  Exemplar-free Class-incremental Learning (CIL) is a challenging problem
because rehearsing data from previous phases is strictly prohibited, causing
catastrophic forgetting of Deep Neural Networks (DNNs). In this paper, we
present iVoro, a holistic framework for CIL, derived from computational
geometry. We found Voronoi Diagram (VD), a classical model for space
subdivision, is especially powerful for solving the CIL problem, because VD
itself can be constructed favorably in an incremental manner -- the newly added
sites (classes) will only affect the proximate classes, making the
non-contiguous classes hardly forgettable. Further, in order to find a better
set of centers for VD construction, we colligate DNN with VD using Power
Diagram and show that the VD structure can be optimized by integrating local
DNN models using a divide-and-conquer algorithm. Moreover, our VD construction
is not restricted to the deep feature space, but is also applicable to multiple
intermediate feature spaces, promoting VD to be multi-centered VD (CIVD) that
efficiently captures multi-grained features from DNN. Importantly, iVoro is
also capable of handling uncertainty-aware test-time Voronoi cell assignment
and has exhibited high correlations between geometric uncertainty and
predictive accuracy (up to ~0.9). Putting everything together, iVoro achieves
up to 25.26%, 37.09%, and 33.21% improvements on CIFAR-100, TinyImageNet, and
ImageNet-Subset, respectively, compared to the state-of-the-art non-exemplar
CIL approaches. In conclusion, iVoro enables highly accurate,
privacy-preserving, and geometrically interpretable CIL that is particularly
useful when cross-phase data sharing is forbidden, e.g. in medical
applications. Our code is available at https://machunwei.github.io/ivoro.
