Formal connection between joint ANF leap and learnability

Establish a formal connection between the joint ANF leap of vector-valued Boolean maps and their learnability, clarifying whether and how this structural quantity predicts learning behavior.

Background

The paper introduces the joint ANF leap as a new measure of how many variables must be introduced at a single step when the joint algebraic normal-form support is optimally ordered. The authors compare this quantity with multilayer-perceptron performance empirically, but distinguish the observed association from a theoretical learning guarantee.

The paper explicitly notes that the joint ANF leap is an ANF-based, vector-valued adaptation of concepts developed for Fourier support and that the existing learning results do not automatically apply. A formal theorem relating this measure to learnability therefore remains unresolved.

References

A formal connection to ANF based learnability is left for future work.

— Representation Redundancy and Structural Complexity in Finite-Field Inversion  (2609.04583 - Zhang et al., 4 Sep 2026) in Section 1, subsection “Two Theorem Chains”

Proving the exact raw ANF values for general $n$, separating the effect of joint ANF leap from algebraic degree, and studying models that explicitly use the Galois action are natural directions for future work.

— Representation Redundancy and Structural Complexity in Finite-Field Inversion  (2609.04583 - Zhang et al., 4 Sep 2026) in Section 7, Conclusion