Deep neural networks (DNNs) have been proven to outperform classical methods on several machine learning benchmarks. However, they have high computational complexity and require powerful processing units. Especially when deployed on embedded systems, model size and inference time must be significantly reduced. We propose SYMOG (symmetric mixture of Gaussian modes), which significantly decreases the complexity of DNNs through low-bit fixed-point quantization. SYMOG is a novel soft quantization method such that the learning task and the quantization are solved simultaneously. During training the weight distribution changes from an unimodal Gaussian distribution to a symmetric mixture of Gaussians, where each mean value belongs to a particular fixed-point mode. We evaluate our approach with different architectures (LeNet5, VGG7, VGG11, DenseNet) on common benchmark data sets (MNIST, CIFAR-10, CIFAR-100) and we compare with state-of-the-art quantization approaches. We achieve excellent results and outperform 2-bit state-of-the-art performance with an error rate of only 5.71% on CIFAR-10 and 27.65% on CIFAR-100.