An overview of our method for creating an ensemble of diverse prediction paths. A network is trained to go from an input that has undergone an unknown distribution shift (e.g. JPEG compression degradation) to a target domain, e.g. surface normals, via several middle domains, e.g. 2D texture edges, low-pass filtering, greyscale, emboss filtering, etc. We then compute the corresponding weights of these predictions based on their uncertainties. The final prediction is obtained by a weighted average. Solid arrows represent learned mappings and dashed ones represent analytical mappings.
How does it work? Each network in each path receives different cues for making a prediction, due to going through different middle domains. Left: Given a distorted pixelated query, each path (columns) is affected differently by the distortion, which is reflected in its prediction, uncertainty, and weights (lighter means higher weights/uncertainty). The inverse variance merging uses the weights to assemble the final prediction that is better than each of the individual predictions. Right: Similarly, for a query with glass blur distortion, the method successfully disregards the degraded predictions and assembles an accurate final prediction. Note that the proposed method (inverse variance merging) obtains significantly better results than learning from the RGB directly (leftmost column of each example) which is the most common approach. The elliptical markers denotes sample regions where the merged result is better than all individual predictions.
We propose a calibration step, denoted as sigma training to encourage the network to output high uncertainties while keeping predictions fixed. The video at the right shows the predictions and uncertainties before and after this step on an image corrupted with increasing distortion. Before sigma training, when the model produces poor results, its uncertainty does not increase correpondingly. After sigma training, the uncertainty estimates have a stronger correlation with error.
Some qualitative results on videos and image queries are shown below. The former are on external YouTube videos and the predictions are made frame-by-frame with no temporal smoothing. Zoom in to see the fine-grained details. See the paper for full details.
• Robustness against natural distortions: We compare against several baselines and show that our method is robust to a wide range of natural distortions. In particular, we compare against adversarial training which is a popular way of making networks robust and show that it does not lead to robustness against natural distortions.
• Robustness against adversarial attacks: The method is also shown to be more robust to attacks compared to baselines without adversarial training.
• Robustness on classification tasks: The improved performance on ImageNet and CIFAR confirms the basic value of using middle domains.
Qualitative results under synthetic and natural distribution shifts for normal, reshading, and depth. The first four rows show the predictions from a query image from the Taskonomy test set under no distortion and increasing speckle noise. Our method degrades less than the other baselines, demonstrating the effectiveness of using different cues to obtain a robust prediction. The last three rows shows the results from external queries. Our method demonstrates better generalization to images considerably different from the training dataset.
Improvements are further supported by quantitative results. The l1 error over a wide range of distortions are lower for the proposed approach (inv. var. merging) compared to the baselines in all three target domains and shift intensities.
Quantitative results: Average l1 loss over 11 unseen distortions from Common Corruptions. Error bars correspond to the bootstrapped standard error. Our proposed approach is more robust against distribution shifts.
Generalization of sigmas to distribution shifts:
We have showed that our method returns predictions that are robust under a wide range of distribution shifts. Are our predicted uncertainties also able to generalize under distribution shifts, i.e. do we get high uncertainties when predictions get worse? To investigate this, we consider epistemic uncertainty which is used to capture the model's uncertainty and is an indicator of distribution shifts.
The video at the right shows the predictions and epistemic uncertainties on an image corrupted with increasing distortion. Deep ensembles produce overconfident uncertainties under distortion, while our method shows an increasing trend.
The proposed method is not limited to regression tasks. The video below shows the performance on ImageNet under increasing distortion and clean inputs. Our method performs noticeably better compared to baselines by only averaging predictions from a diverse set of middle domains. See the paper for more details and additional results.