Diffusion models (DMs) are a class of generative models that allow sampling from a distribution learned over a training set. When applied to solving inverse imaging problems (IPs), the reverse sampling steps of DMs are typically modified to approximately sample from a measurement-conditioned distribution in the image space. However, these modifications may be unsuitable for certain settings (such as in the presence of measurement noise) and non-linear tasks, as they often struggle to correct errors from earlier sampling steps and generally require a large number of optimization and/or sampling steps. To address these challenges, we state three conditions for achieving measurement-consistent diffusion trajectories. Building on these conditions, we propose a new optimization-based sampling method that not only enforces the standard data manifold measurement consistency and forward diffusion consistency, as seen in previous studies, but also incorporates backward diffusion consistency that maintains a diffusion trajectory by optimizing over the input of the pre-trained model at every sampling step. By enforcing these conditions, either implicitly or explicitly, our sampler requires significantly fewer reverse steps. Therefore, we refer to our accelerated method as Step-wise Triple-Consistent Sampling (SITCOM). Compared to existing state-of-the-art baseline methods, under different levels of measurement noise, our extensive experiments across five linear and three non-linear image restoration tasks demonstrate that SITCOM achieves competitive or superior results in terms of standard image similarity metrics while requiring a significantly reduced run-time across all considered tasks.

Combinatorial Optimization (CO) plays a crucial role in addressing various significant problems, among them the challenging Maximum Independent Set (MIS) problem. In light of recent advancements in deep learning methods, efforts have been directed towards leveraging data-driven learning approaches, typically rooted in supervised learning and reinforcement learning, to tackle the NP-hard MIS problem. However, these approaches rely on labeled datasets, exhibit weak generalization, and often depend on problem-specific heuristics. Recently, ReLU-based dataless neural networks were introduced to address combinatorial optimization problems. This paper introduces a novel dataless quadratic neural network formulation, featuring a continuous quadratic relaxation for the MIS problem. Notably, our method eliminates the need for training data by treating the given MIS instance as a trainable entity. More specifically, the graph structure and constraints of the MIS instance are used to define the structure and parameters of the neural network such that training it on a fixed input provides a solution to the problem, thereby setting it apart from traditional supervised or reinforcement learning approaches. By employing a gradient-based optimization algorithm like ADAM and leveraging an efficient off-the-shelf GPU parallel implementation, our straightforward yet effective approach demonstrates competitive or superior performance compared to state-of-the-art learning-based methods. Another significant advantage of our approach is that, unlike exact and heuristic solvers, the running time of our method scales only with the number of nodes in the graph, not the number of edges.

As the popularity of deep learning (DL) in the field of magnetic resonance imaging (MRI) continues to rise, recent research has indicated that DL-based MRI reconstruction models might be excessively sensitive to minor input disturbances, including worst-case additive perturbations. This sensitivity often leads to unstable, aliased images. This raises the question of how to devise DL techniques for MRI reconstruction that can be robust to train-test variations. To address this problem, we propose a novel image reconstruction framework, termed Smoothed Unrolling (SMUG), which advances a deep unrolling-based MRI reconstruction model using a randomized smoothing (RS)-based robust learning approach. RS, which improves the tolerance of a model against input noises, has been widely used in the design of adversarial defense approaches for image classification tasks. Yet, we find that the conventional design that applies RS to the entire DL-based MRI model is ineffective. In this paper, we show that SMUG and its variants address the above issue by customizing the RS process based on the unrolling architecture of a DL-based MRI reconstruction model. Compared to the vanilla RS approach, we show that SMUG improves the robustness of MRI reconstruction with respect to a diverse set of instability sources, including worst-case and random noise perturbations to input measurements, varying measurement sampling rates, and different numbers of unrolling steps. Furthermore, we theoretically analyze the robustness of our method in the presence of perturbations.

Protein folding neural networks (PFNNs) such as AlphaFold predict remarkably accurate structures of proteins compared to other approaches. However, the robustness of such networks has heretofore not been explored. This is particularly relevant given the broad social implications of such technologies and the fact that biologically small perturbations in the protein sequence do not generally lead to drastic changes in the protein structure. In this paper, we demonstrate that AlphaFold does not exhibit such robustness despite its high accuracy. This raises the challenge of detecting and quantifying the extent to which these predicted protein structures can be trusted. To measure the robustness of the predicted structures, we utilize (i) the root-mean-square deviation (RMSD) and (ii) the Global Distance Test (GDT) similarity measure between the predicted structure of the original sequence and the structure of its adversarially perturbed version. We prove that the problem of minimally perturbing protein sequences to fool protein folding neural networks is NP-complete. Based on the well-established BLOSUM62 sequence alignment scoring matrix, we generate adversarial protein sequences and show that the RMSD between the predicted protein structure and the structure of the original sequence are very large when the adversarial changes are bounded by (i) 20 units in the BLOSUM62 distance, and (ii) five residues (out of hundreds or thousands of residues) in the given protein sequence. In our experimental evaluation, we consider 111 COVID-19 proteins in the Universal Protein resource (UniProt), a central resource for protein data managed by the European Bioinformatics Institute, Swiss Institute of Bioinformatics, and the US Protein Information Resource. These result in an overall GDT similarity test score average of around 34%, demonstrating a substantial drop in the performance of AlphaFold.

Given a Markov decision process (MDP) and a linear-time ($\omega$-regular or LTL) specification, the controller synthesis problem aims to compute the optimal policy that satisfies the specification. More recently, problems that reason over the asymptotic behavior of systems have been proposed through the lens of steady-state planning. This entails finding a control policy for an MDP such that the Markov chain induced by the solution policy satisfies a given set of constraints on its steady-state distribution. This paper studies a generalization of the controller synthesis problem for a linear-time specification under steady-state constraints on the asymptotic behavior. We present an algorithm to find a deterministic policy satisfying $\omega$-regular and steady-state constraints by characterizing the solutions as an integer linear program, and experimentally evaluate our approach.

The planning domain has experienced increased interest in the formal synthesis of decision-making policies. This formal synthesis typically entails finding a policy which satisfies formal specifications in the form of some well-defined logic, such as Linear Temporal Logic (LTL) or Computation Tree Logic (CTL), among others. While such logics are very powerful and expressive in their capacity to capture desirable agent behavior, their value is limited when deriving decision-making policies which satisfy certain types of asymptotic behavior. In particular, we are interested in specifying constraints on the steady-state behavior of an agent, which captures the proportion of time an agent spends in each state as it interacts for an indefinite period of time with its environment. This is sometimes called the average or expected behavior of the agent. In this paper, we explore the steady-state planning problem of deriving a decision-making policy for an agent such that constraints on its steady-state behavior are satisfied. A linear programming solution for the general case of multichain Markov Decision Processes (MDPs) is proposed and we prove that optimal solutions to the proposed programs yield stationary policies with rigorous guarantees of behavior.