Research On Incompleteness In Machine Learning

In recent years,machine learning has made great achievements in many fields.However,it is always accompanied by some intractable problems,such as algorithmic biases and adversarial examples,which have caused grave consequences in criminal justice and autonomous driving.Although many solutions have been proposed and tried,these problems have never been solved,and the reasons for their existences have never been clarified convincingly,either.What will be studied in this paper is the incompleteness in machine learning.The incompleteness,a concept from mathematical logic,means the inherent defect in machine learning,so this paper focuses on what can't be done by machine learning.After the formal definitions of the basic concepts and machine learning itself,the incompleteness in machine learning will be studied from data set and learning algorithm.The incompleteness in data set refers to the inherent defect in data set.Specifically,it means that the goal to express what people are thinking can't be achieved by the way of constructing data set,because what we want to express through the data set is very different from what the data set can express.It will be revealed that the reasons for existences of algorithmic biases and adversarial examples are both related to the incompleteness in data set.In addition,an incomplete data which will never be complete is going to be built in this paper,to show that the incompleteness in data set is not always solvable.The incompleteness in learning algorithm refers to the inherent defect in learning algorithm,including the nonexistence of universal learning algorithm for incomplete data sets and the incomputability of specific learning algorithm with good learning.Then,these proven conclusions will be used to illustrate the insolvability of algorithmic biases and adversarial examples from the perspective of incomputability.The incompleteness revealed and proven in this paper is not a temporary problem,but an inherent defect in machine learning,which stems from the outside mathematical understanding of machine learning in this paper,and this is because the current machine learning is only to learn from the outside.If the defect is expected to be avoided,future machine learning must turn to learning from the inside.