A Sparse Coding Model with Synaptically Local Plasticity and Spiking Neurons Can Account for the Diverse Shapes of V1 Simple Cell Receptive Fields
(A) Our network architecture is based on those of Rozell et al.  and Földiák , , and inspired by recent physiology experiments , , . Inputs to the network (from image pixels) contact the neuron at connections (synapses) with strengths , whereas inhibitory recurrent connections between neurons  in the network have strengths . The outputs of the neurons are given by ; these spiking outputs are communicated through the recurrent connections, and also on to subsequent stages of sensory processing, such as cortical area V2, which we do not include in our model. (B) Circuit diagram of our simplified leaky integrate-and-fire  neuron model. The inputs from the stimulus with pixel values , and the other neurons in the network, combine to form the input current to the cell. This current charges up the capacitor, while some current can leak to ground through a resistor in parallel with the capacitor. The resistors are shown as cylinders to highlight the fact that they model the collective action of ion channels in the cell membrane. The internal variable evolves in time via the differential equation for voltage across our capacitor, in response to input current : , which we simulate in discrete time. Once that voltage exceeds threshold , the diode, which models neuronal voltage-gated ion channels, opens, causing the cell to fire a punctate action potential, or spike, of activity. For sake of a complete circuit diagram, the output is denoted as the voltage, , across some (small: ) resistance. After spiking, the unit's internal variable returns to the resting value of , from whence it can again be charged up.