Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs

Théo Lacombe, Yuichi Ike, Mathieu Carrière, Frederic Chazal, Marc Glisse, Yuhei Umeda

Abstract:

Although neural networks are capable of reaching
astonishing performances on a wide variety of con-
texts, properly training networks on complicated
tasks requires expertise and can be expensive from
a computational perspective. In industrial appli-
cations, data coming from an open-world setting
might widely differ from the benchmark datasets on
which a network was trained. Being able to monitor
the presence of such variations without retraining
the network is of crucial importance. In this article,
we develop a method to monitor trained neural net-
works based on the topological properties of their
activation graphs. To each new observation, we as-
sign a Topological Uncertainty, a score that aims to
assess the reliability of the predictions by investi-
gating the whole network instead of its final layer
only, as typically done by practitioners. Our ap-
proach entirely works at a post-training level and
does not require any assumption on the network
architecture, optimization scheme, nor the use of
data augmentation or auxiliary datasets; and can be
faithfully applied on a large range of network ar-
chitectures and data types. We showcase experi-
mentally the potential of Topological Uncertainty
in the context of trained network selection, Out-Of-
Distribution detection, and shift-detection, both on
synthetic and real datasets of images and graphs.