Polynomial Networks
A programme for neural architectures whose algebraic structure is explicit enough to study, control, and reuse.
Polynomial structure can serve as a common language between approximation theory, neural architecture design, and exact interpretation.
Research Questions
Which neural constructions are genuinely new, and which are reparameterisations of polynomial models?
How does polynomial degree govern expressivity, stability, trainability, and computational cost?
Can algebraically constrained networks make attribution exact without surrendering predictive performance?
Research Record
Research Map
From TaylorKAN to a family of polynomial architectures
Generalise the Taylor-series construction beyond a single model and organise polynomial networks by basis, degree, interaction order, and compositional depth.
Expressivity and equivalence
Characterise when new neural modules change representational power and when they merely induce a different parameterisation or optimisation geometry.
Exact interpretation by construction
Co-design architectures and attribution rules so that explanations follow analytically from the model rather than from post-hoc approximation.