Ординатура / Офтальмология / Английские материалы / Computational Maps in the Visual Cortex_Miikkulainen_2005
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Contents xxiii
17.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
17.4.2 Scope and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404
17.4.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
17.4.4 Further Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
17.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406
18 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
18.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
18.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
Appendices
A LISSOM Simulation Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 A.1 Generalized Activation Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 A.2 Default Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 A.3 Choosing Parameters for New Simulations . . . . . . . . . . . . . . . . . . . . . 419 A.4 Retinotopic Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 A.5 Orientation Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 A.6 Ocular Dominance Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 A.7 Direction Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424 A.8 Combined Orientation / Ocular Dominance Maps . . . . . . . . . . . . . . . . 424 A.9 Combined Orientation / Ocular Dominance / Direction Maps . . . . . . 424
B Reduced LISSOM Simulation Specifications . . . . . . . . . . . . . . . . . . . . . . 427
B.1 Plasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
B.2 Tilt Aftereffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
B.3 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428
C HLISSOM Simulation Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
429 |
|
C.1 |
V1 Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
429 |
C.2 |
Face-Selective Area Only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
430 |
C.3 |
Combined V1 and Face-Selective Area . . . . . . . . . . . . . . . . . . . . . . . . |
432 |
D PGLISSOM Simulation Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
D.1 Self-Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
D.2 Grouping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437
D.3 Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438
E SOM Simulation Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
F Visual Coding Simulation Specifications . . . . . . . . . . . . . . . . . . . . . . . . . 441 F.1 Sparse Coding and Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441 F.2 Handwritten Digit Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 442
xxiv Contents
G Calculating Feature Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
G.1 Preference Map Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445
G.2 Retinotopic Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
G.3 Orientation Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
G.4 Ocular Dominance Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 449
G.5 Direction Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
G.6 Orientation Gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 451
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 503
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
List of Figures
1.1 |
Columnar organization of the primary visual cortex . . . . . . . . . . . . . . |
5 |
1.2 |
Spontaneous activity in the retina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
7 |
1.3 |
Perceptual grouping tasks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
9 |
1.4 |
Basic LISSOM model of the primary visual cortex . . . . . . . . . . . . . . . |
11 |
2.1 |
Human visual pathways (top view) . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
16 |
2.2 |
Receptive field types in retina, LGN and V1 . . . . . . . . . . . . . . . . . . . . |
17 |
2.3 |
Measuring cortical maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
19 |
2.4 |
Orientation map in the macaque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
20 |
2.5 |
Hierarchical organization of feature preferences in the macaque . . . . |
21 |
2.6 |
Long-range lateral connections in the macaque . . . . . . . . . . . . . . . . . . |
24 |
2.7 |
Lateral connections in the tree shrew orientation map . . . . . . . . . . . . |
25 |
2.8 |
Spontaneous activity in the cat PGO pathway . . . . . . . . . . . . . . . . . . . |
32 |
2.9 |
Solving the superposition catastrophe through temporal coding . . . . |
34 |
2.10 |
Synchronization of one and two input objects in the cat . . . . . . . . . . . |
35 |
3.1 Computational abstractions of neurons and networks . . . . . . . . . . . . . 41 3.2 Perceptual grouping through temporal coding . . . . . . . . . . . . . . . . . . . 47
3.3General architecture of self-organizing map models of the primary
visual cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.4 Training a self-organizing map with Gaussian activity patterns . . . . . 55 3.5 Self-organization of weight vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.6 Self-organization of a retinotopic map . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.7 Magnification of dense input areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.8 Principal components of data distributions . . . . . . . . . . . . . . . . . . . . . . 60
3.9Approximating nonlinear distributions with principal curves and
folding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.10 Three-dimensional model of ocular dominance . . . . . . . . . . . . . . . . . . 63
4.1 Architecture of the basic LISSOM model . . . . . . . . . . . . . . . . . . . . . . 69 4.2 Afferent weights of ON and OFF neurons in the LGN . . . . . . . . . . . . 71
xxvi List of Figures
