FINN-R: An End-to-End Deep-Learning Framework for Fast Exploration of Quantized Neural Networks. Convolutional Neural Networks have rapidly become the most successful machine learning algorithm, enabling ubiquitous machine vision and intelligent decisions on even embedded computing-systems. While the underlying arithmetic is structurally simple, compute and memory requirements are challenging. One of the promising opportunities is leveraging reduced-precision representations for inputs, activations and model parameters. The resulting scalability in performance, power efficiency and storage footprint provides interesting design compromises in exchange for a small reduction in accuracy. FPGAs are ideal for exploiting low-precision inference engines leveraging custom precisions to achieve the required numerical accuracy for a given application. In this article, we describe the second generation of the FINN framework, an end-to-end tool which enables design space exploration and automates the creation of fully customized inference engines on FPGAs. Given a neural network description, the tool optimizes for given platforms, design targets and a specific precision. We introduce formalizations of resource cost functions and performance predictions, and elaborate on the optimization algorithms. Finally, we evaluate a selection of reduced precision neural networks ranging from CIFAR-10 classifiers to YOLO-based object detection on a range of platforms including PYNQ and AWS,F1, demonstrating new unprecedented measured throughput at 50TOp/s on AWS-F1 and 5TOp/s on embedded devices.