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1. Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation

   Heckel, Reinhard ; Soltanolkotabi, Mahdi ( January 2020 , International Conference on Machine Learning)

   Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denois- ing and compressive sensing with excellent results by simply fitting a neural network model to measurements from a single image or signal without the need for any additional training data. For some applications, this critically requires additional regularization in the form of early stopping the optimization. For signal recovery from a few measurements, however, un-trained convolutional networks have an intriguing self-regularizing property: Even though the network can perfectly fit any image, the network recovers a natural image from few measurements when trained with gradient descent until convergence. In this paper, we provide numerical evidence for this property and study it theoretically. We show that—without any further regularization—an un-trained convolutional neural network can approximately reconstruct signals and images that are sufficiently structured, from a near minimal number of random measurements 

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2. Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators

   Heckel, Reinhard ; Soltanolkotabi, Mahdi ( May 2020 , International Conference on Learning Representations)

   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. 

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3. Denoising and Regularization via Exploiting the Structural Bias of Convolutional Generators. R. Heckel and M. Soltanolkotabi

   Heckel, Reinhard ; Soltanolkotabi, Mahdi ( May 2020 , International Conference on Learning Representations)

   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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4. Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks

   Heckel, R. ; Hand., P. ( April 2019 , International Conference on Learning Representations)

   Deep neural networks, in particular convolutional neural networks, have become highly effective tools for compressing images and solving inverse problems including denoising, inpainting, and reconstruction from few and noisy measurements. This success can be attributed in part to their ability to represent and generate natural images well. Contrary to classical tools such as wavelets, image-generating deep neural networks have a large number of parameters---typically a multiple of their output dimension---and need to be trained on large datasets. In this paper, we propose an untrained simple image model, called the deep decoder, which is a deep neural network that can generate natural images from very few weight parameters. The deep decoder has a simple architecture with no convolutions and fewer weight parameters than the output dimensionality. This underparameterization enables the deep decoder to compress images into a concise set of network weights, which we show is on par with wavelet-based thresholding. Further, underparameterization provides a barrier to overfitting, allowing the deep decoder to have state-of-the-art performance for denoising. The deep decoder is simple in the sense that each layer has an identical structure that consists of only one upsampling unit, pixel-wise linear combination of channels, ReLU activation, and channelwise normalization. This simplicity makes the network amenable to theoretical analysis, and it sheds light on the aspects of neural networks that enable them to form effective signal representations. 

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5. Self-supervised Feature Learning by Cross-modality and Cross-view Correspondences

   Jing, L ; Zhang, L ; Tian, Y ( June 2021 , The 4th Multimodal Learning and Applications (MULA) Workshop in conjunction with CVPR 2021)

   null (Ed.)

   The success of supervised learning requires large-scale ground truth labels which are very expensive, time- consuming, or may need special skills to annotate. To address this issue, many self- or un-supervised methods are developed. Unlike most existing self-supervised methods to learn only 2D image features or only 3D point cloud features, this paper presents a novel and effective self-supervised learning approach to jointly learn both 2D image features and 3D point cloud features by exploiting cross-modality and cross-view correspondences without using any human annotated labels. Specifically, 2D image features of rendered images from different views are extracted by a 2D convolutional neural network, and 3D point cloud features are extracted by a graph convolution neural network. Two types of features are fed into a two-layer fully connected neural network to estimate the cross-modality correspondence. The three networks are jointly trained (i.e. cross-modality) by verifying whether two sampled data of different modalities belong to the same object, meanwhile, the 2D convolutional neural network is additionally optimized through minimizing intra-object distance while maximizing inter-object distance of rendered images in different views (i.e. cross-view). The effectiveness of the learned 2D and 3D features is evaluated by transferring them on five different tasks including multi-view 2D shape recognition, 3D shape recognition, multi-view 2D shape retrieval, 3D shape retrieval, and 3D part-segmentation. Extensive evaluations on all the five different tasks across different datasets demonstrate strong generalization and effectiveness of the learned 2D and 3D features by the proposed self-supervised method. 

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