1 research outputs found
Semantics, Representations and Grammars for Deep Learning
Deep learning is currently the subject of intensive study. However,
fundamental concepts such as representations are not formally defined --
researchers "know them when they see them" -- and there is no common language
for describing and analyzing algorithms. This essay proposes an abstract
framework that identifies the essential features of current practice and may
provide a foundation for future developments.
The backbone of almost all deep learning algorithms is backpropagation, which
is simply a gradient computation distributed over a neural network. The main
ingredients of the framework are thus, unsurprisingly: (i) game theory, to
formalize distributed optimization; and (ii) communication protocols, to track
the flow of zeroth and first-order information. The framework allows natural
definitions of semantics (as the meaning encoded in functions), representations
(as functions whose semantics is chosen to optimized a criterion) and grammars
(as communication protocols equipped with first-order convergence guarantees).
Much of the essay is spent discussing examples taken from the literature. The
ultimate aim is to develop a graphical language for describing the structure of
deep learning algorithms that backgrounds the details of the optimization
procedure and foregrounds how the components interact. Inspiration is taken
from probabilistic graphical models and factor graphs, which capture the
essential structural features of multivariate distributions.Comment: 20 pages, many diagram