4.3 Initial V1 afferent and lateral weights . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.4 Example input and response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.5 Neuron activation function σ(s) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 4.6 Self-organized V1 afferent weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.7 Self-organized afferent and lateral weights across V1 . . . . . . . . . . . . 80 4.8 Self-organization of the retinotopic map . . . . . . . . . . . . . . . . . . . . . . . 81 4.9 Self-organized V1 lateral weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.1Fourier spectrum and gradient of the macaque orientation map . . . . 86
5.2Normal vs. strabismic cat ocular dominance maps and lateral
connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.3 Combined OR/OD map in the macaque . . . . . . . . . . . . . . . . . . . . . . . . 89
5.4Spatiotemporal receptive fields, direction maps, and combined
OR/DR maps in animals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.5 Initial V1 afferent and lateral weights . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.6 Example input and response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.7 Self-organized V1 afferent and lateral weights . . . . . . . . . . . . . . . . . . 98 5.8 Self-organized afferent and lateral weights across V1 . . . . . . . . . . . . 99 5.9 Self-organization of the orientation map . . . . . . . . . . . . . . . . . . . . . . . 100 5.10 Fourier spectrum and gradient of the orientation map . . . . . . . . . . . . . 101 5.11 Retinotopic organization of the orientation map . . . . . . . . . . . . . . . . . 102 5.12 Long-range lateral connections in the orientation map . . . . . . . . . . . . 103 5.13 Effect of training patterns on orientation maps . . . . . . . . . . . . . . . . . . 105 5.14 LISSOM model of ocular dominance . . . . . . . . . . . . . . . . . . . . . . . . . . 107 5.15 Self-organization of afferent weights into OD receptive fields . . . . . . 108 5.16 Self-organized ocular dominance map . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.17 Long-range lateral connections in the ocular dominance map . . . . . . 109
5.18Ocular dominance and long-range lateral connections in the
strabismic ocular dominance map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 5.19 Effect of disparity on ocular dominance maps . . . . . . . . . . . . . . . . . . . 112 5.20 LISSOM model of orientation and direction selectivity . . . . . . . . . . . 114
5.21Self-organization of afferent weights into spatiotemporal RFs . . . . . 115
5.22 Self-organized OR/DR map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.23 Combined OR/DR map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.24 Long-range lateral connections in the combined OR/DR map . . . . . . 118 5.25 Effect of input speed on direction maps . . . . . . . . . . . . . . . . . . . . . . . . 120
5.26LISSOM model of orientation, ocular dominance, and direction
selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.27 Self-organized OR/OD map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.28 Long-range lateral connections in the combined OR/OD map . . . . . . 125 5.29 Combined OR/OD/DR map trained with Gaussians . . . . . . . . . . . . . . 126 5.30 Example natural image input for training the OR/OD/DR map . . . . . 127 5.31 Combined OR/OD/DR map trained with natural images . . . . . . . . . . 128 5.32 Effect of training patterns on OR/OD/DR maps . . . . . . . . . . . . . . . . . 129
List of Figures |
xxvii |
6.1 Reorganization of receptive fields after a retinal lesion . . . . . . . . . . . 134 6.2 Reorganization of receptive fields after a cortical lesion . . . . . . . . . . . 136 6.3 Architecture of the reduced LISSOM model . . . . . . . . . . . . . . . . . . . . 138 6.4 Effect of ON/OFF channels on orientation maps . . . . . . . . . . . . . . . . . 139 6.5 Role of ON/OFF channels in processing various kinds of inputs . . . . 141
6.6Retinal activation and V1 response before and after a retinal scotoma 143
6.7 Reorganization of the orientation map after a retinal scotoma . . . . . . 144
6.8Dynamic RF expansion and perceptual shift after a retinal scotoma . 146
6.9Retinal activation and V1 response before and after a cortical lesion 147
6.10 Cortical response after a cortical lesion . . . . . . . . . . . . . . . . . . . . . . . . 148 6.11 Reorganization of lateral inhibitory weights after a cortical lesion . . 149 6.12 Reorganization of the orientation map after a cortical lesion . . . . . . . 150
7.1 Demonstration of the tilt aftereffect . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 7.2 Tilt aftereffect in human subjects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 7.3 Measuring perceived orientation as vector sum . . . . . . . . . . . . . . . . . . 161 7.4 Cortical response and perceived orientation . . . . . . . . . . . . . . . . . . . . . 163 7.5 Tilt aftereffect in humans and in LISSOM . . . . . . . . . . . . . . . . . . . . . . 164 7.6 Tilt aftereffect over time in humans and in LISSOM . . . . . . . . . . . . . 165 7.7 Components of the tilt aftereffect due to each weight type . . . . . . . . . 167 7.8 Changes in lateral inhibitory weights due to adaptation . . . . . . . . . . . 168
7.9Cortical response during adaptation and during direct and indirect
tilt aftereffect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
8.1 Architecture of the HLISSOM model . . . . . . . . . . . . . . . . . . . . . . . . . . 179 8.2 Effect of afferent normalization on V1 responses . . . . . . . . . . . . . . . . 181 8.3 Effect of afferent normalization on V1 neuron tuning . . . . . . . . . . . . . 182 8.4 Internally generated and environmental input patterns . . . . . . . . . . . . 183
