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Anthony M. — Discrete Mathematics Of Neural Networks
Anthony M. — Discrete Mathematics Of Neural Networks

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Название: Discrete Mathematics Of Neural Networks

Автор: Anthony M.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 131

Добавлена в каталог: 09.01.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$P \neq NP$ conjecture      50
$RP \neq NP$ conjecture      112
2-monotonic Boolean function      16 53
2-monotonic Boolean function, recognition algorithm      53
Accuracy parameter      90
Activation      2
Activation function      3
Affine functions      103
Affinely independent      104
Algorithm for learning      see "Learning algorithm"
Algorithm, efficient      49
Algorithm, polynomial-time      50
Algorithm, randomized      111
Algorithm, running time      50
Antichain      66 74
Antichain, size of      66
Asummability      26
Asummability and polynomial threshold functions      32
Augmented vector      32
Big-O notation      50
Boltzmann machine      1 115
Boltzmann machine for maximum cut      117
Boltzmann machine for optimization      117
Boltzmann machine for traveling salesman problem      118
Boltzmann machine, architecture      115
Boltzmann machine, consensus function      115
Boltzmann machine, parallel computation in      116
Boltzmann machine, sequential computation in      116
Boltzmann machine, states      115
Boolean formula      10
Boolean function      9
Boolean function, 2-monotonic      16 53
Boolean function, classes of      14
Boolean function, CNF representation      13 14
Boolean function, degree of      14
Boolean function, depending on a coordinate      73
Boolean function, DNF representation      12
Boolean function, down-projection of      22
Boolean function, dual of      14
Boolean function, false point of      11
Boolean function, implicant of      13
Boolean function, increasing      15
Boolean function, negative example of      11
Boolean function, nested      76
Boolean function, polynomial threshold representation      31
Boolean function, positive example of      11
Boolean function, prime implicant      13
Boolean function, projection of      23 51
Boolean function, regular      15 17 53
Boolean function, representation by network      61
Boolean function, threshold order of      31
Boolean function, true point of      11
Boolean function, unate      15
Boolean function, up-projection of      22
Boolean hypercube      9
Boolean hypercube as a graph      10
Boolean hypercube, geometry      9
Boolean hypercube, partial order on      10
Boolean polynomial threshold function      30
Boolean threshold function      see "Threshold function"
Boundary points      72
Chain      66
Chebyshev's inequality      96
Chopping      62
Circuit complexity      61 70
Class of networks      109
Closure under projection of polynomial threshold functions      30
Closure under projection of threshold functions      23
CNF formula      13
CNF representation      13 14
Combinatorial optimization      116
Complexity of determining threshold order      52
Complexity of learning      109
Complexity of membership problem      51
Complexity of threshold synthesis      56
Complexity theory      49
Computation unit      2
Confidence parameter      90
Conjunction      11
Conjunctive normal form      13
Consensus function      115
Consistency problem      110
Consistency problem and learnability      111
Consistent learning algorithm      71 84
Convex combination      25
Convex hull      25
Convex hull, rational      27
Convex set      25
Covering      66
Decision lists      17 45 62
Decision lists and other Boolean functions      18
Decision lists and polynomial threshold functions      31
Decision lists and threshold functions      28
Decision lists, based on threshold functions      63
Decision lists, specification number      79
Decision problem      50
Degree of Boolean function      14
Degree of DNF      14
Degree of polynomial threshold function      30
Degree of polynomial threshold unit      5
Directed graph      115
Disjunction      11
Disjunctive normal form      11
DNF formula      11
DNF formula and network      61
DNF formula, degree of      14
DNF formula, irredundant      15 52
DNF non-tautology      50
DNF representation      12
Down-projection      22 77
Down-set      16 94
Dual      14
Dualization      53 54
Dualization algorithm      53 54 58
Efficiency of perceptron learning      87
Efficient algorithm      49
Efficient learning algorithm      109
Efficient learning algorithm for perceptron      110
Efficient learning algorithm, sufficient condition      110
Error of a function      90
Essential examples      77
Exclusive-or function XOR      3 7
False point      11
Feed-forward network      1 2 6
Fibonacci numbers      45
General position      9
Geometrical interpretation of polynomial threshold function      32
Geometrical interpretation of threshold function      25
Graph colorability      50 112
Group action      97
Growth function      91
Growth function and VC-dimension      93
Growth function of perceptron      103
Harmonic analysis      70
Hidden layer      6
Homogeneous threshold function      22 101
Homogeneous threshold function and shattering      101
Hypercube      9
Hyperface function      72
Hyperplane separation      25
Hypothesis      84
Hypothesis space      90
Implicant      13
