Title: Deep Neural Networks,
Abstract: Deep Neural Networks (DNNs) are universal function approximators providing
state-of- the-art solutions on wide range of applications. Common perceptual
tasks such as speech recognition, image classification, and object tracking are
now commonly tackled via DNNs. Some fundamental problems remain: (1) the lack
of a mathematical framework providing an explicit and interpretable
input-output formula for any topology, (2) quantification of DNNs stability
regarding adversarial examples (i.e. modified inputs fooling DNN predictions
whilst undetectable to humans), (3) absence of generalization guarantees and
controllable behaviors for ambiguous patterns, (4) leverage unlabeled data to
apply DNNs to domains where expert labeling is scarce as in the medical field.
Answering those points would provide theoretical perspectives for further
developments based on a common ground. Furthermore, DNNs are now deployed in
tremendous societal applications, pushing the need to fill this theoretical gap
to ensure control, reliability, and interpretability.