Adversarial KA
This addresses the applicability of KA to neural network theory, though it appears incremental as it highlights a specific regularity issue without resolving it.
The paper investigates the robustness of the Kolmogorov-Arnold (KA) representation theorem against adversarial attacks, finding it robust to countable continuous adversaries but identifying a limitation related to the equi-continuity of outer functions that hinders handling continuous groups of adversaries.
Regarding the representation theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or «expressing» functions, we test its robustness by analyzing its ability to withstand adversarial attacks. We find KA to be robust to countable collections of continuous adversaries, but unearth a question about the equi-continuity of the outer functions that, so far, obstructs taking limits and defeating continuous groups of adversaries. This question on the regularity of the outer functions is relevant to the debate over the applicability of KA to the general theory of NNs.