Michel A., Liu D. — Qualitative analysis and synthesis of recurrent neural networks :: Электронная библиотека попечительского совета мехмата МГУ

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Michel A., Liu D. — Qualitative analysis and synthesis of recurrent neural networks

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Название: Qualitative analysis and synthesis of recurrent neural networks

Авторы: Michel A., Liu D.

Аннотация:

In the present book we concern ourselves exclusively with the qualitative analysis and synthesis of recurrent artificial neural networks. There is an abundance of papers, monographs, and books that address qualitative properties of such networks. However, whereas in these works, the analysis of the networks is frequently incidental to the achievement of some other principal goal, in the present book the network itself is the primary object of inquiry. Works in which the primary object of study is the recurrent neural network itself are rare. Consequently, many of the qualitative attributes and limitations of such networks have been ignored and are therefore obscure.

Язык:

Рубрика: Computer science/Генетика, нейронные сети/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 481

Добавлена в каталог: 19.11.2005

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Предметный указатель

AAM      35
Activation function      1 3 17 18 216 217 228 229 250 259 266
Activation function, multi-threshold      229
Address addressable memory      35
Amplification function      48 49 272
Analog Hopfield neural network      3 6 7 18 23 40—44 50 59 170 171 180 216 224 399
Analog Hopfield neural network with infinite gain amplifiers      3 50—51 85
Analog Hopfield neural network, circuit implementation      41 42
Analog Hopfield neural network, symbolic representation      42
Artificial neural network      1 4 19 34 250 292 347
Artificial neural network, sparsely interconnected      427
Associative memory      4 5 12 26 34—37 347 438
Associative memory, storage capacity      378
Asymptotically stable equilibrium      3 11 21 37 73 98 122 124—130 133 135—143 145 153 169 177 178 211 220 221 226 261 262 266 323
Asynchronous mode      6 8 23 38 45 51 59 61 107
Asynchronous solution      11 86 106 107
Back Propagation Algorithm      1
Basin of attraction      37 196
Bias term      1 216 271 375 430 439 444 446
Bipolar vector      19 27 361 370
Brain-state-in-a-box (BSB) model      58
Brouwer’s fixed-point theorem      18 243 266 269
Cellular neural network      5 27 34 37 60 427 438—451 455 456 466 467 469—471
Cellular neural network, nonsymmetric      439
Cellular neural network, two-dimensional      438
Class $\mathcal{KD}$       153
Class $\mathcal{K}$       74 146 153 169
Cloning template      440 467
Cloning template, space-invariant      440 444 449 465 466 470 471
Cloning template, space-varying      465 470 471
Closed hypercube      52
Cohen-Grossberg neural network      7 21 49 60 111
Cohen-Grossberg neural network with multiple delays      20 22 273 291 293 294 302 335
Cohen-Grossberg neural network, global stability      294
Cohen-Grossberg neural network, local stability      302
Column dominance condition      186
Comparison principle      190 226
Comparison system      190
Complete instability      227
completely continuous      277
Completely unstable equilibrium      16 168 179 199 227
Composite system      174 224 225
Correlation memory      348
Decomposition      14 174 225
Delay equation      272
Descendant      108
Differential-difference equation      277 278
Directed acyclic graph      108
Directed graph      108 109
Discrete-time Hopfield neural, network      7 17 44—47 60 206 207 228
Domain of attraction      4 10 16 22 37 109 196 275 328 402 403 411 419
Eigenstructure Method      24—26 360—373 411 417 418 420 433 434 449 454 469 470
Energy function      10—12 21 36 43 55 70 76 80—84 86 100—107 111 117 128—130 139—142 159 160 180 201 222 349 350 365
Energy functional      274 280 286 295 301 304 336 338
Equilibrium      73 77 97 122 133
Equilibrium in the usual sense      97
Equilibrium, asymptotic stability      14 15 73 74 98 122 124—130 133 135—143 169 178
Equilibrium, exponential stability      14 15 167 168 178
Equilibrium, instability      14 16 74 98 122 124 126 133 135 136 138 168 169 179 197 199 227
Equilibrium, isolated      73 167 190
Equilibrium, stability      14 73 98 122 133 169
Equilibrium, uniform asymptotic stability      277
Equilibrium, uniform stability      277
Error estimate      257
Euclidean norm      87 277
Euler’s method      47
Existence theorem      91 93 95 121
Exponentially stable equilibrium      167 168 178 182 187 191 238 240 245 253 256
Extraneous pattern      37
Feedback neural network      1 37 292
Feedback neural network, fully interconnected      37
Feedforward neural network      1 37
Filippov      96
Free subsystem      13 14 174 209 224
Functional differential equation      276 277
Functional differential equation, autonomous      277
Gain      8 23 40 51 52 59 60 322 350
Gastinel — Kahan Theorem      243 269
Generalized Hopfield neural network      7 48—49 60 70 75 109
Globally asymptotically stable equilibrium      13 109 145 153 154
Globally stable neural network      4 10 20 109 273 279 294 295 336 444
Grey levels      405 456
Hahn — Banach theorem      95
Hamming distance      188 212 380 382 390 391
Hard limiter activation function      18 19 234 259 267
Hebb’s hypothesis      348
Hessian matrix      288 305
High gain limit      201 350
Ho — Kashyap recording      414
Hopfield neural network      1 13 20 21 36 165 348
Hopfield neural network with delays      20 278 285 335
Hopfield neural network with infinite gain amplifiers      50—51 85
Hopfield neural network with multiple delays      272
Hopfield neural network, analog model      40—44 50 59 170
Hopfield neural network, continuous-time      39
Hopfield neural network, discrete model      44—47 60
Hopfield neural network, equivalent linear representation      219
Hopfield neural network, generalized model      48—49 60 70 75 109
Hopfield neural network, global stability      273
Hopfield neural network, implementation      41 42
Hurwitz stable      145 240 244 253—255 257 266 267 322 327 329 332 340 342
implementation process      4 19
Index matrix      26 427 470
Index matrix, indexed design problem      428

