We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visual-izations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes in model architecture (and its associate inductive bias) cause visible changes in decision boundaries, while multiple runs with the same architecture yield results with strong similarities, especially in the case of wide architectures. We also use decision boundary methods to visualize double descent phenomena. We see that decision boundary reproducibility depends strongly on model width. Near the threshold of interpolation, neural network decision bound-aries become fragmented into many small decision regions, and these regions are non-reproducible. Meanwhile, very narrows and very wide networks have high levels of re-producibility in their decision boundaries with relatively few decision regions. We discuss how our observations re-late to the theory of double descent phenomena in convex models. Code is available at https://github.com/somepago/dbViz.

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.

In this work we propose a method for optimizing the lossy compression for a network of diverse reconstruction systems. We focus on adapting a standard image compression method to a set of candidate displays, presenting the decompressed signals to viewers. Each display is modeled as a linear operator applied after decompression, and its probability to serve a network user. We formulate a complicated operational rate-distortion optimization trading-off the network's expected mean-squared reconstruction error and the compression bit-cost. Using the alternating direction method of multipliers (ADMM) we develop an iterative procedure where the network structure is separated from the compression method, enabling the reliance on standard compression techniques. We present experimental results showing our method to be the best approach for adjusting high bit-rate image compression (using the state-of-the-art HEVC standard) to a set of displays modeled as blur degradations.

Many information systems employ lossy compression as a crucial intermediate stage among other processing components. While the important distortion is defined by the system's input and output signals, the compression usually ignores the system structure, therefore, leading to an overall suboptimal rate-distortion performance. In this paper we propose a compression methodology for an operational rate-distortion optimization considering a known system layout, modeled using linear operators and noise. Using the alternating direction method of multipliers (ADMM) technique, we show that the design of the new globally-optimized compression reduces to a standard compression of a “system adjusted” signal. Essentially, the proposed framework leverages standard compression techniques to address practical settings of the remote source coding problem. We further explain the main ideas of our method by theoretically studying the case of a cyclo-stationary Gaussian signal. We present experimental results for coding of one-dimensional signals and for video compression using the HEVC standard, showing significant gains by the adjustment to an acquisition-rendering system.

In imaging systems, following acquisition, an image/ video is transmitted or stored and eventually presented to human observers using different and often imperfect display devices. While the resulting quality of the output image may severely be affected by the display, this degradation is usually ignored in the preceding compression. In this paper we model the sub-optimality of the display device as a known degradation operator applied on the decompressed image/video. We assume the use of a standard compression path, and augment it with a suitable pre-processing procedure, providing a compressed signal intended to compensate the degradation without any post-filtering. Our approach originates from an intricate rate-distortion problem, optimizing the modifications to the input image/video for reaching best end-to-end performance. We address this seemingly computationally intractable problem using the alternating direction method of multipliers (ADMM) approach, leading to a procedure in which a standard compression technique is iteratively applied. We demonstrate the proposed method for adjusting HEVC image/video compression to compensate post-decompression visual effects due to a common type of displays. Particularly, we use our method to reduce motion-blur perceived while viewing video on LCD devices. The experiments establish our method as a leading approach for preprocessing high bit-rate compression to counterbalance a postdecompression degradation.

In this paper we propose a method for solving various imaging inverse problems via complexity regularization that leverages existing image compression techniques. Lossy compression has already been proposed in the past for Gaussian denoising - the simplest inverse problem. However, extending this approach to more complicated inverse problems (e.g., deblurring, inpainting, etc.) seemed to result in intractable optimization tasks. In this work we address this difficulty by decomposing the complicated optimization problem via the Half Quadratic Splitting approach, resulting in a sequential solution of a simpler l2-regularized inverse problem followed by a rate-distortion optimization, replaced by an efficient compression technique. In addition, we suggest an improved complexity regularizer that quantifies the average block-complexity in the restored signal, which in turn, extends our algorithm to rely on averaging multiple decompressed images obtained from compression of shifted images. We demonstrate the proposed scheme for inpainting of corrupted images, using leading image compression techniques such as JPEG2000 and HEVC.

In this paper, we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising algorithms. We rely on the recently proposed Plug-and-Play Prior framework, suggesting the solution of general inverse problems via alternating direction method of multipliers, leading to a sequence of Gaussian denoising steps. A key feature in our scheme is a linearization of the compression-decompression process, so as to get a formulation that can be optimized. In addition, we supply a thorough analysis of this linear approximation for several basic compression procedures. The proposed method is suitable for diverse compression techniques that rely on transform coding. In particular, we demonstrate impressive gains in image quality for several leading compression methods-JPEG, JPEG2000, and HEVC.