Non-suspiciousness: a generalisation of convexity in the frame of foundations of numerical analysis and learning
Monica Bianchini, Stefano Fanelli, Marco Gori, Marco Protasi · 2002
The effectiveness of connectionist models in emulating intelligent behaviour is strictly related to the capability of the learning algorithms to find optimal or near-optimal solutions. In this paper, a canonical reduction of gradient descent dynamics is proposed, allowing the formulation of the neural network learning as a finite continuous optimisation problem, under some nonsuspiciousness conditions. In the linear case, the nonsuspect nature of the problem guarantees the implementation of an iterative method with O(n/sup 2/) as computational complexity. Finally, since nonsuspiciousness is a generalisation of the concept of convexity, it is possible to apply this theory to the resolution of nonlinear problems.