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Saccade-related remapping of target representations between topographic maps: a neural network study

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Abstract

The goal of this study was to explore how a neural network could solve the updating task associated with the double-saccade paradigm, where two targets are flashed in succession and the subject must make saccades to the remembered locations of both targets. Because of the eye rotation of the saccade to the first target, the remembered retinal position of the second target must be updated if an accurate saccade to that target is to be made. We trained a three-layer, feed-forward neural network to solve this updating task using back-propagation. The network’s inputs were the initial retinal position of the second target represented by a hill of activation in a 2D topographic array of units, as well as the initial eye orientation and the motor error of the saccade to the first target, each represented as 3D vectors in brainstem coordinates. The output of the network was the updated retinal position of the second target, also represented in a 2D topographic array of units. The network was trained to perform this updating using the full 3D geometry of eye rotations, and was able to produce the updated second-target position to within a 1° RMS accuracy for a set of test points that included saccades of up to 70°. Emergent properties in the network's hidden layer included sigmoidal receptive fields whose orientations formed distinct clusters, and predictive remapping similar to that seen in brain areas associated with saccade generation. Networks with the larger numbers of hidden-layer units developed two distinct types of units with different transformation properties: units that preferentially performed the linear remapping of vector subtraction, and units that performed the nonlinear elements of remapping that arise from initial eye orientation.

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Notes

  1. While networks with 9 and 25 HLUs showed consistent clustering into two groups with orthogonal receptive field boundaries, networks with 100 HLUs show consistent clustering into three groups oriented at 60° intervals, networks with 49 HLUs showed either two or three groups. The principle of the mechanism for generating a hill of activation using three clusters is the same as using two: the output hill is generated at the location where the ridge of excitatory contributions generated by each cluster intersect.

  2. This vector-subtraction, linear remapping is not exactly the same as the canonical vector-subtraction model. In the latter it is the retinal position of the saccade target rather than the motor error of the saccade that is being subtracted. It is similar, however, since the two are closely related.

  3. In our paradigm, the torsional angles for initial eye orientation and saccade motor error for all training and test points were always equal in magnitude and opposite in sign. The torsional sensitivity vectors of these two input quantities were in a ratio of −1:2 with a Pearson r magnitude of >0.99 for all HLUs and in all network trials. This 1:2 ratio arose out of the encoding ratio of saccade motor error to initial eye orientation, where the range of motor error was twice that of eye orientation for the full range of input unit activations. We confirmed that this was the cause by varying the encoding ratio to 1:3, 1:4, and 2:3 in several trials. The torsional sensitivity vectors emerged with consistent ratios of -0.35 ± 0.04, -0.25 ± 0.02, and -0.66 ± 0.03.

  4. There is no reason to believe that the three-fold clustering at 60° intervals to be a limit in the angular regularities observed in motor error sensitivity vectors. Whether higher-level clustering, say four-fold clustering at with clusters at 45° intervals, might occur in networks with more than 100 HLUs, this depends on whether the benefit of such clustering would be significant compared to fully-unclustered HLUs. As the angular spread within each cluster approaches the inter-cluster angular interval, then both utility and definition of clustering disappears and clustering would not appear.

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Acknowledgements

This work was supported by the National Science and Engineering Research Council of Canada (NSERC). G.P. Keith was supported by an OGS scholarship. J.D. Crawford was supported by a Canada Research Chair.

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Authors and Affiliations

  1. York Centre for Vision Research, CIHR Group for Action and Perception, Department of Psychology, York University, Toronto, ON, M3J 1P3, Canada

    Gerald P. Keith & J. Douglas Crawford

  2. York Centre for Vision Research, CIHR Group for Action and Perception, Department of Biology, York University, Toronto, ON, M3J 1P3, Canada

    Gerald P. Keith & J. Douglas Crawford

  3. York Centre for Vision Research, CIHR Group for Action and Perception, Department of Kinesiology, York University, Toronto, ON, M3J 1P3, Canada

    Gerald P. Keith & J. Douglas Crawford

  4. York Centre for Vision Research, CIHR Group for Action and Perception, Department of Health Sciences, York University, Toronto, ON, M3J 1P3, Canada

    Gerald P. Keith & J. Douglas Crawford

  5. Centre for Vision Research, Computer Science and Engineering Building, York University, 4700 Keele Street, Toronto, ON, M3J 1P3, Canada

    Gerald P. Keith & J. Douglas Crawford

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  1. Gerald P. Keith
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Correspondence to J. Douglas Crawford.

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Keith, G.P., Crawford, J.D. Saccade-related remapping of target representations between topographic maps: a neural network study. J Comput Neurosci 24, 157–178 (2008). https://doi.org/10.1007/s10827-007-0046-6

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  • DOI: https://doi.org/10.1007/s10827-007-0046-6

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