can self-organisation generate the discontinuities in the...
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Presenting the two critical patterns more frequently than the others does not lead to co-localisation, e v e n a t v e r y h i g h -frequencies (near right).
T y p i c a l m a x i m a l l y responding units under conditions of high critical pattern preponderance shown (far right).
The two factors can interact so that a higher frequency of pattern presentation reduces the minimum probability of co-presentaion required to generate co-localisation (near right).
Typical arrangement of maximally responding units to the critical inputs shown (far right).
All simulations involve tuning a 12 by 12 grid of units to the inputs from a 12 x 12 input space using the Kohonen algorithm.
We tested the ability of co-activation to generate co-localisation by varying the probability that inputs in row 6 were accompanied by inputs in row 12 and vice versa.
Using our parallel-computing Beowolf cluster, we generated multiple maps at each parameter value.
Co-presentation of patterns leads to their co-localisation in the map, but only at high-frequencies (left). A typical distribution of the maximally responding units for the inputs in rows 6 and 12 when the map demonstrates co-localisation is shown (right).
Kohonen's self-organising feature map algorithm provides a standard way of generating a topographic map by tuning a physical array of units to some set of inputs.
A fishnet plot shows the units positions in the input space according to their maximal response. Immediately adjacent units are joined by a line.
§Desieno, D. (1988). Adding a conscience to competitive learning. Proceedings of the IEEE International Conference on Neural Networks, I, 117-124.§Farah, M. J. (1998). Why does the somatosensory homunculus have hands next to face and feet next to genitals? a hypothesis. Neural Computation, 10(8), 1983-5.§Florence, S. L., Jain, N., Pospichal, M.W., Beck, P. D., Sly, D. L., & Kaas, J. H. (1996). Central reorganization of sensory pathways following peripheral nerve regeneration in fetal monkeys. Nature, 381(6577), 69-71.§Kohonen, T. (1984). Self-organization and associative memory. Springer Verlag.§Penfield, W., & Rasmussen, T. (1950). The cerebral cortex of man: A clinical study of localization of function. New York: Macmillan.§Sengpiel, F., & Kind, P. C. (2002). The role of activity in development of the visual system. Current Biology, 12 (23), R818-26.
Tom Stafford & Stuart P Wilson
Adaptive Behaviour Research GroupDepartment of PsychologyUniversity of SheffieldSheffield, S10 2TP, UK
2.Farah’s hypothesis - self-organisation by co-activation
The primary somatosensory cortex contains a topographic map of the body surface, with two notable discontinuities — the representation of the face is next to that of the hands, and that of the feet is next to the genitals.
Farah (1998) has suggested that these discontinuities are due to the mechanisms of self-organisation which underlie cortical map development. The typical position of the foetus in the womb means that these two pairs of body parts will often touch and hence their representations will be simultaneously co-active, even though they are distal in terms of the body surface.
We use the Kohonen self-organising map algorithm to provide an existence proof of the plausibility of Farah’s hypotheses. We then use the model to test the viability of other possible causes of the known map structure and to explore the limitations of self-organisation for explaining the features of the somatosensory map.
The model shows that a) the Kohonen algorithm requires high frequencies of co-activation to introduce a selective discontinuity into the map b) that high frequency of separate activation of the critical patterns alone is not sufficient to generate the selective discontinuity c) the consistency of near-optimal map formation, and in particular the medial-lateral ordering, cannot be reliably generated by a simple Kohonen algorithm.
Can self-organisation generate the discontinuities in the somatosensory map?
Summary
1. The Somatosensory map contains major discontinuities
3. Kohonen’s self-organising map algorithm
5. Stimulus preponderance does not create discontinuities
6. Predictions and problems
4. Coactivation during self-organisation creates discontinuities
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Pr imary somatosensory cortex contains a topographic map of the body surface.
Generally adjacent body parts are represented by adjacent cortical areas.
Two major discontinuities interrupt the cortical map - the f a c e a n d t h e h a n d representations and the feet and genital representations are adjacent.
Martha Farah (1998) suggests that these discontinuities can be explained by the mechanism of map development and by foetal position.
In the womb the foetal posture is such that the hands and face are likely to touch, and hence become simultaneously active; likewise the feet and the genitals.
Activity-dependent self-organisational process are known to underlie the development of many cortical topographic maps (e.g. in the visual system; Sengpiel & Kind, 2002).
The combination of these two factors, Farah suggests, is sufficient to explain the discontinuities in the somatosensory map.
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Our first step was to confirm that we had the Kohonen algorithm working. A conscience mechanism (Desieno, 1988) which finesses map formation was introduced to ensure a more even spread of the unit tunings throughout the input space.
The plot (right) shows a typical distribution of the units which respond maximally to the inputs in the 12th (green) and 6th (red) rows.
Fishnet plots for basic algorithm with (far left) and without (far right) conscience mechanism.
Our model provides an existence proof of the plausibility of Farah's hypothesis.
However it also shows the limitations of se l f -o rgan isa t ion processes, as instantiated by the Kohonen algorithm, in the case of the somatosensory map.
The model omits major details of the biology of map formation - for example it is known that there is pre-cortical sensory map formation (with the grouping of face and hand and feet and genital afferent beginning as early as the spinal cord).
The Kohonon algorithm doesn't produce acceptably consistent maps without the conscience mechanism, nor does it contain any mechanism for producing a consistent orientation of the resulting map.
The consistency of formation in somatosensory cortex, and in particular the consistent orientation of the map (medial-lateral), cannot be reliably generated by a simple Kohonen algorithm.
Increased preponderance dr ives representations apart (see section 5). Our initial speculation was that the location of the discontinuities may be linked to the fact that they are positioned between the four areas which command the largest representational area. This fact however, by the logic of the Kohonon algorithm, would actually appear to mitigate against co-localisation.
The model lays the foundation for further investigations. Potential topics include the reorganisation of the map following the loss of inputs (i.e. limb amputation), the coordination between multiple maps, and the investigation of the role of the timing of plasticity in producing consistent developmental outcomes (including the critical discontinuities which have been the subject of this initial investigation).
Fishnet plot for rectangular grid of units tuned to a rectangular input space.
Stuart WilsonTom Stafford
from Farah, 1998.
from Haggard, 2003, after Penfield & Rasmussen, 1950.
(c) Natural History Museum
Surface plot of effect of co-presentation and frequency of critical patterns on distance between the resulting representations. Horizontal black lines show the frequencies used in the 2nd plot of section 5.
Probability of copresentation
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Smoothed surface plot of unit activation on input from row 6 (right) or 12 (left) inputs