Increasing Boolean function      15
Incremental perceptron learning algorithm      85
Inner product      21
Input layer      6
Input unit      5
Instance      50
Integral threshold      43
Integral weight-vector      43
Irredundant DNF      15 52
Irrelevant attributes      79
Labeled example      83
Layers      6
Learning      83
Learning algorithm      83 84 89
Learning algorithm for class of networks      109
Learning algorithm, efficiency of      109
Learning, complexity of      109
Learning, probabilistic model      89
Lexicographic order      32 53 58
Linear dimension      102
Linear dimension and VC-dimension      102
Linear inequalities and threshold functions      43
Linear programming      53 85
Linear separability      25
Linear threshold function      see "Threshold function"
Linear threshold network      1
Linear threshold recognition      52
Linear threshold unit      2 3
Linearly separable functions      see "Threshold function"
Literals      10
Lower bound on sample length      98
m-augment      32
Maximal false point      see "MFP"
Maximum cut problem      117
Measurability conditions      99
Membership problem      51
Membership problem, complexity of      51
Membership queries      81
MFP      16 53 73
MFP of regular functions      55
Minimal true point      see "MTP"
Monomial      14
MTP      16 52 73
MTP and prime implicants      16
MTP of dual function      16 53
Multilayer network      6
Negation      13
Negative example      11
Nested function      76
Network and DNF formula      61
Network, classes of      109
Network, depth      6
Network, feed-forward      1 6
Network, linear threshold      1 61
Network, linear threshold, VC-dimension      106
Network, multilayer      6
Network, representation of Boolean functions      9 61
Network, sigmoid      1 70
Network, sigmoid, VC-dimension      107
Network, state      7
Network, stochastic      115
Network, stratified      6 66
Network, VC-dimension of      92
Neural network      see "Network"
neuron      2
NP-complete problem      50
NP-hard problem      50
Number of polynomial threshold functions, lower bound      40
Number of polynomial threshold functions, upper bound      40
Number of threshold functions, asymptotic bound      39
Number of threshold functions, lower bound      38
Number of threshold functions, upper bound      37
Observed error      95
Output function      84
Output layer      6
Output unit      5
PAC learning      89 90
PAC learning and VC-dimension      94 99
PAC learning of finite spaces      91
PAC learning, complexity of      109
PAC learning, extensions of      99
PAC learning, hardness of      112
PAC learning, sample length lower bound      98
PAC learning, sufficient sample length      95
Parameter space      36
Parity function      12
Parity function, network representation of      62 64 66 69
Parity function, threshold order      58
Partial order      10 66 73
Partially ordered set      see "Poset"
Perceptron      3 7
Perceptron, growth function of      103
Perceptron, incremental learning algorithm      85
Perceptron, learning algorithm for      84
Perceptron, sets shattered by      103
Perceptron, VC-dimension of      103
Polynomial threshold function      21 29
Polynomial threshold function and asummability      32
Polynomial threshold function and decision lists      31
Polynomial threshold function, Boolean      30
Polynomial threshold function, closure under projection      30
Polynomial threshold function, degree of      30
Polynomial threshold function, geometrical interpretation      32
Polynomial threshold function, lower bound on number      40
Polynomial threshold function, real      29
Polynomial threshold function, representation of Boolean function      31
Polynomial threshold function, threshold order of      31
Polynomial threshold function, upper bound on number      40
Polynomial threshold function, VC-dimension      104
Polynomial threshold unit      4 5
Polynomial threshold unit, degree of      5
Polynomial-time algorithm      50
POSET      66
Poset, antichain in      66
Poset, chain in      66
Poset, covering in      66
Poset, maximal element      66
Poset, minimal element      66
Poset, rank function      66
Positive example      11
Prime implicant      13 52
Probabilistic model of learning      89
Product probability distribution      90
Projection      23 51
Projection of polynomial threshold function      30
Projection of threshold function      23
Projection property      51
Quadratic programming      117
r-out-of-k function      79
Randomized algorithm      111
Rank function      66
Rational convex hull      27
Real polynomial threshold function      29
Real threshold function      22
Recognition algorithm for 2-monotonic functions      53
Regular Boolean function      15 17 53
Running time      50
Sample complexity      101
Sauer's lemma      93
Self-organization      115
Separating Hyperplanes Theorem      26
Shattered sample      92
Sigmoid function      4
Sigmoid network      1 70
Sigmoid unit      2 4
Sign function      3
Signature      77
Simulated annealing      116
Sizes of weights in nonstandard representation      47
Sizes of weights, can be exponential      44
Sizes of weights, can be superexponential      46
Sizes of weights, upper bound      44
Specification number      71
Specification number, average      79 81
Specifying set      71
Sperner's theorem      66 74
State      7
1 2
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