Adversarial purification for no-reference image-quality metrics: applicability study and new methods
Recently, the area of adversarial attacks on image quality metrics has begun to be explored, whereas the area of defences remains under-researched. In this study, we aim to cover that case and check the transferability of adversarial purification defences from image classifiers to IQA methods. In this paper, we apply several widespread attacks on IQA models and examine the success of the defences against them. The purification methodologies covered different preprocessing techniques, including geometrical transformations, compression, denoising, and modern neural network-based methods. Also, we address the challenge of assessing the efficacy of a defensive methodology by proposing ways to estimate output visual quality and the success of neutralizing attacks. Defences were tested against attack on three IQA metrics -- Linearity, MetaIQA and SPAQ. The code for attacks and defences is available at: (link is hidden for a blind review).
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Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares problems when two precisions are used and review their theoretical guarantees, known shortcomings and when the method can be expected to recognize that the correct solution has been found, and extend uniform precision analysis for an IR approach based on the semi-normal equations to the two-precision case. We focus on the situation where it is desired to refine the solution to the working precision level. It is shown that the IR methods exhibit different sensitivities to the conditioning of the problem and the size of the least-squares residual, which should be taken into account when choosing the IR approach. We also discuss a new approach that is based on solving multiple least-squares problems.
Regression methods dominate the practice of biostatistical analysis, but biostatistical training emphasises the details of regression models and methods ahead of the purposes for which such modelling might be useful. More broadly, statistics is widely understood to provide a body of techniques for "modelling data", underpinned by what we describe as the "true model myth": that the task of the statistician/data analyst is to build a model that closely approximates the true data generating process. By way of our own historical examples and a brief review of mainstream clinical research journals, we describe how this perspective has led to a range of problems in the application of regression methods, including misguided "adjustment" for covariates, misinterpretation of regression coefficients and the widespread fitting of regression models without a clear purpose. We then outline a new approach to the teaching and application of biostatistical methods, which situates them within a framework that first requires clear definition of the substantive research question at hand within one of three categories: descriptive, predictive, or causal. Within this approach, the simple univariable regression model may be introduced as a tool for description, while the development and application of multivariable regression models as well as other advanced biostatistical methods should proceed differently according to the type of question. Regression methods will no doubt remain central to statistical practice as they provide a powerful tool for representing variation in a response or outcome variable as a function of "input" variables, but their conceptualisation and usage should follow from the purpose at hand.
The aim of the present work is to design, analyze theoretically, and test numerically, a generalized Dryja-Smith-Widlund (GDSW) preconditioner for composite Discontinuous Galerkin discretizations of multicompartment parabolic reaction-diffusion equations, where the solution can exhibit natural discontinuities across the domain. We prove that the resulting preconditioned operator for the solution of the discrete system arising at each time step converges with a scalable and quasi-optimal upper bound for the condition number. The GDSW preconditioner is then applied to the EMI (Extracellular - Membrane - Intracellular) reaction-diffusion system, recently proposed to model microscopically the spatiotemporal evolution of cardiac bioelectrical potentials. Numerical tests validate the scalability and quasi-optimality of the EMI-GDSW preconditioner, and investigate its robustness with respect to the time step size as well as jumps in the diffusion coefficients.
Advanced artificial intelligence (AI) systems with access to millions of research papers could inspire new research ideas that may not be conceived by humans alone. However, how interesting are these AI-generated ideas, and how can we improve their quality? Here, we introduce SciMuse, a system that uses an evolving knowledge graph built from more than 58 million scientific papers to generate personalized research ideas via an interface to GPT-4. We conducted a large-scale human evaluation with over 100 research group leaders from the Max Planck Society, who ranked more than 4,000 personalized research ideas based on their level of interest. This evaluation allows us to understand the relationships between scientific interest and the core properties of the knowledge graph. We find that data-efficient machine learning can predict research interest with high precision, allowing us to optimize the interest-level of generated research ideas. This work represents a step towards an artificial scientific muse that could catalyze unforeseen collaborations and suggest interesting avenues for scientists.
