206
Index
F
Ferromagnetic phase, 140
Forward propagation, 49
Free energy, 101
Frustration, 160
G
Gaussian distribution, 32
Generalization, 22, 23
Generalization error, 22
Generative adversarial network, 109
Gradient descent method, 26
Ground state, 166
H
Hamilton equation, 151
Hamiltonian, 36, 58, 96, 99, 105, 139, 151, 167
Heatbath method, 97
Hebb’s rule, 162
Hilbert space, 165
Holographic principle, 175
Holographic QCD, 176
Hopfield model, 102, 157
I
Ill-posed problems, 132
Image recognition, 60
Information, 2, 3
Information entropy, 3
Intelligence, 197
Inverse problem, 129, 173
Ising model, 88, 98, 99, 139
J
Joint probability, 28
K
KdV equation, 72
Ket, 47, 49, 54
Kullback–Leibler divergence, 8, 22
L
Layer, 45, 46
Learning, 22
Least absolute shrinkage and selection operator
(LASSO), 138
Limit cycle, 164
Linear regression, 43
Long short-term memory (LSTM), 66
Lyapunov exponent, 135, 150
Lyapunov function, 159
M
Machine learning, 17
Magnetization, 139
Marginal probability, 28
Markov chain, 88, 125
Markov chain Monte Carlo method, 95
Master equation, 94
Maximum likelihood estimation, 6
Maxwell’s demon, 5, 9
Memory, 66, 157, 161
Metropolis method, 96
Metropolis test, 97, 125
Modified NIST (MNIST), 18, 60
Moore–Penrose inverse, 134
Morozov’s discrepancy principle, 133
Multiclass classification, 40
N
Nearest neighbor, 100
Neural cells, 158
Neurons, 158
Nonlinear, 52
O
Occam’s razor, 24
Ordered phase, 140
Order parameter, 141
Overdetermined system, 133
Over-training, 23
P
Partition function, 54, 99
Perron–Frobenius theorem, 90
Phase transition, 140
Q
Quantum chromodynamics, 176, 187
Qubit, 165
R
Rectified linear units (ReLU), 43
Recurrent neural network, 62, 72
Regression, 42
Regularization, 132
Index
F
Ferromagnetic phase, 140
Forward propagation, 49
Free energy, 101
Frustration, 160
G
Gaussian distribution, 32
Generalization, 22, 23
Generalization error, 22
Generative adversarial network, 109
Gradient descent method, 26
Ground state, 166
H
Hamilton equation, 151
Hamiltonian, 36, 58, 96, 99, 105, 139, 151, 167
Heatbath method, 97
Hebb’s rule, 162
Hilbert space, 165
Holographic principle, 175
Holographic QCD, 176
Hopfield model, 102, 157
I
Ill-posed problems, 132
Image recognition, 60
Information, 2, 3
Information entropy, 3
Intelligence, 197
Inverse problem, 129, 173
Ising model, 88, 98, 99, 139
J
Joint probability, 28
K
KdV equation, 72
Ket, 47, 49, 54
Kullback–Leibler divergence, 8, 22
L
Layer, 45, 46
Learning, 22
Least absolute shrinkage and selection operator
(LASSO), 138
Limit cycle, 164
Linear regression, 43
Long short-term memory (LSTM), 66
Lyapunov exponent, 135, 150
Lyapunov function, 159
M
Machine learning, 17
Magnetization, 139
Marginal probability, 28
Markov chain, 88, 125
Markov chain Monte Carlo method, 95
Master equation, 94
Maximum likelihood estimation, 6
Maxwell’s demon, 5, 9
Memory, 66, 157, 161
Metropolis method, 96
Metropolis test, 97, 125
Modified NIST (MNIST), 18, 60
Moore–Penrose inverse, 134
Morozov’s discrepancy principle, 133
Multiclass classification, 40
N
Nearest neighbor, 100
Neural cells, 158
Neurons, 158
Nonlinear, 52
O
Occam’s razor, 24
Ordered phase, 140
Order parameter, 141
Overdetermined system, 133
Over-training, 23
P
Partition function, 54, 99
Perron–Frobenius theorem, 90
Phase transition, 140
Q
Quantum chromodynamics, 176, 187
Qubit, 165
R
Rectified linear units (ReLU), 43
Recurrent neural network, 62, 72
Regression, 42
Regularization, 132