Recurrent neural networks of integrate-and-fire cells simulating short-term memory and wrist movement tasks derived from continuous dynamic networks

Dynamic recurrent neural networks composed of units with continuous activation functions provide a powerful tool for simulating a wide range of behaviors, since the requisite interconnections can be readily derived by gradient descent methods. However, it is not clear whether more realistic integrate-and-fire cells with comparable connection weights would perform the same functions. We therefore investigated methods to convert dynamic recurrent neural networks of continuous units into networks with integrate-and-fire cells. The transforms were tested on two recurrent networks derived by backpropagation. The first simulates a short-term memory task with units that mimic neural activity observed in cortex of monkeys performing instructed delay tasks. The network utilizes recurrent connections to generate sustained activity that codes the remembered value of a transient cue. The second network simulates patterns of neural activity observed in monkeys performing a step-tracking task with flexion/extension wrist movements. This more complicated network provides a working model of the interactions between multiple spinal and supraspinal centers controlling motoneurons. Our conversion algorithm replaced each continuous unit with multiple integrate-and-fire cells that interact through delayed "synaptic potentials". Successful transformation depends on obtaining an appropriate fit between the activation function of the continuous units and the input-output relation of the spiking cells. This fit can be achieved by adapting the parameters of the synaptic potentials to replicate the input-output behavior of a standard sigmoidal activation function (shown for the short-term memory network). Alternatively, a customized activation function can be derived from the input-output relation of the spiking cells for a chosen set of parameters (demonstrated for the wrist flexion/extension network). In both cases the resulting networks of spiking cells exhibited activity that replicated the activity of corresponding continuous units. This confirms that the network solutions obtained through backpropagation apply to spiking networks and provides a useful method for deriving recurrent spiking networks performing a wide range of functions.