We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a single 2-dimensional visualization. Its algorithm combines the well-known multidimensional scaling (MDS) tool with the $k$-medoids data clustering technique, and enables hierarchical embedding, sparsification and estimation of 2-dimensional coordinates for additional points. While cl-MDS is a generally applicable tool, we also include specific recipes for atomic structure applications. We apply this method to non-linear data of increasing complexity where different layers of locality are relevant, showing a clear improvement in their retrieval and visualization quality.
Partial multi-task learning where training examples are annotated for one of the target tasks is a promising idea in remote sensing as it allows combining datasets annotated for different tasks and predicting more tasks with fewer network parameters. The na\"ive approach to partial multi-task learning is sub-optimal due to the lack of all-task annotations for learning joint representations. This paper proposes using knowledge distillation to replace the need of ground truths for the alternate task and enhance the performance of such approach. Experiments conducted on the public ISPRS 2D Semantic Labeling Contest dataset show the effectiveness of the proposed idea on partial multi-task learning for semantic tasks including object detection and semantic segmentation in aerial images.
Bipartite graphs are a prevalent modeling tool for real-world networks, capturing interactions between vertices of two different types. Within this framework, bicliques emerge as crucial structures when studying dense subgraphs: they are sets of vertices such that all vertices of the first type interact with all vertices of the second type. Therefore, they allow identifying groups of closely related vertices of the network, such as individuals with similar interests or webpages with similar contents. This article introduces a new algorithm designed for the exhaustive enumeration of maximal bicliques within a bipartite graph. This algorithm, called BBK for Bipartite Bron-Kerbosch, is a new extension to the bipartite case of the Bron-Kerbosch algorithm, which enumerates the maximal cliques in standard (non-bipartite) graphs. It is faster than the state-of-the-art algorithms and allows the enumeration on massive bipartite graphs that are not manageable with existing implementations. We analyze it theoretically to establish two complexity formulas: one as a function of the input and one as a function of the output characteristics of the algorithm. We also provide an open-access implementation of BBK in C++, which we use to experiment and validate its efficiency on massive real-world datasets and show that its execution time is shorter in practice than state-of-the art algorithms. These experiments also show that the order in which the vertices are processed, as well as the choice of one of the two types of vertices on which to initiate the enumeration have an impact on the computation time.
Analyzing the behavior of ReLU neural networks often hinges on understanding the relationships between their parameters and the functions they implement. This paper proves a new bound on function distances in terms of the so-called path-metrics of the parameters. Since this bound is intrinsically invariant with respect to the rescaling symmetries of the networks, it sharpens previously known bounds. It is also, to the best of our knowledge, the first bound of its kind that is broadly applicable to modern networks such as ResNets, VGGs, U-nets, and many more. In contexts such as network pruning and quantization, the proposed path-metrics can be efficiently computed using only two forward passes. Besides its intrinsic theoretical interest, the bound yields not only novel theoretical generalization bounds, but also a promising proof of concept for rescaling-invariant pruning.
Since the weak convergence for stochastic processes does not account for the growth of information over time which is represented by the underlying filtration, a slightly erroneous stochastic model in weak topology may cause huge loss in multi-periods decision making problems. To address such discontinuities Aldous introduced the extended weak convergence, which can fully characterise all essential properties, including the filtration, of stochastic processes; however was considered to be hard to find efficient numerical implementations. In this paper, we introduce a novel metric called High Rank PCF Distance (HRPCFD) for extended weak convergence based on the high rank path development method from rough path theory, which also defines the characteristic function for measure-valued processes. We then show that such HRPCFD admits many favourable analytic properties which allows us to design an efficient algorithm for training HRPCFD from data and construct the HRPCF-GAN by using HRPCFD as the discriminator for conditional time series generation. Our numerical experiments on both hypothesis testing and generative modelling validate the out-performance of our approach compared with several state-of-the-art methods, highlighting its potential in broad applications of synthetic time series generation and in addressing classic financial and economic challenges, such as optimal stopping or utility maximisation problems.
When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.
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