  Multi-aspect controllable text generation is a more challenging and practical
task than single-aspect control. Existing methods achieve complex multi-aspect
control by fusing multiple controllers learned from single-aspect, but suffer
from attribute degeneration caused by the mutual interference of these
controllers. To address this, we provide observations on attribute fusion from
a distributional perspective and propose to directly search for the
intersection areas of multiple attribute distributions as their combination for
generation. Our method first estimates the attribute space with an autoencoder
structure. Afterward, we iteratively approach the intersections by jointly
minimizing distances to points representing different attributes. Finally, we
map them to attribute-relevant sentences with a prefix-tuning-based decoder.
Experiments on the three-aspect control task, including sentiment, topic, and
detoxification aspects, reveal that our method outperforms several strong
baselines on attribute relevance and text quality and achieves the SOTA.
Further analysis also supplies some explanatory support for the effectiveness
of our approach.
