that single output

arXiv:1311.1090v1
fatcat:tmpbamvfl5gkhb4cqd32s3gywa
*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. ...##
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Playing Billiard in Version Space
[article]

1995
*
arXiv
*
pre-print

While the Bayes-optimum requires a majority decision over all

arXiv:cond-mat/9508130v1
fatcat:oe5d6qurw5cr7mjt7oroyhuy7y
*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. ...##
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An Algorithm for Building Regularized Piecewise Linear Discrimination Surfaces: The Perceptron Membrane

1995
*
Neural Computation
*

Starting from only one convex

doi:10.1162/neco.1995.7.2.380
fatcat:v6yepuqbyjddvb2qxycpp2usnq
*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 ...##
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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 ...##
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An Analysis of the Anti-learning Phenomenon for the Class Symmetric Polyhedron
[chapter]

2005
*
Lecture Notes in Computer Science
*

Moreover, the analysis leads to a specification of some machine learning procedures which can overcome anti-learning

doi:10.1007/11564089_8
fatcat:v32mzx4xxffyzp3sz6kcvfmdn4
*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. ...##
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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 ...##
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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. ...##
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Warped-Linear Models for Time Series Classification
[article]

2017
*
arXiv
*
pre-print

This article proposes

arXiv:1711.09156v1
fatcat:pb722xhg4feoto3gmkbimztmpa
*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. ...##
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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. ...##
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A no-go theorem for one-layer feedforward networks
[article]

2013
*
arXiv
*
pre-print

An unexpected corollary of our main result is that any prescribed (finite) homotopy type can be realized by removing a

arXiv:1310.3796v1
fatcat:aguv6bipcjeodlwg2fkfi4yvkm
*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. ...##
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THE DESIGN AND COMPLEXITY OF EXACT MULTILAYERED PERCEPTRONS

1991
*
International Journal of Neural Systems
*

It is sufficient if both F( x)

doi:10.1142/s0129065791000170
fatcat:xdmpxh7jkrfjva7gfw2c5tamwi
*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 ...##
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A No-Go Theorem for One-Layer Feedforward Networks

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

doi:10.1162/neco_a_00657
pmid:25149704
fatcat:wsdcrxycjjholhlg35pz2n6k3u
*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. ...##
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Two ways of using artificial neural networks in knowledge discovery from chemical materials data

2010
*
Conference on Theory and Practice of Information Technologies
*

However, they

dblp:conf/itat/Holena10
fatcat:eqma6dtygfcpnj3yje6le7qtbi
*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. ...##
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Learning convex polyhedra with margin
[article]

2021
*
arXiv
*
pre-print

an optimal

arXiv:1805.09719v3
fatcat:45r3lo7zhvbllgfyo7wq4txgna
*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. ...##
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Cognitive Technologies in the Management and Formation of Directions of the Priority Development of Industrial Enterprises

2020
*
Management Systems in Production Engineering
*

The possibility of introduction of the

doi:10.2478/mspe-2020-0020
fatcat:5xczl3ilvzg77j54ve762lglry
*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} ...
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