Abstract: Cross-domain training tasks are currently an open challenge in the field of machine learning. At present, the latest researches are discussing the use of the cross-domain invariance of real features to predict unknown domain data, so as to achieve cross-domain generalization capabilities. But in fact, when it is known that the data comes from a certain domain, the comprehensive use of real features and false features will achieve better prediction results. This paper focuses on this issue and designs a learning model that is suitable for both cross-domain generalization and adaptation tasks(CDGA). The core of the model is still to separate the real features, so this paper proposes a new more stable training risk function, which not only has a higher test accuracy in the cross-domain generalization problem, but also overcomes the shortcomings of traditional methods that are easy to overfit, so it can be well embedded in the CDGA model. In addition, through the designed training method, the data expression part of the CDGA model can effectively separate the real features and false features, and the classifier part adaptively learns to select the generalized classifier or the classifier of the specific environment, thereby combining the application of false features to achieve efficient prediction in cross-domain tasks. Finally, it is tested on the constructed Colored MNIST data set, and the results are significantly better than the existing methods.