  The extreme multi-label classification~(XMC) task involves learning a
classifier that can predict from a large label set the most relevant subset of
labels for a data instance. While deep neural networks~(DNNs) have demonstrated
remarkable success in XMC problems, the task is still challenging because it
must deal with a large number of output labels, which make the DNN training
computationally expensive. This paper addresses the issue by exploring the use
of random circular vectors, where each vector component is represented as a
complex amplitude. In our framework, we can develop an output layer and loss
function of DNNs for XMC by representing the final output layer as a fully
connected layer that directly predicts a low-dimensional circular vector
encoding a set of labels for a data instance. We conducted experiments on
synthetic datasets to verify that circular vectors have better label encoding
capacity and retrieval ability than normal real-valued vectors. Then, we
conducted experiments on actual XMC datasets and found that these appealing
properties of circular vectors contribute to significant improvements in task
performance compared with a previous model using random real-valued vectors,
while reducing the size of the output layers by up to 99%.
