  Embedding of large but redundant data, such as images or text, in a hierarchy
of lower-dimensional spaces is one of the key features of representation
learning approaches, which nowadays provide state-of-the-art solutions to
problems once believed hard or impossible to solve. In this work, in a plot
twist with a strong meta aftertaste, we show how trained deep models are as
redundant as the data they are optimized to process, and how it is therefore
possible to use deep learning models to embed deep learning models. In
particular, we show that it is possible to use representation learning to learn
a fixed-size, low-dimensional embedding space of trained deep models and that
such space can be explored by interpolation or optimization to attain
ready-to-use models. We find that it is possible to learn an embedding space of
multiple instances of the same architecture and of multiple architectures. We
address image classification and neural representation of signals, showing how
our embedding space can be learnt so as to capture the notions of performance
and 3D shape, respectively. In the Multi-Architecture setting we also show how
an embedding trained only on a subset of architectures can learn to generate
already-trained instances of architectures it never sees instantiated at
training time.
