| Abstract: |
| A large driver contributing to the undeniable success of deep learning
models is their ability to synthesize 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
modeling, 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. |
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