Convolutional Neural Networks (CNNs) have emerged as highly successful tools for image
generation, recovery, and restoration. This success is often attributed to large amounts of
training data. However, recent experimental findings challenge this view and instead suggest
that a major contributing factor to this success is that convolutional networks impose strong
prior assumptions about natural images. A surprising experiment that highlights this architectural bias towards natural images is that one can remove noise and corruptions from a natural image without using any training data, by simply fitting (via gradient descent) a randomly initialized, over-parameterized convolutional generator to the single corrupted image. While this over-parameterized network can fit the corrupted image perfectly, surprisingly after a few iterations of gradient descent one obtains the uncorrupted image. This intriguing phenomena
enables state-of-the-art CNN-based denoising and regularization of linear inverse problems such as compressive sensing. In this paper we take a step towards demystifying this experimental phenomena by attributing this effect to particular architectural choices of convolutional networks, namely convolutions with fixed interpolating filters. We then formally characterize the dynamics of fitting a two layer convolutional generator to a noisy signal and prove that earlystopped gradient descent denoises/regularizes. This results relies on showing that convolutional generators fit the structured part of an image significantly faster than the corrupted portion
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Finding the Needle in the Haystack with Convolutions: on the benefits of architectural bias
Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional Neural Networks (CNNs) are known to perform much better than Fully-Connected Networks (FCNs) on spatially structured data: the architectural structure of CNNs benefits from prior knowledge on the features of the data, for instance their translation invariance. The aim of this work is to understand this fact through the lens of dynamics in the loss landscape. We introduce a method that maps a CNN to its equivalent FCN (denoted as eFCN). Such an embedding enables the comparison of CNN and FCN training dynamics directly in the FCN space. We use this method to test a new training protocol, which consists in training a CNN, embedding it to FCN space at a certain relax time'', then resuming the training in FCN space. We observe that for all relax times, the deviation from the CNN subspace is small, and the final performance reached by the eFCN is higher than that reachable by a standard FCN of same architecture. More surprisingly, for some intermediate relax times, the eFCN outperforms the CNN it stemmed, by combining the prior information of the CNN and the expressivity of the FCN in a complementary way. The practical interest of our protocol is limited by the very large size of the highly sparse eFCN. However, it offers interesting insights into the persistence of architectural bias under stochastic gradient dynamics. It shows the existence of some rare basins in the FCN loss landscape associated with very good generalization. These can only be accessed thanks to the CNN prior, which helps navigate the landscape during the early stages of optimization.
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- NSF-PAR ID:
- 10159684
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Convolutional Neural Networks (CNNs) have emerged as highly successful tools for image generation, recovery, and restoration. A major contributing factor to this success is that convolutional networks impose strong prior assumptions about natural images. A surprising experiment that highlights this architectural bias towards natural images is that one can remove noise and corruptions from a natural image without using any training data, by simply fitting (via gradient descent) a randomly initialized, over-parameterized convolutional generator to the corrupted image. While this over-parameterized network can fit the corrupted image perfectly, surprisingly after a few iterations of gradient descent it generates an almost uncorrupted image. This intriguing phenomenon enables state-of-the-art CNN-based denoising and regularization of other inverse problems. In this paper, we attribute this effect to a particular architectural choice of convolutional networks, namely convolutions with fixed interpolating filters. We then formally characterize the dynamics of fitting a two-layer convolutional generator to a noisy signal and prove that early-stopped gradient descent denoises/regularizes. Our proof relies on showing that convolutional generators fit the structured part of an image significantly faster than the corrupted portion.more » « less
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Flooding is one of the leading threats of natural disasters to human life and property, especially in densely populated urban areas. Rapid and precise extraction of the flooded areas is key to supporting emergency-response planning and providing damage assessment in both spatial and temporal measurements. Unmanned Aerial Vehicles (UAV) technology has recently been recognized as an efficient photogrammetry data acquisition platform to quickly deliver high-resolution imagery because of its cost-effectiveness, ability to fly at lower altitudes, and ability to enter a hazardous area. Different image classification methods including SVM (Support Vector Machine) have been used for flood extent mapping. In recent years, there has been a significant improvement in remote sensing image classification using Convolutional Neural Networks (CNNs). CNNs have demonstrated excellent performance on various tasks including image classification, feature extraction, and segmentation. CNNs can learn features automatically from large datasets through the organization of multi-layers of neurons and have the ability to implement nonlinear decision functions. This study investigates the potential of CNN approaches to extract flooded areas from UAV imagery. A VGG-based fully convolutional network (FCN-16s) was used in this research. The model was fine-tuned and a k-fold cross-validation was applied to estimate the performance of the model on the new UAV imagery dataset. This approach allowed FCN-16s to be trained on the datasets that contained only one hundred training samples, and resulted in a highly accurate classification. Confusion matrix was calculated to estimate the accuracy of the proposed method. The image segmentation results obtained from FCN-16s were compared from the results obtained from FCN-8s, FCN-32s and SVMs. Experimental results showed that the FCNs could extract flooded areas precisely from UAV images compared to the traditional classifiers such as SVMs. The classification accuracy achieved by FCN-16s, FCN-8s, FCN-32s, and SVM for the water class was 97.52%, 97.8%, 94.20% and 89%, respectively.more » « less
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null (Ed.)Abstract—The state-of-the-art branch predictor, TAGE, re- mains inefficient at identifying correlated branches deep in a noisy global branch history. We argue this inefficiency is a fundamental limitation of runtime branch prediction and not a coincidental artifact due to the design of TAGE. To further improve branch prediction, we need to relax the constraint of runtime only training and adopt more sophisticated prediction mechanisms. To this end, Tarsa et al. proposed using convo- lutional neural networks (CNNs) that are trained at compile- time to accurately predict branches that TAGE cannot. Given enough profiling coverage, CNNs learn input-independent branch correlations that can accurately predict branches when running a program with unseen inputs. We build on their work and introduce BranchNet, a CNN with a practical on-chip inference engine tailored to the needs of branch prediction. At runtime, BranchNet predicts a few hard-to-predict branches, while TAGE- SC-L predicts the remaining branches. This hybrid approach reduces the MPKI of SPEC2017 Integer benchmarks by 7.6% (and up to 15.7%) when compared to a very large (impractical) MTAGE-SC baseline, demonstrating a fundamental advantage in the prediction capabilities of BranchNet compared to TAGE- like predictors. We also propose a practical resource-constrained variant of BranchNet that improves the MPKI by 9.6% (and up to 17.7%) compared to a 64KB TAGE-SC-L without increasing the prediction latency.more » « less
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