Statistical-mechanical analysis of pre-training and fine tuning in deep learning
This provides theoretical insights into deep learning mechanisms for researchers, though it is incremental as it uses a simplified model rather than direct analysis of multi-layer networks.
The paper tackles the problem of understanding the role of unsupervised pre-training and supervised fine-tuning in deep learning by using a statistical-mechanical analysis with a simple perceptron model, finding a phase transition in generalization error dependent on unlabeled data quantity.
In this paper, we present a statistical-mechanical analysis of deep learning. We elucidate some of the essential components of deep learning---pre-training by unsupervised learning and fine tuning by supervised learning. We formulate the extraction of features from the training data as a margin criterion in a high-dimensional feature-vector space. The self-organized classifier is then supplied with small amounts of labelled data, as in deep learning. Although we employ a simple single-layer perceptron model, rather than directly analyzing a multi-layer neural network, we find a nontrivial phase transition that is dependent on the number of unlabelled data in the generalization error of the resultant classifier. In this sense, we evaluate the efficacy of the unsupervised learning component of deep learning. The analysis is performed by the replica method, which is a sophisticated tool in statistical mechanics. We validate our result in the manner of deep learning, using a simple iterative algorithm to learn the weight vector on the basis of belief propagation.