Ismail R. Alkhouri

Chaoyan Huang, Cheng-Han Huang, Ismail R. Alkhouri et al.

Recently, Deep Image Prior (DIP) has demonstrated strong capabilities for solving inverse imaging problems (IIPs) by optimizing a randomly initialized convolutional neural network in a training-data-free regime. However, DIP suffers from overfitting to noisy measurements due to network over-parameterization, making early stopping (ES) essential. The most successful ES method tracks fluctuations in the running variance of the network output to detect overfitting. However, in many applications, these fluctuations may appear prematurely, leading to unstable reconstructions. In this paper, we first show that nearly optimal DIP early stopping can be achieved when two independent noisy copies of the degraded image are available. Motivated by this observation, and since obtaining two fully independent copies is infeasible, we propose an overfitting detection framework based on constructing pseudo self-referenced images, resulting in three IIP-specific algorithms. Our approach is further supported by theoretical results on single-reference validation, pseudo-validation estimation, and the impact of shared noise. Across different IIPs, ranging from natural image restoration to medical image reconstruction, and under varying noise levels and noise types, our methods consistently outperform existing DIP early stopping approaches, all without requiring an accurate estimate of the noise level.

Ismail R. Alkhouri, George K. Atia, Alvaro Velasquez

The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. In this paper, we propose a radically different approach in that no data is required for training the neural networks that produce the solution. In particular, we reduce the combinatorial optimization problem to a neural network and employ a dataless training scheme to refine the parameters of the network such that those parameters yield the structure of interest. We consider the combinatorial optimization problems of finding maximum independent sets and maximum cliques in a graph. In principle, since these problems belong to the NP-hard complexity class, our proposed approach can be used to solve any other NP-hard problem. Additionally, we propose a universal graph reduction procedure to handle large scale graphs. The reduction exploits community detection for graph partitioning and is applicable to any graph type and/or density. Experimental evaluation on both synthetic graphs and real-world benchmarks demonstrates that our method performs on par with or outperforms state-of-the-art heuristic, reinforcement learning, and machine learning based methods without requiring any data.

Alvaro Velasquez, Susmit Jha, Ismail R. Alkhouri

This paper surveys studies on the use of neural networks for optimization in the training-data-free setting. Specifically, we examine the dataless application of neural network architectures in optimization by re-parameterizing problems using fully connected (or MLP), convolutional, graph, and quadratic neural networks. Although MLPs have been used to solve linear programs a few decades ago, this approach has recently gained increasing attention due to its promising results across diverse applications, including those based on combinatorial optimization, inverse problems, and partial differential equations. The motivation for this setting stems from two key (possibly over-lapping) factors: (i) data-driven learning approaches are still underdeveloped and have yet to demonstrate strong results, as seen in combinatorial optimization, and (ii) the availability of training data is inherently limited, such as in medical image reconstruction and other scientific applications. In this paper, we define the dataless setting and categorize it into two variants based on how a problem instance -- defined by a single datum -- is encoded onto the neural network: (i) architecture-agnostic methods and (ii) architecture-specific methods. Additionally, we discuss similarities and clarify distinctions between the dataless neural network (dNN) settings and related concepts such as zero-shot learning, one-shot learning, lifting in optimization, and over-parameterization.

Xitong Zhang, Ismail R. Alkhouri, Rongrong Wang

Deep Neural Networks (DNNs) have achieved remarkable success in addressing many previously unsolvable tasks. However, the storage and computational requirements associated with DNNs pose a challenge for deploying these trained models on resource-limited devices. Therefore, a plethora of compression and pruning techniques have been proposed in recent years. Low-rank decomposition techniques are among the approaches most utilized to address this problem. Compared to post-training compression, compression-promoted training is still under-explored. In this paper, we present a theoretically-justified technique termed Low-Rank Induced Training (LoRITa), that promotes low-rankness through the composition of linear layers and compresses by using singular value truncation. This is achieved without the need to change the structure at inference time or require constrained and/or additional optimization, other than the standard weight decay regularization. Moreover, LoRITa eliminates the need to (i) initialize with pre-trained models, (ii) specify rank selection prior to training, and (iii) compute SVD in each iteration. Our experimental results (i) demonstrate the effectiveness of our approach using MNIST on Fully Connected Networks, CIFAR10 on Vision Transformers, and CIFAR10/100 and ImageNet on Convolutional Neural Networks, and (ii) illustrate that we achieve either competitive or state-of-the-art results when compared to leading structured pruning and low-rank training methods in terms of FLOPs and parameters drop. Our code is available at \url{https://github.com/XitongSystem/LoRITa/tree/main}.

Xiang Li, Soo Min Kwon, Shijun Liang et al.

Diffusion models have recently gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration problems, many existing techniques achieve data consistency by incorporating additional likelihood gradient steps into the reverse sampling process of diffusion models. However, the additional gradient steps pose a challenge for real-world practical applications as they incur a large computational overhead, thereby increasing inference time. They also present additional difficulties when using accelerated diffusion model samplers, as the number of data consistency steps is limited by the number of reverse sampling steps. In this work, we propose a novel diffusion-based image restoration solver that addresses these issues by decoupling the reverse process from the data consistency steps. Our method involves alternating between a reconstruction phase to maintain data consistency and a refinement phase that enforces the prior via diffusion purification. Our approach demonstrates versatility, making it highly adaptable for efficient problem-solving in latent space. Additionally, it reduces the necessity for numerous sampling steps through the integration of consistency models. The efficacy of our approach is validated through comprehensive experiments across various image restoration tasks, including image denoising, deblurring, inpainting, and super-resolution.

Ismail R. Alkhouri, Alvaro Velasquez, George K. Atia

The design of additive imperceptible perturbations to the inputs of deep classifiers to maximize their misclassification rates is a central focus of adversarial machine learning. An alternative approach is to synthesize adversarial examples from scratch using GAN-like structures, albeit with the use of large amounts of training data. By contrast, this paper considers one-shot synthesis of adversarial examples; the inputs are synthesized from scratch to induce arbitrary soft predictions at the output of pre-trained models, while simultaneously maintaining high similarity to specified inputs. To this end, we present a problem that encodes objectives on the distance between the desired and output distributions of the trained model and the similarity between such inputs and the synthesized examples. We prove that the formulated problem is NP-complete. Then, we advance a generative approach to the solution in which the adversarial examples are obtained as the output of a generative network whose parameters are iteratively updated by optimizing surrogate loss functions for the dual-objective. We demonstrate the generality and versatility of the framework and approach proposed through applications to the design of targeted adversarial attacks, generation of decision boundary samples, and synthesis of low confidence classification inputs. The approach is further extended to an ensemble of models with different soft output specifications. The experimental results verify that the targeted and confidence reduction attack methods developed perform on par with state-of-the-art algorithms.