  We examine the influence of input data representations on learning
complexity. For learning, we posit that each model implicitly uses a candidate
model distribution for unexplained variations in the data, its noise model. If
the model distribution is not well aligned to the true distribution, then even
relevant variations will be treated as noise. Crucially however, the alignment
of model and true distribution can be changed, albeit implicitly, by changing
data representations. "Better" representations can better align the model to
the true distribution, making it easier to approximate the input-output
relationship in the data without discarding useful data variations. To quantify
this alignment effect of data representations on the difficulty of a learning
task, we make use of an existing task complexity score and show its connection
to the representation-dependent information coding length of the input.
Empirically we extract the necessary statistics from a linear regression
approximation and show that these are sufficient to predict relative learning
performance outcomes of different data representations and neural network types
obtained when utilizing an extensive neural network architecture search. We
conclude that to ensure better learning outcomes, representations may need to
be tailored to both task and model to align with the implicit distribution of
model and task.
