GCNO: Gramian Chebyshev Neural Operator for Physics-Based Compression of Wireless Channels

What the math gives to ML

The paper exposes a useful alternative to fixed-dimensional neural compression: represent a complex matrix by a variable number of physically meaningful rank-one atoms, and let the decoder reconstruct those atoms analytically rather than learning a second large network. The transferable mathematical asset is the separable array-response dictionary, together with off-grid first-order corrections and a least-squares recovery step for coefficients. This can become a structured bottleneck for neural models that process array-valued or Fourier-like data, where the encoder predicts only the number of significant modes and their continuous coordinates. The most practical first test is a differentiable sparse spectral encoder for complex channel matrices, comparing payload-versus-error against a conventional fixed latent autoencoder.