We present a greedy-based approach to construct an efficient single hidden layer neural network with the ReLU activation that approximates a target function. In our approach we obtain a shallow network by utilizing a greedy algorithm with the prescribed dictionary provided by the available training data and a set of possible inner weights. To facilitate the greedy selection process we employ an integral representation of the network, based on the ridgelet transform, that significantly reduces the cardinality of the dictionary and hence promotes feasibility of the greedy selection. Our approach allows for the construction of efficient architectures which can be treated either as improved initializations to be used in place of random-based alternatives, or as fully-trained networks in certain cases, thus potentially nullifying the need for backpropagation training. Numerical experiments demonstrate the tenability of the proposed concept and its advantages compared to the conventional techniques for selecting architectures and initializations for neural networks.
The dictionary reduction step in our approach heavily relies on neural network integral representations, particularly on the so called ridgelet transform. Other similar approaches include those in @cite_0 and @cite_2 .
@cite_0 @cite_2
1604316327 1987618706
A new initialization method for hidden parameters in a neural network is proposed. Derived from the integral representation of the neural network, a nonparametric probability distribution of hidden parameters is introduced. In this proposal, hidden parameters are initialized by samples drawn from this distribution, and output parameters are fitted by ordinary linear regression. Numerical experiments show that backpropagation with proposed initialization converges faster than uniformly random initialization. Also it is shown that the proposed method achieves enough accuracy by itself without backpropagation in some cases. Abstract We present a strategy for learning optimal control. The approach uses functional-link neural network implementations which have several beneficial properties giving advantages over the more common generalized delta rule implementations. The learning task is decomposed into three parts: identification and monitoring, one-step-ahead control generation, and control path optimization. Each of these parts is accomplished with its own functional-link net and these are coordinated to provide the real-time learning of the optimal control path.