Title: End-to-end Quantized Training via Log-Barrier Extensions. Abstract: Quantization of neural network parameters and activations has emerged as a successful approach to reducing the model size and inference time on hardware that sup-ports native low-precision arithmetic.   Fully quantized training would facilitate further computational speed-ups as well as enable model training on embedded devices, a feature that would alleviate privacy concerns resulting from the transfer of sensitive data and models that is necessitated by off-device training.  Existing approaches to quantization-aware training (QAT) perform “fake” quantization in the forward pass in order to learn model parameters that will perform well when quantized, but rely on higher precision variables to avoid overflow in large matrix multiplications, which is unsuitable for training on fully low-precision (e.g. 8-bit)hardware. To enable fully end-to-end quantized training, we propose Log BarrierTail-bounded Quantization (LogBTQ). LogBTQ introduces a loss term, inspired by the log-barrier for constrained optimization, that enforces soft constraints on the range of values that model parameters can take on. By constraining and sparsifying model parameters, activations and inputs, our approach eliminates over-flow in practice, allowing for fully quantized 8-bit training of deep neural network models. We show that models trained using our approach achieve results competitive with state-of-the-art full-precision networks on the MNIST, CIFAR-10 andImageNet classification benchmarks.