CNet: A Complex-Valued Deep Learning Framework with Wirtinger Autodifferentiation and FFT--Hadamard Convolution

Key points

• Complex models are underexplored yet natural where data is intrinsically complex -- RF/IQ communications, MRI k-space, radar/SAR, audio spectra -- and phase carries information real networks discard.1
• CNet is physics-native: a network is a cascade of complex (often unitary) operations on an amplitude vector, and classification is a Born-rule measurement pk = |zk|^2/||z||^2 rather than a softmax over real logits.1
• Its library of complex layers makes conv(x,k) = IFFT(FFT(x).FFT(k)) learnable via signal-processing primitives -- spectral-padding local kernels (Pad), the inverse DFT, a magnitude nonlinearity |z|^2 (CModulus2), holomorphic powers z^M (CPower), and mean pooling (MeanPool) -- with GPU kernels for every layer, a GPU true-Adam optimizer, and a reduced-memory inference mode.1
• We introduce Born-rule attention: a content-based causal mixer whose weights are quantum-measurement probabilities |<Qk,Kj>|^2 of one token against another -- the first attention mechanism built on the Born rule.1

Sources (1)

• [1]CNet: A Complex-Valued Deep Learning Framework with Wirtinger Autodifferentiation and FFT--Hadamard Convolution
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 03:57 PM

  CNet is a C++/CUDA framework for building deep complex-valued neural networks (CVNNs) and optimizing complex functions by gradient descent with Wirtinger derivatives.

  Complex models are underexplored yet natural where data is intrinsically complex -- RF/IQ communications, MRI k-space, radar/SAR, audio spectra -- and phase carries information real networks discard.

Extractive summary: sentences quoted from the sources.