Title: Fast Test-Time Adaptation Using Hints. Abstract: We propose a framework for adapting neural networks to distribution shifts at test-time. The primary idea is to leverage proper adaptation objectives based on known general properties of the target task, e.g. multi-view geometry for 3D tasks, or hierarchical structure for semantic tasks. These properties can be instantiated as adaptation signals at test-time, which we refer to as "hints". These hints are robust to distribution shifts, thus, they make adaptation more reliable compared to existing test-time adaptation methods, e.g. entropy minimization. Next, we show that this optimization during test-time can be amortized using a side-network, thus, making the adaptation orders of magnitude faster. We call this variant of test-time adaption Rapid Network Adaptation (RNA). We demonstrate consistent improvements over the baselines on diverse tasks (depth, optical flow, semantic segmentation, classification), datasets (Taskonomy, Replica, ScanNet, COCO, ImageNet) and distribution shifts (Common Corruptions, 3D Common Corruptions, cross-datasets).