Ebook Probabilistic models of the brain: Part 2
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Ebook Probabilistic models of the brain: Part 2
Part II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2ry visual cortex have localized orientation selective receptive fields that are organized in a cortical orientation map. Many models based on different mechanisms have been pul forward to explain then development driven by neuronal activity [31, 30, 16, 21]. Here, we propose a global optimization cr Ebook Probabilistic models of the brain: Part 2iterion for the receptive field development, derive effective cortical activity dynamics and a development model from it, and present simulation resulEbook Probabilistic models of the brain: Part 2
ts for the activity driven development process, rhe model aims to explain the development of (i) cortical simple cell receptive fields and (jtji) oriePart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2cortical development process, then derive models for the neuronal mechanisms involved, and finally present and discuss results of model simulations.Practically all models that have been proposed for the development of simple cell receptive fields and the formation of cortical maps are based on the a Ebook Probabilistic models of the brain: Part 2ssumption that orientation selective neurons develop by some simple and universal mechanism driven by neuronal activity, rhe models, however, differ iEbook Probabilistic models of the brain: Part 2
n the exact mechanisms they assume and in the type of activity patterns that may drive the development.Orientation selective receptive fields are genePart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2ff responding regions. The models assume that neuronal activity is propagated from the lateral geniculate nucleus to the visual cortex and elicits an activity pattern that causes the geniculo-cortical synaptic connections to modify by Hebbian [17,20,21, 23] or anti-Hebbian learning rules [25].Indepe Ebook Probabilistic models of the brain: Part 2ndently of how the cortical network exactly works, a universal mechanism for the development should modify the network to achieve optimal information1Ebook Probabilistic models of the brain: Part 2
82 Natural Image Statistics for Cortical Orientation Map Developmentprocessing in some sense. It has been proposed that the goal of coding should be tPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2stem that processes natural images projected onto the retina. The images are typically highly redundant, because they contain correlations in space and time. Some of the redundancy is already reduced in the retina: the On-Off response properties of retinal ganglion cells, c.g., effectively serve as Ebook Probabilistic models of the brain: Part 2local spatial decorrelation filters. Ideally, a layer of linear On-Off ganglion cells with identical receptive field profiles could "whiten" the imageEbook Probabilistic models of the brain: Part 2
power spectrum and decorrelate the activities of any pair of ganglion cells [81. In a subsequent step, simple cells in the primary visual cortex decoPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2 correlations of higher order, i.e., between many neurons al a time. In other words, simple cell feature detectors could result from a development model that aims to reduce the redundany between neuronal activities in a natural viewing scenario. It has been demonstrated in simulations that developme Ebook Probabilistic models of the brain: Part 2nt models based on the independent component analysis algorithm or a sparse representation lead to orientation selective patterns that resemble simpleEbook Probabilistic models of the brain: Part 2
cell receptive field profiles [23, 2j. We conclude that it is a reasonable goal for simple cell development to reduce the redundancy of neurons' respPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2on neuronal activity [5J. Without activity, the receptive fields remain large, unspecific, and only coarsely topographically organized. Activity leads to the emergence of orientation selective simple cells and an orientation map. The activity patterns during the first phase of the development, howev Ebook Probabilistic models of the brain: Part 2er, do not depend on visual stimulation and natural images [7J. Some orientation selective neurons may be found ill VI up to 10 days before the openinEbook Probabilistic models of the brain: Part 2
g of the eyes in ferrets, and an orientation map is present as early as recordings can be made after eye Opening [61. The activity patterns that have Part II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2ss the retina [331. These waves arc autonomously generated within the retina independently of visual stimulation and it has been hypothesized that these activity patterns might serve to drive the geniculate and even cortical development. Nevertheless, the receptive fields and the orientation map are Ebook Probabilistic models of the brain: Part 2 not fully developed at eye opening and remain plastic for some lime [14]. A lack of stimulation causes cortical responses to fade, and rearing animalEbook Probabilistic models of the brain: Part 2
s in environments with unnatural visual environments leads to cortical reorganization [7]. We conclude that visual experience is essential for a correPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2e, a successful model should be able to predict the development of orientation selectivity for the types of spontaneous activity patterns present before eye opening as well as for natural viewing conditions. Whilst theNatural Image Statistics for Cortical Orientation Map Development183activity patte Ebook Probabilistic models of the brain: Part 2rns change, the mechanism that shapes simple cell receptive fields is unlikely to be very different in both phases of the development [9]. One type ofEbook Probabilistic models of the brain: Part 2
models, the correlation based models, have been simulated for pre-natal white noise retinal activity 120] or for waves of neuronal activity as they aPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2 if the model condition is fulfilled that geniculate activities are anti-correlated [241. Another type of models, the seh-organizing map, has been shown to yield an orientation selectivity map, if it is trained with short oriented edges [21]. Models based on sparse coding driven by natural images re Ebook Probabilistic models of the brain: Part 2sult in oriented receptive fields [23].From the above, it becomes clear that one needs to make a few more critical assumptions to derive a simple cellEbook Probabilistic models of the brain: Part 2
development model that makes neurons' responses less redundant, rhe most important one is the model neurons' response function. Models have been propPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2l network dynamics [21]. For linear neurons, a development model that leads to independent activities, in general, extracts the "principal component” from the ensemble of presented input images. The many degenerate principal components for sets of natural images filtered by ganglion cells are global Ebook Probabilistic models of the brain: Part 2 patterns of alternating On and Off patches. Each of these patterns covers the whole visual field. Tn correlation based learning models that limit eacEbook Probabilistic models of the brain: Part 2
h receptive field to only a small section of the visual field [16, 20, 19] this leads to oriented simple cell receptive fields of any orientation. ModPart II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2el some kind of nonlinear input-oupul relations. One variant—the sparse coding framework—leads to oriented receptive fields only, if the input patterns contain oriented edges [23J. The extreme case of a sparse coding model is the winner-take-all network: for each input pattern, only one simple cell Ebook Probabilistic models of the brain: Part 2(and its neighbors) respond. Tn any case, independently of whether the inlracorlical dynamics are explicitly simulated or just approximated by a simplEbook Probabilistic models of the brain: Part 2
e expression, with respect to ĩĩebbian development, the key property of the model is the nonlinearity in the mapping between the geniculate input and Part II: Neural Function9 Natural Image Statistics for Cortical Orientation Map DevelopmentChristian PiepenbrockIntroductionSimple cells in (he primar Ebook Probabilistic models of the brain: Part 2 turned out, however, that the orientation tuning is sharper than can be expected from the geniculate input alone. Tills may be explained by a network effect of interacting cortical neurons [10]: cells that respond well to a stimulus locally excite each other and suppress the response of other neuro Ebook Probabilistic models of the brain: Part 2ns. Such a nonlinear network effect may be interpreted as a competition between the neurons to represent an input stimulus and has been modeled, e.g.,Ebook Probabilistic models of the brain: Part 2
by divisive inhibition [3].The formation of the simple cells' arrangement in a cortical map is in most models a direct consequence of local interactiGọi ngay
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