Principled tractable models for higher-order interactions

Develop tractable probabilistic models that capture the diverse effects of higher-order interactions in complex systems in a principled manner, overcoming the combinatorial explosion inherent to exhaustive high-order representations while retaining interpretability and analytic tractability.

Background

Higher-order interactions (HOIs) are pervasive across biological and artificial neural systems and are linked to phenomena such as bistability, hysteresis, and explosive phase transitions. However, modeling HOIs typically leads to an exponential increase in parameters when higher-order terms are considered exhaustively. This challenge has limited prior studies to highly homogeneous scenarios or to relatively low-order models.

The paper introduces curved neural networks derived from a generalized maximum entropy principle as one approach to address these challenges. While this framework provides a tractable avenue, the broader problem of constructing principled, tractable HOI models remains a central motivation and is explicitly noted as unresolved in the introduction.