  Recent work on Vision Transformers (VTs) showed that introducing a local
inductive bias in the VT architecture helps reducing the number of samples
necessary for training. However, the architecture modifications lead to a loss
of generality of the Transformer backbone, partially contradicting the push
towards the development of uniform architectures, shared, e.g., by both the
Computer Vision and the Natural Language Processing areas. In this work, we
propose a different and complementary direction, in which a local bias is
introduced using an auxiliary self-supervised task, performed jointly with
standard supervised training. Specifically, we exploit the observation that the
attention maps of VTs, when trained with self-supervision, can contain a
semantic segmentation structure which does not spontaneously emerge when
training is supervised. Thus, we explicitly encourage the emergence of this
spatial clustering as a form of training regularization. In more detail, we
exploit the assumption that, in a given image, objects usually correspond to
few connected regions, and we propose a spatial formulation of the information
entropy to quantify this object-based inductive bias. By minimizing the
proposed spatial entropy, we include an additional self-supervised signal
during training. Using extensive experiments, we show that the proposed
regularization leads to equivalent or better results than other VT proposals
which include a local bias by changing the basic Transformer architecture, and
it can drastically boost the VT final accuracy when using small-medium training
sets. The code is available at https://github.com/helia95/SAR.
