In many real-world prediction tasks, class labels contain information about
the relative order between labels that are not captured by commonly used loss
functions such as multicategory cross-entropy. Recently, the preference for
unimodal distributions in the output space has been incorporated into models
and loss functions to account for such ordering information. However, current
approaches rely on heuristics that lack a theoretical foundation. Here, we
propose two new approaches to incorporate the preference for unimodal
distributions into the predictive model. We analyse the set of unimodal
distributions in the probability simplex and establish fundamental properties.
We then propose a new architecture that imposes unimodal distributions and a
new loss term that relies on the notion of projection in a set to promote
unimodality. Experiments show the new architecture achieves top-2 performance,
while the proposed new loss term is very competitive while maintaining high
unimodality.

提出了两种新的方法，一种是通过新的架构来实现偏好的单峰分布，另一种则通过利用映射的概念来建立新的损失函数，以促进单峰性，实践结果表明新架构获得了最佳性能，并且新损失项在维持高单峰性的同时具有很强的竞争力。