As a computational neural network model for real-time computing on time-varying inputs, the LSM’s performance on pattern recognition tasks mainly depends on its parameter settings. Two parameters are of particular interest: distribution of synaptic strengths and synaptic connectivity. To design an efficient liquid filter that performs desired kernel functions, these parameters need to be optimized. In this chapter, performance as a function of these parameters for several models of synaptic connectivity is studied. Results show that in order to achieve good performance, large synaptic weights are required to compensate for a small number of synapses in the liquid filter, and vice versa. In addition, a larger variance of the synaptic weights results in better performance. We also propose a genetic algorithmbased approach to evolve the liquid filter from a minimum structure with no connections, to an optimized kernel with a minimal number of synapses and high classification accuracy. This approach facilitates the design of an optimal LSM with reduced computational complexity. Results obtained using this genetic programming approach show that the synaptic weight distribution after evolution is similar in shape to that found in cortical circuitry.