Equivariance
Neural networks have achieved state-of-the-art results in many fields, however it's not clear how to design networks the respect, and account for, the inductive biases of a particular task. This line of work studies principled ways to encode, and learn, inductive biases in neural networks, resulting in better performance, interpretability, and reduced numbers of parameters.

Relevant papers:
- "Learning linear groups in neural networks"

Structured representations
Learning meaningful representations is instrumental for most learning problems. Representations with appropriate properties can reduce model sizes, improve performance. and be more interpretable by being better suited to the task at hand. This line of work studies how to construct networks whose representations satisfy these given constraints.

Relevant papers:
- "On the convergence of group-sparse autoencoders"
- "Towards improving discriminative reconstruction via simultaneous dense and sparse coding"

Tropical geometry
Linear algebra powers most learning systems today; however, there are nonlinear algebras that are more expressive and better suited for certain applications. This line of work studies how these algebras can be used in various machine learning settings to model problems of interest, resulting in new algorithms, unified formulations, and intuitive explanations.

Relevant papers:
- "Tropical Geometry and Machine Learning"
- "Tropical modeling of weighted transducers algorithms on graphs"