8.5Effect of different input streams and initial organizations on the
self-organizing process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
9.1Effect of internally generated prenatal training patterns on
orientation maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 9.2 Prenatal orientation maps in animals and in HLISSOM . . . . . . . . . . . 194
9.3Effect of environmental postnatal training patterns on orientation
maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 9.4 Postnatal orientation maps in animals and in HLISSOM . . . . . . . . . . 197
9.5Distribution of orientation preferences in animals and in HLISSOM 198
9.6 Effect of prenatal and postnatal training on orientation maps . . . . . . 200
10.1 Measuring newborn face preferences . . . . . . . . . . . . . . . . . . . . . . . . . . 205 10.2 Face preferences in newborns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206 10.3 Face preferences in young infants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207 10.4 Self-organization of the scaled-up orientation map . . . . . . . . . . . . . . . 215 10.5 Self-organization of the FSA map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
xxviiiList of Figures
10.6Response to schematic images by Goren et al. (1975) and Johnson
et al. (1991) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
220 |
10.7Response to schematic images by Valenza et al. (1996) and Simion
et al. (1998a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221 10.8 Spurious responses to the inverted three-dot pattern . . . . . . . . . . . . . . 222 10.9 Response to natural images . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 10.10 Response variation with size and viewpoint . . . . . . . . . . . . . . . . . . . . . 224 10.11 Effect of training patterns on face preferences . . . . . . . . . . . . . . . . . . . 226 10.12 Initial afferent weights across prenatally trained and na¨ıve FSA
networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 10.13 Face and object images in postnatal training . . . . . . . . . . . . . . . . . . . . 229 10.14 Example postnatal training presentations . . . . . . . . . . . . . . . . . . . . . . . 230 10.15 Prenatally established bias for learning faces . . . . . . . . . . . . . . . . . . . . 231 10.16 Postnatal decline in response to schematic images . . . . . . . . . . . . . . . 232 10.17 Mother preferences based on both internal and external features . . . 234
11.1 Architecture of the PGLISSOM model . . . . . . . . . . . . . . . . . . . . . . . . . 243 11.2 The leaky integrator neuron model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 11.3 Self-organized afferent weights and retinotopic organization . . . . . . 250 11.4 Self-organized orientation map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 11.5 Long-range lateral connections in GMAP . . . . . . . . . . . . . . . . . . . . . . 253 11.6 Activating neurons with collinear and cocircular RFs . . . . . . . . . . . . . 254
11.7Distribution of lateral connections in animals and in PGLISSOM . . 254
12.1 Synchronized and desynchronized modes of firing . . . . . . . . . . . . . . . 259 12.2 Effect of connection type and decay rate on synchronization . . . . . . . 261 12.3 Effect of excitatory connection range on synchronization . . . . . . . . . 262 12.4 Binding and segmentation with different connection types . . . . . . . . 264 12.5 Effect of noise on desynchronization . . . . . . . . . . . . . . . . . . . . . . . . . . 266 12.6 Effect of relative input size on synchronization . . . . . . . . . . . . . . . . . . 267 12.7 Overcoming noise with strong excitation . . . . . . . . . . . . . . . . . . . . . . . 268 12.8 Overcoming noise with a long refractory period . . . . . . . . . . . . . . . . . 269
13.1 Demonstration of contour integration . . . . . . . . . . . . . . . . . . . . . . . . . . 274 13.2 Association fields for contour integration . . . . . . . . . . . . . . . . . . . . . . . 275 13.3 Edge-induced vs. line-end-induced illusory contours . . . . . . . . . . . . . 276 13.4 Contour completion across edge inducers . . . . . . . . . . . . . . . . . . . . . . 279 13.5 Measuring local response as multi-unit activity . . . . . . . . . . . . . . . . . . 281
13.6Contour integration process with varying degrees of orientation jitter 283
13.7Contour integration performance in humans and in PGLISSOM . . . 284
13.8 Quantifying the spatial relationship between two receptive fields . . . 285
13.9Edge cooccurrence in nature and long-range lateral connections in
PGLISSOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 13.10 Contour segmentation process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 13.11 Contour segmentation performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
List of Figures |
xxix |
13.12 Contour completion process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 13.13 Afferent contribution in contour completion . . . . . . . . . . . . . . . . . . . . 290
13.14Contour completion process with different kinds of connections . . . 291
13.15Contour completion performance with different kinds of connections 291
13.16 |
Contour completion process in the illusory triangle . . . . . . . . . . . . . . |
292 |
13.17 |
Salience of complete vs. incomplete illusory triangles . . . . . . . . . . . . |
293 |
13.18 |
Contour completion performance in the illusory triangle . . . . . . . . . . |
293 |
13.19 |
Contour completion performance in closed vs. open contours . . . . . . |
295 |
13.20 |
Orientation selectivity in SMAP with different input distributions . . |
297 |
13.21 |
Lateral excitatory connections in GMAP with different input |
|
|
frequencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
298 |
13.22 |
Lateral excitatory connections in GMAP with different curvature |
