  Implicit neural representations (INR) suffer from worsening spectral bias,
which results in overly smooth solutions to the inverse problem. To deal with
this problem, we propose a universal framework for processing inverse problems
called \textbf{High-Order Implicit Neural Representations (HOIN)}. By refining
the traditional cascade structure to foster high-order interactions among
features, HOIN enhances the model's expressive power and mitigates spectral
bias through its neural tangent kernel's (NTK) strong diagonal properties,
accelerating and optimizing inverse problem resolution. By analyzing the
model's expression space, high-order derivatives, and the NTK matrix, we
theoretically validate the feasibility of HOIN. HOIN realizes 1 to 3 dB
improvements in most inverse problems, establishing a new state-of-the-art
recovery quality and training efficiency, thus providing a new general paradigm
for INR and paving the way for it to solve the inverse problem.
