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Convolutional Neural Networks: Estimating Relations in the Ising Model on Overfitting

A CNN (Convolutional Neural Network) is one of actively researched and broadly applied deep machine learning methods. A CNN is composed of a feed-forward neural network that takes in images as inputs, and outputs a probability value associated to a class that best describes the image. As well, it is constructed of multiple layers, which include convolutional, max-pooling and fully connected layers. However, the training set has a large influence on the accuracy of a network, and hence it is paramount to create a network architecture that prevents overfitting (when a trained model cannot differentiate newly input data from its test data) and underfitting (the inability of a model to find relationships among inputs). This paper addresses the above deficiencies by comparing the statistics of CNN image recognition algorithms to the Ising model. The Ising model consists of magnetic dipole moments that can be in one of two states: +1 or −1. Using a two-dimensional square-lattice array once a training set of such data is complete, we determine the impact that network parameters, specifically learning rate and regularization rate, have on the adaptability of convolutional neural networks for image classification. Our results not only contribute to a better theoretical understanding of a CNN, but also provide concrete guidance on preventing model overfitting and underfitting when a CNN is applied for image recognition.