A large driver contributing to the undeniable success of deep-learning
models is their ability to synthesise task-specific features from data.
For a long time, the predominant belief was that 'given enough data, all
features can be learned.' However, as large language models are hitting
diminishing returns in output quality while requiring an ever-increasing
amount of training data and compute, new approaches are required. One
promising avenue involves focusing more on aspects of modelling, which
involves the development of novel *inductive biases* such as invariances
that cannot be readily gleaned from the data. This approach is
particularly useful for data sets that model real-world phenomena, as
well as applications where data availability is scarce. Given their dual
nature, geometry and topology provide a rich source of potential
inductive biases. In this talk, I will present novel advances in
harnessing multi-scale geometrical-topological characteristics of data.
A special focus will be given to show how geometry and topology can
improve representation learning tasks. Underscoring the generality of
a hybrid geometrical-topological perspective, I will furthermore
showcase applications from a diverse set of data domains, including
point clouds, graphs, and higher-order combinatorial complexes.