We study asymptotic statistical inference in the space of bounded functions endowed with the supremums norm over an arbitrary metric space $S$ using a novel concept: Simultaneous COnfidence Region of Excursion (SCoRE) Sets. They simultaneously quantify the uncertainty of several lower and upper excursion sets of a target function. We investigate their connection to multiple hypothesis tests controlling the familywise error rate in the strong sense and show that they grant a unifying perspective on several statistical inference tools such as simultaneous confidence bands, quantification of uncertainties in level set estimation, for example, CoPE sets, and multiple hypothesis testing over $S$, for example, finding relevant differences or regions of equivalence within $S$. In particular, our abstract setting allows us to refine and reduce the assumptions in recent articles on CoPE sets and relevance and equivalence testing using the supremums norm.
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Binary similarity involves determining whether two binary programs exhibit similar functionality, often originating from the same source code. In this work, we propose VexIR2Vec, an approach for binary similarity using VEX-IR, an architecture-neutral Intermediate Representation (IR). We extract the embeddings from sequences of basic blocks, termed peepholes, derived by random walks on the control-flow graph. The peepholes are normalized using transformations inspired by compiler optimizations. The VEX-IR Normalization Engine mitigates, with these transformations, the architectural and compiler-induced variations in binaries while exposing semantic similarities. We then learn the vocabulary of representations at the entity level of the IR using the knowledge graph embedding techniques in an unsupervised manner. This vocabulary is used to derive function embeddings for similarity assessment using VexNet, a feed-forward Siamese network designed to position similar functions closely and separate dissimilar ones in an n-dimensional space. This approach is amenable for both diffing and searching tasks, ensuring robustness against Out-Of-Vocabulary (OOV) issues. We evaluate VexIR2Vec on a dataset comprising 2.7M functions and 15.5K binaries from 7 projects compiled across 12 compilers targeting x86 and ARM architectures. In diffing experiments, VexIR2Vec outperforms the nearest baselines by $40\%$, $18\%$, $21\%$, and $60\%$ in cross-optimization, cross-compilation, cross-architecture, and obfuscation settings, respectively. In the searching experiment, VexIR2Vec achieves a mean average precision of $0.76$, outperforming the nearest baseline by $46\%$. Our framework is highly scalable and is built as a lightweight, multi-threaded, parallel library using only open-source tools. VexIR2Vec is $3.1$-$3.5 \times$ faster than the closest baselines and orders-of-magnitude faster than other tools.
We address the challenge of online convex optimization where the objective function's gradient exhibits sparsity, indicating that only a small number of dimensions possess non-zero gradients. Our aim is to leverage this sparsity to obtain useful estimates of the objective function's gradient even when the only information available is a limited number of function samples. Our motivation stems from distributed queueing systems like microservices-based applications, characterized by request-response workloads. Here, each request type proceeds through a sequence of microservices to produce a response, and the resource allocation across the collection of microservices is controlled to balance end-to-end latency with resource costs. While the number of microservices is substantial, the latency function primarily reacts to resource changes in a few, rendering the gradient sparse. Our proposed method, CONGO (Compressive Online Gradient Optimization), combines simultaneous perturbation with compressive sensing to estimate gradients. We establish analytical bounds on the requisite number of compressive sensing samples per iteration to maintain bounded bias of gradient estimates, ensuring sub-linear regret. By exploiting sparsity, we reduce the samples required per iteration to match the gradient's sparsity, rather than the problem's original dimensionality. Numerical experiments and real-world microservices benchmarks demonstrate CONGO's superiority over multiple stochastic gradient descent approaches, as it quickly converges to performance comparable to policies pre-trained with workload awareness.
Shape abstraction is an important task for simplifying complex geometric structures while retaining essential features. Sweep surfaces, commonly found in human-made objects, aid in this process by effectively capturing and representing object geometry, thereby facilitating abstraction. In this paper, we introduce \papername, a novel approach to shape abstraction through sweep surfaces. We propose an effective parameterization for sweep surfaces, utilizing superellipses for profile representation and B-spline curves for the axis. This compact representation, requiring as few as 14 float numbers, facilitates intuitive and interactive editing while preserving shape details effectively. Additionally, by introducing a differentiable neural sweeper and an encoder-decoder architecture, we demonstrate the ability to predict sweep surface representations without supervision. We show the superiority of our model through several quantitative and qualitative experiments throughout the paper. Our code is available at //mingrui-zhao.github.io/SweepNet/
Human body parsing remains a challenging problem in natural scenes due to multi-instance and inter-part semantic confusions as well as occlusions. This paper proposes a novel approach to decomposing multiple human bodies into semantic part regions in unconstrained environments. Specifically we propose a convolutional neural network (CNN) architecture which comprises of novel semantic and contour attention mechanisms across feature hierarchy to resolve the semantic ambiguities and boundary localization issues related to semantic body parsing. We further propose to encode estimated pose as higher-level contextual information which is combined with local semantic cues in a novel graphical model in a principled manner. In this proposed model, the lower-level semantic cues can be recursively updated by propagating higher-level contextual information from estimated pose and vice versa across the graph, so as to alleviate erroneous pose information and pixel level predictions. We further propose an optimization technique to efficiently derive the solutions. Our proposed method achieves the state-of-art results on the challenging Pascal Person-Part dataset.
