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<Paper uid="W98-1228">
  <Title>Selective Attention and the Acquisition of Spatial Semantics</Title>
  <Section position="7" start_page="0" end_page="0" type="evalu">
    <SectionTitle>
5 Representation and Model
</SectionTitle>
    <Paragraph position="0"/>
    <Section position="1" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
Implementation
</SectionTitle>
      <Paragraph position="0"> As envisaged by Koch and successive co-authors, it is the role of the saliency map to determine the most salient input region, and to gate visual input so as to highlight this attended region for more detailed processing. In this way, selective attention is sited conceptually amongst detection of elementary features, and decoupled from more sophisticated representations computed further along the visual pathway. Yet while the selection mechanism typically isolates a salient region for high-resolution representation and processing (in part accomplished through suppression of competing stimuli}, modulation may also be reflected in a relatively low-resolution representation of the entire field - highlighting the attended object at the expense of less salient ones. As the modulating signal is thought to be directed back to primary visual cortex, such reduced maps may be computed at a number of points along the visual processing hierarchy, as required by the sophistication of the relation to be represented 16.</Paragraph>
      <Paragraph position="1"> While acknowledging, therefore, the importance of pre-processing as identified by (Regier, 1992), the present work does not employ feature extraction machinery of the same sophistication. In part, this may be justified by noting that much of the computational difficulty of the problem is removed once the fovea has been positioned - limiting the class of examples with which the system may be faced. Yet a more powerful justification is philosophical: the representations considered below require neither a high level of genetic determinism nor a long period of inductive learning to become established.</Paragraph>
    </Section>
    <Section position="2" start_page="0" end_page="0" type="sub_section">
      <SectionTitle>
5.1 Random Receptive Fields
</SectionTitle>
      <Paragraph position="0"> (Hogan and Diederich, 1994), (Hogan and Diederich, 1995) considered a novel class of connectionist networks in which connectivity is determined randomly, in accordance with biologically plausible probabilities. Briefly, probability of connection between each pair of neurons is dependent upon the &amp;quot;distance&amp;quot; between them - the local probability being constant within some local radius R of each 16Notwithstanding the clear separation in this discussion between the saliency mechanism and further processing, the reduced representations discussed below are computed directly from the saliency map on the grounds of computational simplicity.</Paragraph>
      <Paragraph position="1"> Hogan, Diederich and Finn 241 Selective Attention and Acquisition of Spatial Semantics unit, and decaying exponentially outside this region.</Paragraph>
      <Paragraph position="2"> This earlier work established that networks of moderate size may harbour small subnetworks (known as candidate architectures) which could be usefully recruited in the representation of Boolean concepts lr.</Paragraph>
      <Paragraph position="3"> In the present work, the approach is extended to produce random receptive field units, receiving projections from a high-resolution input map (30 x 30 units) under similar probability and radius restrictions as those above. Reduced maps of this type provide a kind of probabilistic localisation - proximal objects being represented with high probability, and distal objects being represented with low (but still significant) probability. Thus, the representation is flexible within the bounds provided by foveal alignment, allowing significant fault tolerance in the boundary of each field. Computationally, the approach provides a substantial reduction of dimension, producing an encoding of the problem allowing recruitment at the output network without propagation of an error signal to the underlying representation. null We conclude this section with an example reduced map, demonstrating that simple receptive fields of this type are sufficient to discriminate concepts such as above is. In the limit of a large number of possible projections, the response of each receptive field unit may be modelled through the use of Gaussian domain .response units 19 developed for this purpose and trainable through gradient-descent. The significance of these simulations therefore lies not in the method of acquisition of the representation, but rather in the fact that such a representation may perform successfully.</Paragraph>
      <Paragraph position="4"> Figure 3 shows the combined (weighted) response map of receptive fields for above obtained by training on example images showing a smaller object above a larger object 2deg. As will be clear from the graphic, the strong positive response to activation in the centre of the upper region ensures that the map lrThis approach is based upon evidence from cognitive neuroscience - see (Ramachandran, 1993) for a review.</Paragraph>
      <Paragraph position="5"> 18Similar representations have also been obtained for other English directional concepts such as below, left and right. A representation specific to in cannot be demonstrated in this way, requiring the attentional mechanism to highlight a detectable change of state within the local region - the change only appearing over time.</Paragraph>
      <Paragraph position="6"> l~The unit response to the intensity of each input is weighted according to a Gaussian function of the distance between the input and the unit centre.</Paragraph>
      <Paragraph position="7"> 2degTypical training sets include strongly positive examples, coupled with a similar number of strongly negative examples of the concept, randomly positioned and labelled manually. The network successfully generalises to unseen weakly positive examples.</Paragraph>
      <Paragraph position="8"> provides strong identification of prototypical positive and negative examples. However, the decaying rather than hard-limiting response of the fields provides sufficient flexibility that weakly positive examples with typical locations and prototypical examples with atypical locations are also correctly identified. For example, table 5.1 shows results using this field, outputs encoded in the interval \[0, 1\], with 1.0 indicating a strongly positive result. The approximate location of the TR with respect to the LM is indicated using points of the compass, and the weak positive examples were not assigned a numeric target value.</Paragraph>
    </Section>
  </Section>
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