Stability and Generalization for Randomized Coordinate Descent

Randomized coordinate descent (RCD) is a popular optimization algorithm with wide applications in various machine learning problems, which motivates a lot of theoretical analysis on its convergence behavior. As a comparison, there is no work studying how the models trained by RCD would generalize to test examples. In this paper, we initialize the generalization analysis of RCD by leveraging the powerful tool of algorithmic stability. We establish argument stability bounds of RCD for both convex and strongly convex objectives, from which we develop optimal generalization bounds by showing how to early-stop the algorithm to tradeoff the estimation and optimization. Our analysis shows that RCD enjoys better stability as compared to stochastic gradient descent.

Fine-grained Generalization Analysis of Structured Output Prediction

In machine learning we often encounter structured output prediction problems (SOPPs), i.e. problems where the output space admits a rich internal structure. Application domains where SOPPs naturally occur include natural language processing, speech recognition, and computer vision. Typical SOPPs have an extremely large label set, which grows exponentially as a function of the size of the output. Existing generalization analysis implies generalization bounds with at least a square-root dependency on the cardinality d of the label set, which can be vacuous in practice. In this paper, we significantly improve the state of the art by developing novel high-probability bounds with a logarithmic dependency on d. Furthermore, we leverage the lens of algorithmic stability to develop generalization bounds in expectation without any dependency on d. Our results therefore build a solid theoretical foundation for learning in large-scale SOPPs. Furthermore, we extend our results to learning with weakly dependent data.

ALGORITHMIC STABILITY OF DEEP LEARNING NEURAL NETWORKS IN RECOGNIZING THE MICROSTRUCTURE OF MATERIALS

The division of data for training a neural network into training and test data in various proportions to each other is investigated. The question is raised about how the quality of data distribution and their correct annotation can affect the final result of constructing a neural network model. The paper investigates the algorithmic stability of training a deep neural network in problems of recognition of the microstructure of materials. The study of the stability of the learning process makes it possible to estimate the performance of a neural network model on incomplete data distorted by up to 10%. Purpose. Research of the stability of the learning process of a neural network in the classification of microstructures of functional materials. Materials and methods. Artificial neural network is the main instrument on the basis of which produced the study. Different subtypes of deep convolutional networks are used such as VGG and ResNet. Neural networks are trained using an improved backpropagation method. The studied model is the frozen state of the neural network after a certain number of learning epochs. The amount of data excluded from the study was randomly distributed for each class in five different distributions. Results. Investigated neural network learning process. Results of experiments conducted computing training with gradual decrease in the number of input data. Distortions of calculation results when changing data with a step of 2 percent are investigated. The percentage of deviation was revealed, equal to 10, at which the trained neural network model loses its stability. Conclusion. The results obtained mean that with an established quantitative or qualitative deviation in the training or test set, the results obtained by training the network can hardly be trusted. Although the results of this study are applicable to a particular case, i.e., microstructure recognition problems using ResNet-152, the authors propose a simpler technique for studying the stability of deep learning neural networks based on the analysis of a test, not a training set.

Neural Network Model for Assessing the Physical and Mechanical Properties of a Metal Material Based on Deep Learning

The paper investigates the algorithmic stability of learning a deep neural network in problems of recognition of the materials microstructure. It is shown that at 8% of quantitative deviation in the basic test set the algorithm trained network loses stability. This means that with such a quantitative or qualitative deviation in the training or test sets, the results obtained with such trained network can hardly be trusted. Although the results of this study are applicable to the particular case, i.e. problems of recognition of the microstructure using ResNet-152, the authors propose a cheaper method for studying stability based on the analysis of the test, rather than the training set.

Theoretical analysis of skip connections and batch normalization from generalization and optimization perspectives

Deep neural networks (DNNs) have the same structure as the neocognitron proposed in 1979 but have much better performance, which is because DNNs include many heuristic techniques such as pre-training, dropout, skip connections, batch normalization (BN), and stochastic depth. However, the reason why these techniques improve the performance is not fully understood. Recently, two tools for theoretical analyses have been proposed. One is to evaluate the generalization gap, defined as the difference between the expected loss and empirical loss, by calculating the algorithmic stability, and the other is to evaluate the convergence rate by calculating the eigenvalues of the Fisher information matrix of DNNs. This overview paper briefly introduces the tools and shows their usefulness by showing why the skip connections and BN improve the performance.