Linsker has reported the development of centre---surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analysed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an expla(cid:173) nation of the emergence of centre---surround and certain oriented structures. Linsker [Linsker, 1986, Linsker, 1988] has studied by simulation the evolution of weight vectors under a Hebb-type teacherless learning rule in a feed-forward linear network. The equation for the evolution of the weight vector w of a single neuron, derived by ensemble averaging the Hebbian rule over the statistics of the input patterns, is:!

We propose a novel rigorous approach for the analysis of Linsker's unsupervised Hebbian learning network. The behavior of this model is determined by the underlying nonlinear dynamics which are parameterized by a set of parameters originating from the Hebbian rule and the arbor density of the synapses. These parameters determine the presence or absence of a specific receptive field (also referred to as a'connection pattern') as a saturated fixed point attractor of the model. In this paper, we perform a qualitative analysis of the underlying nonlinear dynamics over the parameter space, determine the effects of the system parameters on the emergence of various receptive fields, and predict precisely within which parameter regime the network will have the potential to develop a specially designated connection pattern. In particular, this approach exposes, for the first time, the crucial role played by the synaptic density functions, and provides a complete precise picture of the parameter space that defines the relationships among the different receptive fields. Our theoretical predictions are confirmed by numerical simulations.

We propose a novel rigorous approach for the analysis of Linsker's unsupervised Hebbian learning network. The behavior of this model is determined by the underlying nonlinear dynamics which are parameterized by a set of parameters originating from the Hebbian rule and the arbor density of the synapses. These parameters determine the presence or absence of a specific receptive field (also referred to as a'connection pattern') as a saturated fixed point attractor of the model. In this paper, we perform a qualitative analysis of the underlying nonlinear dynamics over the parameter space, determine the effects of the system parameters on the emergence of various receptive fields, and predict precisely within which parameter regime the network will have the potential to develop a specially designated connection pattern. In particular, this approach exposes, for the first time, the crucial role played by the synaptic density functions, and provides a complete precise picture of the parameter space that defines the relationships among the different receptive fields. Our theoretical predictions are confirmed by numerical simulations.

His simulations have shown that for appropriate parameter regimes, several structured connection patterns (e.g., centre-surround and oriented afferent receptive fields (aRFs)) occur progressively as the Hebbian evolution of the weights is carried out layer by layer. The behavior of Linsker's model is determined by the underlying nonlinear dynamics which are parameterized by a set of parameters originating from the Hebbian rule and the arbor density of the synapses.

Sereno, 1987) showed that a feedforward network with area VIlike input-layer units and a Hebb rule can develop area MTlike 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 MTlike 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.

Sereno, 1987) showed that a feedforward network with area VIlike input-layer units and a Hebb rule can develop area MTlike 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 MTlike 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.

Sereno, 1987) showed that a feedforward network with area VIlike input-layer units and a Hebb rule can develop area MTlike 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 MTlike 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.

Linsker has reported the development of centre---surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analysed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an explanation of the emergence of centre---surround and certain oriented structures. Linsker [Linsker, 1986, Linsker, 1988] has studied by simulation the evolution of weight vectors under a Hebb-type teacherless learning rule in a feed-forward linear network. The equation for the evolution of the weight vector w of a single neuron, derived by ensemble averaging the Hebbian rule over the statistics of the input patterns, is:!

Linsker has reported the development of centre---surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analysed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an explanation of the emergence of centre---surround and certain oriented structures. Linsker [Linsker, 1986, Linsker, 1988] has studied by simulation the evolution of weight vectors under a Hebb-type teacherless learning rule in a feed-forward linear network. The equation for the evolution of the weight vector w of a single neuron, derived by ensemble averaging the Hebbian rule over the statistics of the input patterns, is:!

Linsker has reported the development of centre---surround receptive fields and oriented receptive fields in simulations of a Hebb-type equation in a linear network. The dynamics of the learning rule are analysed in terms of the eigenvectors of the covariance matrix of cell activities. Analytic and computational results for Linsker's covariance matrices, and some general theorems, lead to an explanation ofthe emergence of centre---surround and certain oriented structures. Linsker [Linsker, 1986, Linsker, 1988] has studied by simulation the evolution of weight vectors under a Hebb-type teacherless learning rule in a feed-forward linear network. The equation for the evolution of the weight vector w of a single neuron, derived by ensemble averaging the Hebbian rule over the statistics of the input patterns, is:!