Traditional low-rank approximation is a powerful tool to compress the huge data matrices that arise in simulations of partial differential equations (PDE), but suffers from high computational cost and requires several passes over the PDE data. The compressed data may also lack interpretability thus making it difficult to identify feature patterns from the original data. To address this issue, we present an online randomized algorithm to compute the interpolative decomposition (ID) of large-scale data matrices in situ. Compared to previous randomized IDs that used the QR decomposition to determine the column basis, we adopt a streaming ridge leverage score-based column subset selection algorithm that dynamically selects proper basis columns from the data and thus avoids an extra pass over the data to compute the coefficient matrix of the ID. In particular, we adopt a single-pass error estimator based on the non-adaptive Hutch++ algorithm to provide real-time error approximation for determining the best coefficients. As a result, our approach only needs a single pass over the original data and thus is suitable for large and high-dimensional matrices stored outside of core memory or generated in PDE simulations. We also provide numerical experiments on turbulent channel flow and ignition simulations, and on the NSTX Gas Puff Image dataset, comparing our algorithm with the offline ID algorithm to demonstrate its utility in real-world applications.
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We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Based on the techniques of stochastic thermodynamics, we derive the speed-accuracy trade-off for the diffusion models, which is a trade-off relationship between the speed and accuracy of data generation in diffusion models. Our result implies that the entropy production rate in the forward process affects the errors in data generation. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the conservative force in stochastic thermodynamics and the geodesic of space by the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy trade-off for the diffusion models with different noise schedules such as the cosine schedule, the conditional optimal transport, and the optimal transport.
We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Based on the techniques of stochastic thermodynamics, we derive the speed-accuracy trade-off for the diffusion models, which is a trade-off relationship between the speed and accuracy of data generation in diffusion models. Our result implies that the entropy production rate in the forward process affects the errors in data generation. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the conservative force in stochastic thermodynamics and the geodesic of space by the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy trade-off for the diffusion models with different noise schedules such as the cosine schedule, the conditional optimal transport, and the optimal transport.
Due to the effective performance of multi-scale feature fusion, Path Aggregation FPN (PAFPN) is widely employed in YOLO detectors. However, it cannot efficiently and adaptively integrate high-level semantic information with low-level spatial information simultaneously. We propose a new model named MAF-YOLO in this paper, which is a novel object detection framework with a versatile neck named Multi-Branch Auxiliary FPN (MAFPN). Within MAFPN, the Superficial Assisted Fusion (SAF) module is designed to combine the output of the backbone with the neck, preserving an optimal level of shallow information to facilitate subsequent learning. Meanwhile, the Advanced Assisted Fusion (AAF) module deeply embedded within the neck conveys a more diverse range of gradient information to the output layer. Furthermore, our proposed Re-parameterized Heterogeneous Efficient Layer Aggregation Network (RepHELAN) module ensures that both the overall model architecture and convolutional design embrace the utilization of heterogeneous large convolution kernels. Therefore, this guarantees the preservation of information related to small targets while simultaneously achieving the multi-scale receptive field. Finally, taking the nano version of MAF-YOLO for example, it can achieve 42.4% AP on COCO with only 3.76M learnable parameters and 10.51G FLOPs, and approximately outperforms YOLOv8n by about 5.1%. The source code of this work is available at: //github.com/yang-0201/MAF-YOLO.
This paper deals with a novel nonlinear coupled nonlocal reaction-diffusion system proposed for image restoration, characterized by the advantages of preserving low gray level features and textures.The gray level indicator in the proposed model is regularized using a new method based on porous media type equations, which is suitable for recovering noisy blurred images. The well-posedness, regularity, and other properties of the model are investigated, addressing the lack of theoretical analysis in those existing similar types of models. Numerical experiments conducted on texture and satellite images demonstrate the effectiveness of the proposed model in denoising and deblurring tasks.
Measuring a qubit is a fundamental yet error prone operation in quantum computing. These errors can stem from various sources such as crosstalk, spontaneous state-transitions, and excitation caused by the readout pulse. In this work, we utilize an integrated approach to deploy neural networks (NN) on to field programmable gate arrays (FPGA). We demonstrate that it is practical to design and implement a fully connected neural network accelerator for frequency-multiplexed readout balancing computational complexity with low latency requirements without significant loss in accuracy. The neural network is implemented by quantization of weights, activation functions, and inputs. The hardware accelerator performs frequency-multiplexed readout of 5 superconducting qubits in less than 50 ns on RFSoC ZCU111 FPGA which is first of its kind in the literature. These modules can be implemented and integrated in existing Quantum control and readout platforms using a RFSoC ZCU111 ready for experimental deployment.