Instability      197 227
Interconnected system      13—15 174 224
Interconnecting structure      14 22 174 209 224 225
Interconnection constraints      1 5 14 26 378 380 382
Ordinary differential equation      72 167
Ordinary differential equation, autonomous      72
Ordinary differential equation, existence theorem      91 93 95 121
Orthonormal basis      367
Outer Product Method      1 22 23 347—352 368 414—416 419
output sequence      11 104 106
Output vector      11 86 97 99 100 111 260
Output vector, stable      11 86 99 100 105 106
Output vector, unstable      99
P-matrix      151
Parameter perturbation      17 19 249 250 265 266 269 270 392 411 419 449
Perceptron      25 34 373 376 420
Perceptron based training algorithm      25 27 373—395 417 445—449 470 471
Perceptron, Convergence Theorem      374 420
Perceptron, multi-layer      1
Perceptron, training algorithm      347 374 417 420 445
Permutation      104 120 217
Perturbation model      234 260
Perturbed equilibrium      241 268
Perturbed system      4 260 268
Projection learning rule      23 347 352—360 367 368 416 417 419
Projection Learning Rule, extensions      355—360
Projection Learning Rule, iterative algorithm      357—360 417
Pseudo-inverse      353 357 368 416
Quasimonotonically increasing      190
Quinquediagonal matrix      459
Recurrent neural network      1 2 4 19 34 37 271 347
Recurrent neural network with multiple delays      272
Recurrent neural network, fully interconnected      34 37
Recurrent neural network, partially interconnected      34
Reduced linear system      120 132 223
Restriction to a matrix      427 469
Robust stability      22 236 241 275 331
Robustness      18 250
Robustness, analysis      27 259—265 389—395
Row dominance condition      186
Sard’s theorem      79 279 294
Saturated mode      12 116 117 120
Saturation function      7 19 39 44 57 60 61 131 152 216 228 234 259 267 426
Sector condition      22 275 322 339
Sgn function      6 37—39 45 50 59 85 201 348
Sigmoidal function      3 6 18 39 40 170 202 233 234 250 266 271 278 389 390
Singular value decomposition      24 366 368 396
Sliding mode      10 11 85 96 97 103 111 112
Small gain condition      22 322 325
Sparse design problem      27 427—438
Sparsity constraints      5 450 469 470
Spurious state      4 24 37 44 365 412 413 417
Stable equilibrium      21 73 98 122 133 145 153 169
Stable memory      19
storage capacity      4 5 378 413—415
Structural perturbation      17 200
Symmetric design      387 388 418 448 463 465
Symmetric group      118
Synchronous mode      7 17 23 39 46 47 59 206 207 228
Synthesis problem      361 427
Synthesis procedure      26 366 370 376 387 391 428 434 435 437 443 446 448
Synthesis strategy      362
System $(H^{'}_{i})$       170
System $(H_{i})$       170
System $(M_{d_{i}})$       131
System $(M_{d_{\xi}})$       131
System $(M_{d})$       131 160
System $(N_{d})$       107
System $(N_{\xi i})$       88
System $(N_{\xi})$       88
System $(S_{i})$       5 174
System $(W_{i})$       209
System $(\Omega)$       209
System $(\Sigma)$       173
System $(\widetilde{S})$       234
System (A)      190
System (C)      193
System (D)      168
System (E)      72 167
System (F)      276
System (FA)      277
System (L)      70 75 109
System (M)      120
System (N)      85 110
System (S)      233
System (VC)      190
System (W)      208
Test matrix      14 15 185 225
Threshold logic unit      37
Time delay      4 271—342
Time sequence      104
Trajectory      16 75
Trajectory, bounds      16 193 213
Transmission delay      19
Transportation delay      272
Uniformly asymptotically stable equilibrium      277
Uniformly stable equilibrium      277
Unsaturated mode      147
Unsaturated region      390
Unstable equilibrium      74 98 122 124 126 133 135 136 138 168 169 176 179 199 227
Unstable equilibrium, completely unstable      168 179 199 227
Variable structure system      3 8 10 60 110 112
Vector Lyapunov function      190 192 226
Weak-coupling conditions      185

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