Structure Learning for Deep Neural Networks Based on Multiobjective Optimization

This paper focuses on the connecting structure of deep neural networks and proposes a layerwise structure learning method based on multiobjective optimization. A model with better generalization can be obtained by reducing the connecting parameters in deep networks. The aim is to find the optimal structure with high representation ability and better generalization for each layer. Then, the visible data are modeled with respect to structure based on the products of experts. In order to mitigate the difficulty of estimating the denominator in PoE, the denominator is simplified and taken as another objective, i.e., the connecting sparsity. Moreover, for the consideration of the contradictory nature between the representation ability and the network connecting sparsity, the multiobjective model is established. An improved multiobjective evolutionary algorithm is used to solve this model. Two tricks are designed to decrease the computational cost according to the properties of input data. The experiments on single-layer level, hierarchical level, and application level demonstrate the effectiveness of the proposed algorithm, and the learned structures can improve the performance of deep neural networks.