UCSD COGS 107B - Learning to See Rotation (7 pages)

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Learning to See Rotation



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Learning to See Rotation

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Pages:
7
School:
University of California, San Diego
Course:
Cogs 107b - Systems Neuroscience
Systems Neuroscience Documents
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In R P Lippmann J Moody and D S Touretzky eds 1991 Advances in Neural Information Processing Systems 3 San Mateo CA Morgan Kaufmann Publishers pp 320 326 Learning to See Rotation and Dilation with a Hebb Rule Martin I Sereno and Margaret E Sereno Cognitive Science D 015 University of California San Diego La Jolla CA 92093 0115 Abstract Previous work M I Sereno 1989 cf M E Sereno 1987 showed that a feedforward network with area V1 like input layer units and a Hebb rule can develop area MT like second layer units that solve the aperture problem for pattern motion The present study extends this earlier work to more complex motions Saito et al 1986 showed that neurons with large receptive fields in macaque visual area MST are sensitive to different senses of rotation and dilation irrespective of the receptive field location of the movement singularity A network with an MT like second layer was trained and tested on combinations of rotating dilating and translating patterns Third layer units learn to detect specific senses of rotation or dilation in a position independent fashion despite having position dependent direction selectivity within their receptive fields 1 INTRODUCTION The visual systems of mammals and especially primates are capable of prodigious feats of movement object and scene recognition under noisy conditions feats we would like to copy with artificial networks We are just beginning to understand how biological networks are wired up during development and during learning in the adult Even at this stage however it is clear that explicit error signals and the apparatus for propagating them backwards across layers are probably not involved On the other hand there is a growing body of evidence for connections whose strength can be modified via NMDA channels as functions of the correlation between pre and post synaptic activity The present project was to try to learn to detect pattern rotation and dilation by example using a simple Hebb rule By building up complex filters in stages using a simple realistic learning rule we reduce the complexity of what must be learned with more explicit supervision at higher levels 1 1 ORIENTATION SELECTIVITY Some of the connections responsible for the selectivity of cortical neurons to local stimulus features develop in the absence of patterned visual experience For example primary visual cortex V1 or area 17 contains orientation selective neurons at birth in several animals Linsker 1986a b has shown that feedforward networks with gaussian topographic interlayer connections linear summation and simple hebb rules develop orientation selective units in higher layers when trained on noise In his linear system weight updates for a layer can be written as a function of the two point correlation characterizing the previous layer Noise applied to the input layer causes the emergence of connections that generate gaussian correlations at the second layer This in turn drives the development of more complex correlation functions in the third layer e g difference ofgaussians Rotational symmetry is broken in higher layers with the emergence of Gaborfunction like connection patterns reminiscent of simple cells in the cortex 1 2 PATTERN MOTION SELECTIVITY The ability to see coherent motion fields develops late in primates Human babies for example fail to see the transition from unstructured to structured motion e g the transition between randomly moving dots and circular 2 D motion for several months The transition from horizontally moving dots with random y axis velocities to dots with sinusoidal y axis velocities which gives the percept of a rotating 3 D cylinder is seen even later Spitz Stiles Davis Siegel 1988 This suggests that the cortex requires many experiences of moving displays in order to learn how to recognize the various types of coherent texture motions However orientation gradients shape from shading and pattern translation dilation and rotation cannot be detected with the kinds of filters that can be generated solely by noise The correlations present in visual scenes are required in order for these higher level filters to arise 1 3 NEUROPHYSIOLOGICAL MOTIVATION Moving stimuli are processed in successive stages in primate visual cortical areas The first cortical stage is layer 4C of V1 which receives its main ascending input from the magnocellular layers of the lateral geniculate nucleus Layer 4C projects to layer 4B which contains many tightly tuned direction selective neurons These neurons however respond to moving contours as if these contours were moving perpendicular to their local orientation Movshon et al 1985 Layer 4B neurons project directly and indirectly to area MT where a subset of neurons show a relatively narrow peak in the direction tuning curve for a plaid that is lined up with the peak for a single grating These neurons therefore solve the aperture problem for pattern translation presented to them by the local motion detectors in layer 4B of V1 MT neurons however appear to be largely blind to the sense of pattern rotation or dilation Saito et al 1986 Thus there is a higher order aperture problem that is solved by the neurons in the parts of areas MST and 7a that distinguish senses of pattern rotation and dilation The present model provides a rationale for how these stages might naturally arise in development 2 RESULTS In previous work M I Sereno 1989 cf M E Sereno 1987 a simple 2 layer feedforward architecture sufficed for an MT like solution to the aperture problem for local translational motion Units in the first layer were granted tuning curves like those in V1 layer 4B Each first layer unit responded to a particular range of directions and speeds of the component of movement perpendicular to a local contour Second layer units developed MT like receptive fields that solved the aperture problem for local pattern translation when trained on locally jiggled gratings rigidly moving in randomly chosen pattern directions 2 1 NETWORK ARCHITECTURE A similar architecture was used for second to third layer connections see Fig 1 a sample network with 5 directions and 3 speeds As with Linsker a new input layer was constructed from a canonical unit suitably transformed Thus second layer units were granted tuning curves resembling those found in MT as well as those generated by firstto second layer learning that is they responded to the local pattern translation but were blind to particular senses of local rotation dilation and


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