Feature reconstruction networks have achieved remarkable performance in few-shot fine-grained classification tasks. Nonetheless, traditional feature reconstruction networks rely on linear regression. This linearity may cause the loss of subtle discriminative cues, ultimately resulting in less precise reconstructed features. Moreover, in situations where the background predominantly occupies the image, the background reconstruction errors tend to overshadow foreground reconstruction errors, resulting in inaccurate reconstruction errors. In order to address the two key issues, a novel approach called the Foreground-Aware Kernelized Feature Reconstruction Network (FKFRN) is proposed. Specifically, to address the problem of imprecise reconstructed features, we introduce kernel methods into linear feature reconstruction, extending it to nonlinear feature reconstruction, thus enabling the reconstruction of richer, finer-grained discriminative features. To tackle the issue of inaccurate reconstruction errors, the foreground-aware reconstruction error is proposed. Specifically, the model assigns higher weights to features containing more foreground information and lower weights to those dominated by background content, which reduces the impact of background errors on the overall reconstruction. To estimate these weights accurately, we design two complementary strategies: an explicit probabilistic graphical model and an implicit neural network-based approach. Extensive experimental results on eight datasets validate the effectiveness of the proposed approach for few-shot fine-grained classification.

This study aimed to propose a definition of linearity in image reconstruction and demonstrate, by reductio ad absurdum, that the row-action maximum likelihood algorithm (RAMLA) and ordered subset expectation maximization (OSEM) are nonlinear when the number of iterations is low and linear approximation when the number of iterations increases. Block sequential regularized expectation maximization (BSREM) and one-step late maximum a posteriori expectation maximization (OSLEM), which serve as regularized versions of RAMLA and OSEM, respectively, remain nonlinear regardless of the number of iterations. Simulations using ideal two-dimensional (2D) parallel beam projections validated the results of the reductio ad absurdum proof. The three numerical phantoms were point source , represented by 2D Gaussian with a full width at half maximum of 3 pixels positioned at the center of disk background; point source , separated by 24 pixels along the x-axis; and point source , is the sum of and . In numerical experiment, when the difference of the area under the curve (AUC) or recovery for reconstructed image of and the summed reconstructed images of and is within reference values, or when AUC profiles are visually consistent, we defined image reconstruction as linear approximation. RAMLA and OSEM were deemed nonlinear when less than 20 iterations were performed with 64 subsets and linear approximation when iterations were used. By contrast, BSREM and OSLEM remained nonlinear. Algebraic reconstruction technique is linear and its regularized variant has a tendency of linear approximation, indicating that the same regularization function works differently in linear and nonlinear image reconstructions.

High - Quality Decoding of RGB Images from the Neuronal Signals of the Pigeon Optic Tectum.

Current assistive hearing devices, such as hearing aids and cochlear implants, lack the ability to adapt to the listener’s focus of auditory attention, limiting their effectiveness in complex acoustic environments like cocktail party scenarios where multiple conversations occur simultaneously. Neuro-steered hearing devices aim to overcome this limitation by decoding the listener’s auditory attention from neural signals, such as electroencephalography (EEG). While many auditory attention decoding (AAD) studies have used high-density scalp EEG, such systems are impractical for daily use as they are bulky and uncomfortable. Therefore, AAD with wearable and unobtrusive EEG systems that are comfortable to wear and can be used for long-term recording are required. Around-ear EEG systems like cEEGrids have shown promise in AAD, but in-ear EEG, recorded via custom earpieces offering superior comfort, remains underexplored. We present a new AAD dataset with simultaneously recorded scalp, around-ear, and in-ear EEG, enabling a direct comparison. Using a classic linear stimulus reconstruction algorithm, a significant performance gap between all three systems exists, with AAD accuracies of 83.4% (scalp EEG), 67.2% (around-ear EEG), and 61.1% (in-ear EEG) on 60s decision windows. These results highlight the trade-off between decoding performance and practical usability. Yet, while the ear-based EEG systems using basic algorithms might currently not yield accurate enough performances for a decision speed-sensitive application in hearing aids, their significant performance suggests potential for attention monitoring on longer timescales. Furthermore, adding an external reference or a few scalp electrodes via greedy forward selection substantially and quickly boosts accuracy by over 10 percent point, especially for in-ear EEG. These findings position in-ear EEG as a promising component in EEG sensor networks for AAD.

