  The performance of a lifelong learning (L3) model degrades when it is trained
on a series of tasks, as the geometrical formation of the embedding space
changes while learning novel concepts sequentially. The majority of existing L3
approaches operate on a fixed-curvature (e.g., zero-curvature Euclidean) space
that is not necessarily suitable for modeling the complex geometric structure
of data. Furthermore, the distillation strategies apply constraints directly on
low-dimensional embeddings, discouraging the L3 model from learning new
concepts by making the model highly stable. To address the problem, we propose
a distillation strategy named L3DMC that operates on mixed-curvature spaces to
preserve the already-learned knowledge by modeling and maintaining complex
geometrical structures. We propose to embed the projected low dimensional
embedding of fixed-curvature spaces (Euclidean and hyperbolic) to
higher-dimensional Reproducing Kernel Hilbert Space (RKHS) using a
positive-definite kernel function to attain rich representation. Afterward, we
optimize the L3 model by minimizing the discrepancies between the new sample
representation and the subspace constructed using the old representation in
RKHS. L3DMC is capable of adapting new knowledge better without forgetting old
knowledge as it combines the representation power of multiple fixed-curvature
spaces and is performed on higher-dimensional RKHS. Thorough experiments on
three benchmarks demonstrate the effectiveness of our proposed distillation
strategy for medical image classification in L3 settings. Our code
implementation is publicly available at
https://github.com/csiro-robotics/L3DMC.
