We propose an efficient method to learn deep local descriptors for instance-level recognition. The training only requires examples of positive and negative image pairs and is performed as metric learning of sum-pooled global image descriptors. At inference, the local descriptors are provided by the activations of internal components of the network. We demonstrate why such an approach learns local descriptors that work well for image similarity estimation with classical efficient match kernel methods. The experimental validation studies the trade-off between performance and memory requirements of the state-of-the-art image search approach based on match kernels. Compared to existing local descriptors, the proposed ones perform better in two instance-level recognition tasks and keep memory requirements lower. We experimentally show that global descriptors are not effective enough at large scale and that local descriptors are essential. We achieve state-of-the-art performance, in some cases even with a backbone network as small as ResNet18.