The French Broad River in eastern Tennessee is a critical water resource for the Tennessee Valley Authority’s hydropower and drought relief, yet its instrumental record spans less than a century. To evaluate new dendrochronological tools and examine long-term streamflow trends, we extended the stream record by 1500 years using linear regression and machine learning reconstruction models informed by the tree-ring-derived self-calibrating Palmer Drought Severity Index (scPDSI). Linear regression models provided skillful reconstruction and stable performance across calibration and validation periods. Random Forest and Deep Learning achieved higher skill but lost some of their skill advantage with validation periods, indicating overfitting. All models captured drought years more reliably than flood years, reflecting the sensitivity of scPDSI to soil moisture but its limitations for high-flow extremes in the Appalachian region. Trend analyses identified a significant change point in 1271 CE, separating a drought-dominated early period (500–1272 CE) from a wetter, less variable regime (1273–1970 CE). An emerging trend shows higher average flow interrupted by severe single-year droughts, consistent with regional evidence and projected changes to hydrologic regimes in Appalachia. These findings provide a millennial perspective on hydrologic extremes and guidance on using paleohydrology tools for water resource planning in a changing climate.

ABSTRACT The peculiar velocity field of the local Universe provides direct insights into its matter distribution and the underlying theory of gravity, and is essential in cosmological analyses for modelling deviations from the Hubble flow. Numerous methods have been developed to reconstruct the density and velocity fields at $z \lesssim 0.05$, typically constrained by redshift-space galaxy positions or by direct distance tracers such as the Tully–Fisher relation, the Fundamental Plane, or Type Ia supernovae. We introduce a validation framework to evaluate the accuracy of these reconstructions against catalogues of direct distance tracers. Our framework assesses the goodness-of-fit of each reconstruction using Bayesian evidence, residual redshift discrepancies, velocity scaling, and the need for external bulk flows. Applying this framework to a suite of reconstructions – including those derived from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm and from linear theory – we find that the non-linear BORG reconstruction consistently outperforms others. We highlight the utility of such a comparative approach for supernova or gravitational wave cosmological studies, where selecting an optimal peculiar velocity model is essential. Additionally, we present calibrated bulk flow curves predicted by the reconstructions and perform a density–velocity cross-correlation using a linear theory reconstruction to constrain the growth factor, yielding $S_8 = 0.793 \pm 0.035$. The result is in good agreement with both weak lensing and Planck, but is in strong disagreement with some peculiar velocity studies.

Accurate ultrasonic focus localization is paramount for the safety and efficacy of the focused ultrasound (FUS) applications. Nonlinear effects at the focus generate frequency-multiplied harmonics, establishing it as the dominant harmonic source. Consequently, detecting these nonlinear harmonics enables localization of the harmonic source, corresponding to the FUS focus. This study introduces and validates this focus localization mechanism experimentally using two complementary systems. For the sound field scanning system, the focus position determined by the peak amplitude of the acoustic field was compared with that derived from the time difference of arrival (TDOA) calculations of harmonic signals. For the phased-array ultrasound system, the geometric focus location derived from the B-mode image of the FUS transducer edge was compared with locations obtained by TDOA calculation and harmonic source reconstruction. Experimental results demonstrate that harmonic source localization accurately determines the FUS focus. TDOA calculations achieved superior axial accuracy compared to linear array-based harmonic reconstruction (0.182 mm vs 0.438 mm axial deviation). Results consistently show sub-wavelength-scale agreement between harmonic-based localization and reference standards. This work establishes nonlinear harmonics as reliable acoustic signatures for focus tracking, offering significant potential for therapeutic FUS monitoring applications.