We address the problem of computing the eigenvalue backward error of the Rosenbrock system matrix under various types of block perturbations. We establish computable formulas for these backward errors using a class of minimization problems involving the Sum of Two generalized Rayleigh Quotients (SRQ2). For computational purposes and analysis, we reformulate such optimization problems as minimization of a rational function over the joint numerical range of three Hermitian matrices. This reformulation eliminates certain local minimizers of the original SRQ2 minimization and allows for convenient visualization of the solution. Furthermore, by exploiting the convexity within the joint numerical range, we derive a characterization of the optimal solution using a Nonlinear Eigenvalue Problem with Eigenvector dependency (NEPv). The NEPv characterization enables a more efficient solution of the SRQ2 minimization compared to traditional optimization techniques. Our numerical experiments demonstrate the benefits and effectiveness of the NEPv approach for SRQ2 minimization in computing eigenvalue backward errors of Rosenbrock systems.
Pairwise sequence comparison is one of the most fundamental problems in string processing. The most common metric to quantify the similarity between sequences S and T is edit distance, d(S,T), which corresponds to the number of characters that need to be substituted, deleted from, or inserted into S to generate T. However, fewer edit operations may be sufficient for some string pairs to transform one string to the other if larger rearrangements are permitted. Block edit distance refers to such changes in substring level (i.e., blocks) that "penalizes" entire block removals, insertions, copies, and reversals with the same cost as single-character edits (Lopresti & Tomkins, 1997). Most studies to calculate block edit distance to date aimed only to characterize the distance itself for applications in sequence nearest neighbor search without reporting the full alignment details. Although a few tools try to solve block edit distance for genomic sequences, such as GR-Aligner, they have limited functionality and are no longer maintained. Here, we present SABER, an algorithm to solve block edit distance that supports block deletions, block moves, and block reversals in addition to the classical single-character edit operations. Our algorithm runs in O(m^2.n.l_range) time for |S|=m, |T|=n and the permitted block size range of l_range; and can report all breakpoints for the block operations. We also provide an implementation of SABER currently optimized for genomic sequences (i.e., generated by the DNA alphabet), although the algorithm can theoretically be used for any alphabet. SABER is available at //github.com/BilkentCompGen/saber
Threshold selection is a fundamental problem in any threshold-based extreme value analysis. While models are asymptotically motivated, selecting an appropriate threshold for finite samples is difficult and highly subjective through standard methods. Inference for high quantiles can also be highly sensitive to the choice of threshold. Too low a threshold choice leads to bias in the fit of the extreme value model, while too high a choice leads to unnecessary additional uncertainty in the estimation of model parameters. We develop a novel methodology for automated threshold selection that directly tackles this bias-variance trade-off. We also develop a method to account for the uncertainty in the threshold estimation and propagate this uncertainty through to high quantile inference. Through a simulation study, we demonstrate the effectiveness of our method for threshold selection and subsequent extreme quantile estimation, relative to the leading existing methods, and show how the method's effectiveness is not sensitive to the tuning parameters. We apply our method to the well-known, troublesome example of the River Nidd dataset.
Prediction models are used to predict an outcome based on input variables. Missing data in input variables often occurs at model development and at prediction time. The missForestPredict R package proposes an adaptation of the missForest imputation algorithm that is fast, user-friendly and tailored for prediction settings. The algorithm iteratively imputes variables using random forests until a convergence criterion (unified for continuous and categorical variables and based on the out-of-bag error) is met. The imputation models are saved for each variable and iteration and can be applied later to new observations at prediction time. The missForestPredict package offers extended error monitoring, control over variables used in the imputation and custom initialization. This allows users to tailor the imputation to their specific needs. The missForestPredict algorithm is compared to mean/mode imputation, linear regression imputation, mice, k-nearest neighbours, bagging, miceRanger and IterativeImputer on eight simulated datasets with simulated missingness (48 scenarios) and eight large public datasets using different prediction models. missForestPredict provides competitive results in prediction settings within short computation times.
We investigate the estimation properties of the mixture of experts (MoE) model in a high-dimensional setting, where the number of predictors is much larger than the sample size, and for which the literature is particularly lacking in theoretical results. We consider the class of softmax-gated Gaussian MoE (SGMoE) models, defined as MoE models with softmax gating functions and Gaussian experts, and focus on the theoretical properties of their $l_1$-regularized estimation via the Lasso. To the best of our knowledge, we are the first to investigate the $l_1$-regularization properties of SGMoE models from a non-asymptotic perspective, under the mildest assumptions, namely the boundedness of the parameter space. We provide a lower bound on the regularization parameter of the Lasso penalty that ensures non-asymptotic theoretical control of the Kullback--Leibler loss of the Lasso estimator for SGMoE models. Finally, we carry out a simulation study to empirically validate our theoretical findings.
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