Abstract
The construction of filters arising from linear neural networks with feed-backward excitatory-inhibitory connections is presented. Spatially invariant coupling between neurons and the distribution of neuron-receptor units in the form of a uniform square grid yield the TBT (Toeplitz-Block-Toeplitz) connection matrix. Utilizing the relationship between spectral properties of such matrices and their generating functions, the method for construction of recurrent linear networks is addressed. By appropriately bounding the generating function, the connection matrix eigenvalues are kept in the desired range allowing for large matrix inverse to be approximated by a convergent power series. Instead of matrix inversion, the single pass convolution with the filter obtained from the network connection weights is applied when solving the network. For the case of inter-neuron coupling in the form of a function that is expandable in a Fourier series in polar angle, the network response filter is shown to be steerable.
Highlights
This paper addresses the construction of filters arising from neural networks with feed-backward connections accounting for lateral inhibition and excitation
Assuming that inter-neuron coupling is spatially invariant for the sensory distribution given in Fig. 1 the connection matrix is of TBT type
By bounding the generating function, the spectral radius of the connection matrix is maintained in the interval 0,1
Summary
This paper addresses the construction of filters arising from neural networks with feed-backward connections accounting for lateral inhibition and excitation. Such networks are often used when modeling biological vision systems. This allows one to characterize the spectral properties of the TBT matrix B Bn,m based on the corresponding generating function Such characterization can be used when choosing neural network inter-neuron coupling functions. In [5] and [6] the microscopic neuron network solution for the 2D receptor grid with recurrent lateral inhibition was found by approximating the inverse of the following matrix by a convergent power series:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
