An auto-encoder which can be split into two parts is designed. The two parts can work well separately. The top half is an abstract network which is trained by supervised learning and can be used to classify and regress. The bottom half is a concrete network which is accomplished by inverse function and trained by self-supervised learning. It can generate the input of abstract network from concept or label. It is tested by tensorflow and mnist dataset. The abstract network is like LeNet-5. The concrete network is the inverse of the abstract network. A picture can change to label that is compression, then change it back from label that is decompression. So compression and decompression can be realized by the autoencoder. Through test, the absolute function can do generation task well, while the leaky relu function can do classification task well. Lossy compression can be achieved by abstract network and concrete network with absolute function. With one-hot encoding, the compression ratio is 5.1% when decompression quality is good. With binary encoding, the compression ratio is 2% when decompression quality is ok. The mean PNSR of five pictures is 19.48 dB. When jump connection and negative feedback are used, the decompression performance is good. The mean PNSR of five pictures is 29.86 dB. The compression ratio is 56.1%.