CNet preprint reports fewer training steps for complex-valued language model

Researchers report that a complex-valued language model built with their CNet framework matched a real-valued comparison model on character-level tiny-shakespeare in under half the training steps. The preprint introduces a C++/CUDA framework for neural networks that retain phase information in complex-valued data. Its language model uses a causal Fourier mixer, which combines information from preceding tokens. A separate attention mechanism assigns weights using squared magnitudes rather than softmax and reaches 1.52 nats/char, matching softmax self-attention. The training-step comparison is against a parameter-matched real causal FNet on a character-level task; it does not establish equivalent savings for large-scale language-model training.