Evaluation of Complex-Valued Neural Networks on Real-Valued Classification Tasks

Complex-valued neural networks are not a new concept, however, the use of real-valued models has often been favoured over complex-valued models due to difficulties in training and performance. When comparing real-valued versus complex-valued neural networks, existing literature often ignores the number of parameters, resulting in comparisons of neural networks with vastly different sizes. We find that when real and complex neural networks of similar capacity are compared, complex models perform equal to or slightly worse than real-valued models for a range of real-valued classification tasks. The use of complex numbers allows neural networks to handle noise on the complex plane. When classifying real-valued data with a complex-valued neural network, the imaginary parts of the weights follow their real parts. This behaviour is indicative for a task that does not require a complex-valued model. We further investigated this in a synthetic classification task. We can transfer many activation functions from the real to the complex domain using different strategies. The weight initialisation of complex neural networks, however, remains a significant problem.Comment: preprint, 18 pages, 8 figures, 8 table

Bayesian Sparsification Methods for Deep Complex-valued Networks

With continual miniaturization ever more applications of deep learning can be found in embedded systems, where it is common to encounter data with natural complex domain representation. To this end we extend Sparse Variational Dropout to complex-valued neural networks and verify the proposed Bayesian technique by conducting a large numerical study of the performance-compression trade-off of C-valued networks on two tasks: image recognition on MNIST-like and CIFAR10 datasets and music transcription on MusicNet. We replicate the state-of-the-art result by Trabelsi et al. [2018] on MusicNet with a complex-valued network compressed by 50-100x at a small performance penalty.Comment: Findings and conclusions unchanged. Improved overall presentation and redid the plots with larger markers and annotations. Coherent story about compression, CVNN, BI to SGVB with local reparameterization and additive noise. Better coverage in lit-review, clearer connections of Dropout to Bayes, VD, and prunin