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Independent component analysis is to extract independent signals from their linear mixtures without assuming prior knowledge of their mixing coefficients. As we know, a number of factors are likely to affect separation results in practical applications, such as the number of active sources, the distribution of source signals, and noise. The purpose of this paper to develop a general framework of blind separation from a practical point of view with special emphasis on the activation function adaptation. First, we propose the exponential generative model for probability density functions. A method of constructing an exponential generative model from the activation functions is discussed. Then, a Learning algorithm is derived to update the parameters in the exponential generative model. The learning algorithm for the activation function adaptation is consistent with the one for training the denting model. Stability analysis of the learning algorithm for the activation function is also discussed. Both theoretical analysis and simulations show that the proposed approach is universally convergent regardless of the distributions of sources. Finally, computer simulations are given to demonstrate the effectiveness and validity of the approach. [ABSTRACT FROM AUTHOR]