  Can transformers generalize efficiently on problems that require dealing with
examples with different levels of difficulty? We introduce a new task tailored
to assess generalization over different complexities and present results that
indicate that standard transformers face challenges in solving these tasks.
These tasks are variations of pointer value retrieval previously introduced by
Zhang et al. (2021). We investigate how the use of a mechanism for adaptive and
modular computation in transformers facilitates the learning of tasks that
demand generalization over the number of sequential computation steps (i.e.,
the depth of the computation graph). Based on our observations, we propose a
transformer-based architecture called Hyper-UT, which combines dynamic function
generation from hyper networks with adaptive depth from Universal Transformers.
This model demonstrates higher accuracy and a fairer allocation of
computational resources when generalizing to higher numbers of computation
steps. We conclude that mechanisms for adaptive depth and modularity complement
each other in improving efficient generalization concerning example complexity.
Additionally, to emphasize the broad applicability of our findings, we
illustrate that in a standard image recognition task, Hyper- UT's performance
matches that of a ViT model but with considerably reduced computational demands
(achieving over 70\% average savings by effectively using fewer layers).