Flexible antenna arrays (FAAs), distinguished by their rotatable, bendable, and foldable properties, are extensively employed in flexible radio systems to achieve customized radiation patterns. This paper aims to illustrate that FAAs, capable of dynamically adjusting surface shapes, can enhance communication performances with both omni-directional and directional antenna patterns, in terms of multi-path channel power and channel angle Cram\'{e}r-Rao bounds. To this end, we develop a mathematical model that elucidates the impacts of the variations in antenna positions and orientations as the array transitions from a flat to a rotated, bent, and folded state, all contingent on the flexible degree-of-freedom. Moreover, since the array shape adjustment operates across the entire beamspace, especially with directional patterns, we discuss the sum-rate in the multi-sector base station that covers the $360^\circ$ communication area. Particularly, to thoroughly explore the multi-sector sum-rate, we propose separate flexible precoding (SFP), joint flexible precoding (JFP), and semi-joint flexible precoding (SJFP), respectively. In our numerical analysis comparing the optimized FAA to the fixed uniform planar array, we find that the bendable FAA achieves a remarkable $156\%$ sum-rate improvement compared to the fixed planar array in the case of JFP with the directional pattern. Furthermore, the rotatable FAA exhibits notably superior performance in SFP and SJFP cases with omni-directional patterns, with respective $35\%$ and $281\%$.
We present an algorithm and package, Redistributor, which forces a collection of scalar samples to follow a desired distribution. When given independent and identically distributed samples of some random variable $S$ and the continuous cumulative distribution function of some desired target $T$, it provably produces a consistent estimator of the transformation $R$ which satisfies $R(S)=T$ in distribution. As the distribution of $S$ or $T$ may be unknown, we also include algorithms for efficiently estimating these distributions from samples. This allows for various interesting use cases in image processing, where Redistributor serves as a remarkably simple and easy-to-use tool that is capable of producing visually appealing results. For color correction it outperforms other model-based methods and excels in achieving photorealistic style transfer, surpassing deep learning methods in content preservation. The package is implemented in Python and is optimized to efficiently handle large datasets, making it also suitable as a preprocessing step in machine learning. The source code is available at //github.com/paloha/redistributor.
We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the inverse PDE PINN solutions. Recently, the Bayesian PINN (BPINN) method was proposed, where the posterior distribution of the PINN parameters was formulated using the Bayes' theorem and sampled using approximate inference methods such as the Hamiltonian Monte Carlo (HMC) and variational inference (VI) methods. In this work, we demonstrate that HMC fails to converge for non-linear inverse PDE problems. As an alternative to HMC, we sample the distribution by solving the stochastic optimization problem obtained by randomizing the PINN loss function. The effectiveness of the rPINN method is tested for linear and non-linear Poisson equations, and the diffusion equation with a high-dimensional space-dependent diffusion coefficient. The rPINN method provides informative distributions for all considered problems. For the linear Poisson equation, HMC and rPINN produce similar distributions, but rPINN is on average 27 times faster than HMC. For the non-linear Poison and diffusion equations, the HMC method fails to converge because a single HMC chain cannot sample multiple modes of the posterior distribution of the PINN parameters in a reasonable amount of time.
Predicting the consensus structure of a set of aligned RNA homologs is a convenient method to find conserved structures in an RNA genome, which has many applications including viral diagnostics and therapeutics. However, the most commonly used tool for this task, RNAalifold, is prohibitively slow for long sequences, due to a cubic scaling with the sequence length, taking over a day on 400 SARS-CoV-2 and SARS-related genomes (~30,000nt). We present LinearAlifold, a much faster alternative that scales linearly with both the sequence length and the number of sequences, based on our work LinearFold that folds a single RNA in linear time. Our work is orders of magnitude faster than RNAalifold (0.7 hours on the above 400 genomes, or ~36$\times$ speedup) and achieves higher accuracies when compared to a database of known structures. More interestingly, LinearAlifold's prediction on SARS-CoV-2 correlates well with experimentally determined structures, substantially outperforming RNAalifold. Finally, LinearAlifold supports two energy models (Vienna and BL*) and four modes: minimum free energy (MFE), maximum expected accuracy (MEA), ThreshKnot, and stochastic sampling, each of which takes under an hour for hundreds of SARS-CoV variants. Our resource is at: //github.com/LinearFold/LinearAlifold (code) and //linearfold.org/linear-alifold (server).
This study explores the application of genetic algorithms in generating highly nonlinear substitution boxes (S-boxes) for symmetric key cryptography. We present a novel implementation that combines a genetic algorithm with the Walsh-Hadamard Spectrum (WHS) cost function to produce 8x8 S-boxes with a nonlinearity of 104. Our approach achieves performance parity with the best-known methods, requiring an average of 49,399 iterations with a 100% success rate. The study demonstrates significant improvements over earlier genetic algorithm implementations in this field, reducing iteration counts by orders of magnitude. By achieving equivalent performance through a different algorithmic approach, our work expands the toolkit available to cryptographers and highlights the potential of genetic methods in cryptographic primitive generation. The adaptability and parallelization potential of genetic algorithms suggest promising avenues for future research in S-box generation, potentially leading to more robust, efficient, and innovative cryptographic systems. Our findings contribute to the ongoing evolution of symmetric key cryptography, offering new perspectives on optimizing critical components of secure communication systems.
Iterative deblurring, notably the Richardson-Lucy algorithm with and without regularization, is analyzed in the context of nuclear and high-energy physics applications. In these applications, probability distributions may be discretized into a few bins, measurement statistics can be high, and instrument performance can be well understood. In such circumstances, it is essential to understand the deblurring first without any explicit noise considerations. We employ singular value decomposition for the blurring matrix in a low-count pixel system. A strong blurring may yield a null space for the blurring matrix. Yet, a nonnegativity constraint for images built into the deblurring may help restore null-space content in a high-contrast image with zero or low intensity for a sufficient number of pixels. For low-contrast images, the control over null-space content may be gained through regularization. When the regularization is applied, the blurred image is, in practice, restored to an image that is still blurred but less than the starting one.
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