|
|
ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
298 |
13.23 |
Contour integration process with different input frequencies . . . . . . . |
300 |
13.24 |
Contour integration process with different curvature ranges . . . . . . . |
301 |
13.25 |
Contour integration performance with different input distributions . . |
302 |
14.1 Self-organized vs. isotropic lateral connections . . . . . . . . . . . . . . . . . . 310
14.2Sparse, redundancy-reduced coding with self-organized lateral
connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312 14.3 Architecture of the handwritten digit recognition system . . . . . . . . . . 315 14.4 Handwritten digit examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 14.5 Self-organized SOM afferent weights . . . . . . . . . . . . . . . . . . . . . . . . . . 320 14.6 Self-organized LISSOM afferent and lateral weights . . . . . . . . . . . . . 321 14.7 SOM activity patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 14.8 LISSOM activity patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
15.1 Scaling retinal and cortical area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 15.2 Scaling retinal density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 15.3 Scaling cortical density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 15.4 Training time and memory usage in LISSOM vs. GLISSOM . . . . . . 333 15.5 Weight interpolation in GLISSOM . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334 15.6 Scaling cortical density in GLISSOM . . . . . . . . . . . . . . . . . . . . . . . . . . 336 15.7 Self-organization of LISSOM and GLISSOM orientation maps . . . . 338
15.8Accuracy of the final GLISSOM map as a function of the initial
network size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 15.9 Orientation maps in LISSOM and GLISSOM . . . . . . . . . . . . . . . . . . . 339 15.10 Simulation time and memory usage in LISSOM vs. GLISSOM . . . . 340
16.1 Local microcircuit for lateral interactions . . . . . . . . . . . . . . . . . . . . . . 351
17.1 High-level influence on illusory contour perception . . . . . . . . . . . . . . 393 17.2 Example Topographica model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404 17.3 Example Topographica screenshot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
A.1 Mapping between neural sheets in LISSOM . . . . . . . . . . . . . . . . . . . . |
421 |
List of Tables
A.1 |
Parameters for the LISSOM reference simulation . . . . . . . . . . . . . . . . . |
417 |
A.2 |
Defaults for constant parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
419 |
A.3 |
Default parameter change schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
420 |
C.1 |
Defaults for FSA simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
430 |
C.2 |
Parameters for different types of face training patterns . . . . . . . . . . . . . |
431 |
C.3 |
Parameter change schedule for postnatal FSA simulations . . . . . . . . . . |
431 |
C.4 |
Parameter change schedule for combined V1 and FSA simulations . . |
432 |
D.1 |
Defaults for PGLISSOM simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . |
436 |
D.2 |
Parameter change schedule for PGLISSOM simulations . . . . . . . . . . . |
437 |
E.1 |
Defaults for SOM simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
440 |
Part I
FOUNDATIONS
1
Introduction
How can a system as complex as the human visual system be constructed? How can it be specified genetically, still allowing it to adapt to the environment? How can it perform complicated functions such as recognizing faces and identifying coherent objects immediately and automatically?
This book aims at developing a computational theory of the visual cortex to answer these questions. While these questions have been open for quite some time, and much experimental work remains to be done to answer them conclusively, computational models serve an important role in this process: They provide a formal description of the principles and processes that are going on in biology. It is possible to use the models in lieu of biology, to test ideas that are difficult to establish experimentally, and to direct experiment to areas that are not understood well. Once verified, computational models provide a precise theory of the system.
The computational theory is expressed in detail in LISSOM, a laterally connected self-organizing map model of the visual cortex. LISSOM models the structure, development, and function of the visual cortex at the level of maps and their connections. The theory is based on three computational principles: Cortical columns constitute the basic computational unit, the units continuously adapt to visual and internal input, and the units synchronize and desynchronize their activity. Simulated experiments with LISSOM demonstrate how a wide variety of phenomena follow from these principles, including columnar map organization and patchy connectivity, recovery from retinal and cortical injury, psychophysical phenomena such as tilt aftereffects and contour integration, and newborn preference for faces. The model is used to gain a precise understanding of existing data, and to make specific predictions for future experimental and theoretical research.
The LISSOM model therefore suggests specific, computational answers to the above questions: (1) The cortical structures are constructed through input-driven selforganization; (2) the self-organization is driven both by external visual inputs and by genetically determined internal inputs; and (3) perceptual grouping takes place automatically through synchronization of neuronal activity, mediated by self-organized lateral connections. In this chapter, these three hypotheses are motivated in detail and