Neural Abstraction Pyramid Architecture - Hierarchical Neural Networks for Image Interpretation - page 68

Lateral

Backward

projection

projection

Hypercolumn

Forward

projection

Feature

Feature

2j

cell

i

2i array

Layer (l−1)

j

j/2

k i/2

Layer (l+1)

Hyper−neighborhood

Layer

l

Fig. 4.3. A feature cell with its projections. Such a cell is addressed by its layer l , its feature
array number k , and its array position (i,j) . Lateral projections originate from the hyper-
neighborhood in the same layer. Forward projections come from the hyper-neighborhood of
the corresponding position (2i, 2j) in the next lower layer (l−1) . Backward projections start
from the hyper-neighborhood at position (i/2,j/2) in layer (l + 1) .

action is not only necessary between neighboring cells within a feature array k , but
also across arrays since the code used is a distributed one.
The use of distributed codes is much more efficient than the use of localized
encodings. A binary local 1-out-of- N code can provide at most log N bits of infor-
mation while in a dense codeword of the same length, N bits can be stored. The
use of sparse codes lowers the storage capacity of a code, but it facilitates decoding
and associative completion of patterns [172]. Sparse codes are also energetically
efficient since most spikes are devoted to the most active feature-detecting cells.
One important idea of the Neural Abstraction Pyramid architecture is that each
layer maintains a complete image representation in an array of hypercolumns. The
degree of abstraction of these representations increases as one ascends in the hi-
erarchy. At the bottom of the pyramid, features correspond to local measurements
of a signal, the image intensity. Subsymbolic representations, like the responses of
edge detectors or the activities of complex feature cells are present in the middle
layers of the network. When moving upwards, the feature cells respond to image
windows of increasing size, represent features of increasing complexity, and are in-
creasingly invariant to image deformations. At the top of the pyramid, the images
are described in terms of very complex features that respond invariantly to large im-
age parts. These representations are almost symbolic, but they are still encoded in a
distributed manner.
This sequence of more and more abstract representations resembles the abstrac-
tion hierarchy found along the ventral visual pathway. Every step changes the na-
ture of the representation only slightly, but all steps follow the same direction. They