Since the introduction of whole-body photon-counting detector CT (PCD-CT) into clinical practice, extensive physics assessments have been conducted to elucidate its image quality advantages over energy-integrating detector CT (EID-CT) and to support its clinical adoption. However, evaluations of its three-dimensional (3D) noise power spectrum (NPS), which simultaneously quantifies in-plane and through-plane noise texture and magnitude, remain limited. To experimentally evaluate the 3D NPS of an NAEOTOM Alpha PCD-CT system and its dependence on scan mode, reconstruction image type, quantum iterative reconstruction (QIR) strength, mono-energy (keV) level, spiral pitch, and radiation dose. Repeated scans of a 20cm water phantom and a 30cm PMMA phantom were conducted under the clinical Standard mode, clinical Ultra-High-Resolution (UHR) mode, and an Expert Service mode. Reconstructed image types include T3D, virtual monoenergetic image (VMI), and T1 (a linear reconstruction of total-energy bin available via the Expert Service mode). Data were collected at seven dose levels (0.4-24 mGy) and four spiral pitch levels (0.35-1.5). T3D and VMI images were reconstructed with varying QIR strengths, and VMIs were reconstructed at energies ranging from 40 to 190 keV. The 3D NPS, , was calculated from each ensemble of 3D image volumes. Axial ​ was obtained by integrating NPS3D along , while ​ was obtained by integrating NPS3D over and . ​ of T1 images were flat, indicating no noise correlation across PCD rows. In contrast, all clinical-mode reconstructions exhibited through-plane noise correlation, as reflected in the shape of their . ​For clinical-mode reconstructions, the shape of their 3D NPS showed a mild to moderate dependence on dose, with lower doses producing NPS profiles shifted towards lower frequencies in both axial and z directions. With a matched post-object radiation exposure, the larger phantom resulted in higher noise and stronger noise correlation compared to the smaller phantom. QIR only mildly enhanced noise correlation. For a given CTDIvol, spiral pitch has a negligible impact on 3D NPS. Due to through-plane noise correlation, the variance of T3D and VMI decreases with slice thickness ( ) approximately as , in contrast to the scaling observed in T1 images. The shape of the 3D NPS of VMI showed only weak dependence on the keV level along the axial frequency direction. Compared to the Standard mode, the UHR mode reduced image variance by 26% when using a soft-tissue (Br44) kernel and by 77% with a sharp (Br76) kernel. However, 3D NPS analysis revealed stronger through-plane noise correlation in UHR images. The 3D NPS provides new insight into the noise characteristics of PCD-CT: Noise in the native PCD-CT projection data is uncorrelated across detector rows, but clinical reconstruction processes introduce noise spatial correlation along both axial and z directions, particularly at higher QIR strengths, lower radiation doses, or with larger image objects that increase the percentage of scattered photons. Compared to the Standard mode, UHR mode reconstruction exhibits stronger noise correlation due to its superior detector spatial resolution, allowing for more aggressive spatial smoothing to achieve the desired spatial resolution in the final image.

We present the pupil phase series (PPS), a fast and accurate forward scattering algorithm for simulating and inverting multiple light scattering in large biological samples. PPS achieves high-angle scattering accuracy and energy conservation simultaneously by introducing a spatially varying phase modulation in the pupil plane. By expanding the scattering term into a Taylor series, PPS achieves high precision while maintaining computational efficiency. We integrate PPS into a quasi-Newton inverse solver to reconstruct the three-dimensional refractive index of a 180 μm-thick human organoid. Compared to linear reconstruction, our method recovers subcellular features-such as nuclei and vesicular structures-deep within the sample volume. PPS offers a scalable and interpretable alternative to conventional solvers, paving the way for high-throughput, label-free imaging of optically thick biological tissues.

Abstract In this paper, we introduce high-order tensor-train (TT) finite-volume methods for the shallow-water equations (SWEs). We present the implementation of the third-order upwind and the fifth-order upwind and weighted essentially nonoscillatory (WENO) reconstruction schemes in the TT format. It is shown in detail that the linear upwind schemes can be implemented by directly manipulating the TT cores, while the WENO scheme requires the use of TT cross interpolation for the nonlinear reconstruction. In the development of numerical fluxes, we directly compute the flux for the linear SWEs without using TT rounding or cross interpolation. For the nonlinear SWEs where the TT reciprocal of the shallow water layer thickness is needed for fluxes, we develop an approximation algorithm using Taylor series to compute the TT reciprocal. The performance of the TT finite-volume solver with linear and nonlinear reconstruction options is investigated under a physically relevant set of validation problems. In all test cases, the TT finite-volume method maintains the formal high-order accuracy of the corresponding traditional finite-volume method. In terms of speed, the TT solver achieves up to 124 times acceleration of the traditional full-tensor scheme.

