COSMO-INR: Complex Sinusoidal Modulation for Implicit Neural Representations

Implicit neural representations (INRs) are a powerful paradigm for modeling data, offering a continuous alternative to discrete signal representations. Their ability to compactly encode complex signals has led to strong performance in many vision tasks. Prior work shows INR performance is highly sensitive to the choice of activation function in the underlying multilayer perceptron, yet the theoretical reasons remain unclear. Key limitations also persist, including spectral bias (reduced sensitivity to high-frequency content), limited robustness to noise, and difficulty capturing local and global structure jointly. We analyze INR signal representation using harmonic analysis and Chebyshev polynomials. We prove that modulating activation functions with a complex sinusoidal term yields richer and more complete spectral support throughout the network. Building on this, we introduce a new activation function tailored to INRs and validate our theory using Chebyshev analysis and extensive experiments. We additionally use a regularized deep prior, extracted from a task-specific model, to adapt the activations, further improving convergence speed and stability. Across image reconstruction (average PSNR gain of +5.67 dB over the nearest counterpart on a diverse dataset), denoising (+0.46 dB PSNR), super-resolution (+0.64 dB over the nearest SOTA method for 6X upscaling), inpainting, and 3D shape reconstruction, our activation consistently outperforms existing state-of-the-art alternatives.