Multilayer feedforward networks are universal approximators
Neural Networks
Learning internal representations by error propagation
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
On the Problem of Local Minima in Backpropagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A learning algorithm for continually running fully recurrent neural networks
Neural Computation
Mathematical and Computer Modelling: An International Journal
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In the majority of the existing supervised learning paradigms, a neural network is trained by minimizing an error function using a learning rule. The commonly used learning rules are gradient-based learning rules such as the popular backpropagation algorithm. This paper addresses an important issue on error minimization in supervised learning of neural networks using gradient-based learning rules. This paper characterizes asymptotic properties of training errors for various forms of neural networks in supervised learning and discusses their practical implications for designing neural networks via remarks and examples. The analytical results presented in this paper reveal the dependency of quality of supervised learning on the rank of training samples and associated steady activation stales. The analytical results also reveal the complexity of achieving a zero training error.