  The underspecification of most machine learning pipelines means that we
cannot rely solely on validation performance to assess the robustness of deep
learning systems to naturally occurring distribution shifts. Instead, making
sure that a neural network can generalize across a large number of different
situations requires to understand the specific way in which it solves a task.
In this work, we propose to study this problem from a geometric perspective
with the aim to understand two key characteristics of neural network solutions
in underspecified settings: how is the geometry of the learned function related
to the data representation? And, are deep networks always biased towards
simpler solutions, as conjectured in recent literature? We show that the way
neural networks handle the underspecification of these problems is highly
dependent on the data representation, affecting both the geometry and the
complexity of the learned predictors. Our results highlight that understanding
the architectural inductive bias in deep learning is fundamental to address the
fairness, robustness, and generalization of these systems.
