- . Cascade Error Projection Learning Algorithm

In this paper, we workout a detailed mathematical analysis for a new learning algorithm termed Cascade Error Projection (CEP) and a general learning frame work. This frame work can be used to ob(ain the cascade correlation learning algorithm by choosing a particular set of parameters. Furthemlore, CEP learning algorithm is operated only on one layer, whereas the other set of weights can be calculated deterministically. In association wilh the dynamical stepsize change concept to convert the weight update from infinite space into a finite space, the relation between the current stepsize and the previous energy level is also given and the estimation procedure for optimal stepsize is used for validation of our proposed technique. The weight values of zero are used for starting the learning for every layer, and a single hidden unit is applied instead of using a pool of candidate hidden units as in the cascade correlation scheme. Therefore, simplicity in hardware implementation is also obtained. Furthemwre, this analysis allows us to select jiom other methods (such as the conjugate gradient descent or the Newton’s second order) one of which will be a good candidate for the learning technique. The choice of learning technique depends on the constraints of the problem (e.g., speed, petiorrnance, and hardware implementation); one technique may be more suitable than others. Moreover, for a discrete weight space, the theoretical analysis presents the capability of learning with limited weight quantization. Finally, 5to 8-bit parity problems are investigated; the simulation results demonstrate that only three hidden units are required to learn a 5-bit parity problem pe~ectly and to learn a 6-bit parity with just one pattern error. Four hidden units are suficient for a 7-bit parity problem with no error and for an tl-bit parity problem with one pattern error. We have restricted the learning to a jixed 100 epoch iterations for each single-layer perception (each single hidden unit) learning. In addition, with 3to 4bit weight resolution, it is demonstrated that this technique is capable of learning reliably 5to 8-bit parity problems by incorporating additional hidden units (up to a maximum of 20).