Electrolyser cell performance is usually limited by transport and ohmic losses due to evolution of gas bubbles on the electrode surfaces especially at higher operating current densities. In the advancements of electrolyser cell design, the electrolyser with zero-gap cell design performs at higher current densities over the conventional design and also utilizing of economic and abundantly available materials (such as Ni and porous carbon). However, the resistances from the electrolyte and gas bubbles on the back surface of electrodes still limit the full potential performance of the zero-gap cell electrolyser. This work addressed the gas bubble resistances by providing additional insight into the gas bubble nucleation, growth and detachment at the interface of electrode and gas diffusion layer (GDL) by a computational approach. Due to the lower surface energy at interfaces, the probability of nucleation of gas bubbles is energetically favorable. The bubble nucleates and grows with contact of two solid surfaces (electrode and GDL strut) provided that there is a state of supersaturation of gas in the electrolyte. The nucleation of bubbles at the interface is detrimental to the performance of electrolyser, where the bubbles have stronger adhesion to the interface surfaces and delay the detachment time. Hence the magnitude of buoyancy force is high in relative to detachment of bubbles at non-interface sites. Using openFoam, we investigated the effects of interface surface texture on the detachment time of bubbles. The porous layer (electrode) and the GDL struts are considered orthogonal to each other, the porous layer architectures were considered to be cubic and to be a primitive triply periodic minimal surface (TPMS), respectively, both with an area of 1 mm2 and thickness of 200 µm. The volume fraction of the cubic and primitive TPMS was chosen to be 0.6. The GDL struts interface with the considered porous layers, the GDL architecture was chosen as an open triangular block with sides of rectangular and cylindrical shapes of different thickness of 70 µm, 100 µm and 150 µm, respectively. The dimensions chosen are representative of electrolyser systems, in the multiphase simulations, the nucleation of bubble at multiple sites of the interface geometries was studied. The spherical shape and growth of the bubble was defined by the parabolic inlet at the interfaces (nucleation sites), where the growth rate of bubble was mimicked by inducing the mass flow rate of gas through the interface. The growth profile of the bubble chosen in the simulation corresponds to operating current density and supersaturation of the water (electrolyte) with dissolved gas (oxygen). The geometric volume of fluid (VOF) method was implemented to track the advection of the interface of water and gas bubble. The outcomes of the simulation studies portray the time scales of growth and detachment of bubbles with emphasis on critical bubble radius at the interfaces. These results were compared with a relative study of critical radius of bubble and bubble detachment times at non-interface sites. Further, the effect of temperature and pressure in the simulation studies was implemented by the variation in surface tension of water and oxygen. Contact angles of the electrode and GDL surfaces are varied from aerophilic to aerophobic (contact angle of bubble to solid surface in aqueous media), which induces a decrease in adhesion strength of the bubble. Due to the convergence issues, it is necessary to run the simulations at very low time steps (10-6 to 10-12 s), which is computationally expensive. The implementation of a piece-wise linear interface reconstruction of the distance function (PLIC-RDF) improved the time frames.The analysis and insights stress the need of surface engineering of the electrode and GDL interfaces for enhanced detachment time of gas bubbles. The work-flow we described in this work can be extended to study other complex interfaces of GDL and electrode, that paves the way to design water electrolyser system to perform at higher operating current densities with low losses. Figure 1

Suspended particles in hazy medium absorb and scatter light, severely degrading imaging quality. Numerous single-image dehazing methods have been proposed to reconstruct clear images from hazy ones. However, most of them focus on increasing depth and width to improve dehazing performance, which incurs high computation and energy costs. To address this issue, we propose a lightweight spiking convolutional neural network (CNN) referred to as retina-inspired spiking CNN (RI-SCNN) for the reconstruction of hazy images. Unlike conventional dehazing techniques, first, our proposed network simulates the hierarchical structure and cellular function of the retina and devises five network modules to efficiently encode and extract image features through ON and OFF roads. Furthermore, the linear reconstruction mechanism is introduced to integrate the outputs from different roads, adaptively preserving regions with optimal details and constructing a comprehensive visual representation. Finally, by the transformed atmospheric scattering formula, our network can generate the dehazy image. Incorporating the microscale spiking mechanism of the brain, the entire network leverages discrete binary spike trains for information encoding and transmission, directly trained by spiking surrogate gradient learning on integrate-and-fire (IF) neurons. Experimental results demonstrate the superiority of the proposed RI-SCNN in terms of quantitative dehazing performance, qualitative visual effect, energy efficiency, and run speed. Considering its lightweight architecture with ultralow computation and energy costs, the network is encouraged to be deployed in the visual sensor hardware to improve overall performance.

