Tabea Heusel

• This Bachelor thesis investigates the learning rules of the Hebbian, Oja and BCM neuron models for their convergence to, and the stability of, the fixed points. Existing research is presented in a structured manner using consistent notation. Hebbian learning is neither convergent nor stable. Oja learning converges to a stable fixed point, which is the eigenvector corresponding to the largest eigenvalue of the covariance matrix of the input data. BCM learning converges to a fixed point which is stable, when assuming a discrete distribution of orthogonal inputs that occur with equal probability. Hebbian learning can therefore not be used in further applications, where convergence to a stable fixed point is required. Furthermore, this Bachelor thesis came to the conclusion that determining the fixed points of the BCM learning rule explicitly involves extensive calculation and other methods for verifying the stability of possible fixed points should be considered.