Specialization after Generalization: Towards Understanding Test-Time
  Training in Foundation Models
Authors: name: Jonas Hübotter, name: Patrik Wolf, name: Alexander Shevchenko, name: Dennis Jüni, name: Andreas Krause, name: Gil Kur
Organization: LAS @ ETH Zurich

Recent empirical studies have explored the idea of continuing to train a
model at test-time for a given task, known as test-time training (TTT), and
have found it to yield significant performance improvements. However, there is
limited understanding of why and when TTT is effective. Earlier explanations
mostly focused on the observation that TTT may help when applied to
out-of-distribution adaptation or used with privileged data. However, the
growing scale of foundation models with most test data being in-distribution
questions these explanations. We instead posit that foundation models remain
globally underparameterized, with TTT providing a mechanism for specialization
after generalization, focusing capacity on concepts relevant to the test task.
Specifically, under the linear representation hypothesis, we propose a model in
which TTT achieves a substantially smaller in-distribution test error than
global training. We empirically validate our model's key assumptions by
training a sparse autoencoder on ImageNet, showing that semantically related
data points are explained by only a few shared concepts. Finally, we perform
scaling studies across image and language tasks that confirm the practical
implications of our model, identifying the regimes where specialization is most
effective.