A network architecture for multi-multi-instance learning

We study an extension of the multi-instance learning problem where examples are organized as nested bags of instances (e.g., a document could be represented as a bag of sentences, which in turn are bags of words). This framework can be useful in various scenarios, such as graph classification, image classification and translation-invariant pooling in convolutional neural network. In order to learn multi-multi instance data, we introduce a special neural network layer, called bag-layer, whose units aggregate sets of inputs of arbitrary size. We prove that the associated class of functions contains all Boolean functions over sets of sets of instances. We present empirical results on semi-synthetic data showing that such class of functions can be actually learned from data. We also present experiments on citation graphs datasets where our model obtains competitive results.