In this work, we present a workflow to construct generic and robust generative image priors from magnitude-only images. The priors can then be used for regularization in reconstruction to improve image quality. The workflow begins with the preparation of training datasets from magnitude-only magnetic resonance (MR) images. This dataset is then augmented with phase information and used to train generative priors of complex images. Finally, trained priors are evaluated using both linear and nonlinear reconstruction for compressed sensing parallel imaging with various undersampling schemes. The results of our experiments demonstrate that priors trained on complex images outperform priors trained only on magnitude images. In addition, a prior trained on a larger dataset exhibits higher robustness. Finally, we show that the generative priors are superior to -wavelet regularization for compressed sensing parallel imaging with high undersampling. These findings stress the importance of incorporating phase information and leveraging large datasets to raise the performance and reliability of the generative priors for MR imaging (MRI) reconstruction. Phase augmentation makes it possible to use existing image databases for training.This article is part of the theme issue ‘Generative modelling meets Bayesian inference: a new paradigm for inverse problems’.

Tomographic reconstruction of quantum states plays a fundamental role in benchmarking quantum systems and accessing information encoded in quantum-mechanical systems. Among the informationally complete sets of quantum measurements, the tight ones provide a linear reconstruction formula and minimize the propagation of statistical errors. However, implementing tight measurements in the lab is challenging due to the high number of required measurement projections, involving a series of experimental setup preparations. In this work, we introduce the notion of cyclic tight measurements, which allow us to perform full quantum state tomography while considering only repeated application of a single unitary-based quantum device during the measurement stage. This type of measurement significantly simplifies the complexity of the experimental setup required to retrieve the quantum state of a physical system. Additionally, we design a feasible setup preparation procedure that produces well-approximated cyclic tight measurements in every finite dimension.

Convolutional neural networks (CNNs) have succeeded remarkably in various computer vision tasks. However, they are not intrinsically explainable. While feature-level understanding of CNNs reveals where the models looked, concept-based explainability methods provide insights into what the models saw. However, their assumption of linear reconstructability of image activations fails to capture the intricate relationships within these activations. Their fidelity-only approach to evaluating global explanations also presents a new concern. For the first time, we address these limitations with the novel transformative nonlinear concept explainer (TraNCE) for CNNs. Unlike linear reconstruction assumptions made by existing methods, TraNCE captures the intricate relationships within the activations. This study presents three original contributions to the CNN explainability literature: 1) an automatic concept discovery mechanism based on variational autoencoders (VAEs). This transformative concept discovery process enhances the identification of meaningful concepts from image activations; 2) a visualization module that leverages the Bessel function to create a smooth transition between prototypical image pixels, revealing not only what the CNN saw but also what the CNN avoided, thereby mitigating the challenges of concept duplication as documented in previous works; and 3) a new metric, the faith score, integrates both coherence and fidelity for comprehensive evaluation of explainer faithfulness and consistency. Based on the investigations on publicly available datasets, we prove that a valid decomposition of a high-dimensional image activation should follow a nonlinear reconstruction, contributing to the explainer's efficiency. We also demonstrate quantitatively that, besides accuracy, consistency is crucial for the meaningfulness of concepts and human trust. The code is available at https://github.com/daslimo/TrANCE.

This study establishes a novel mathematical framework for stochastic maintenance optimization in production systems by integrating Markov decision processes (MDPs) with convex programming theory. We develop a Z-transformation-based dual-space decomposition method to reconstruct MDPs into a solvable linear programming form, resolving the inherent instability of traditional models caused by uncertain initial conditions and non-stationary state transitions. The proposed approach introduces three mathematical innovations: (i) a spectral clustering mechanism that reduces state-space dimensionality while preserving Markovian properties, (ii) a Lagrangian dual formulation with adaptive penalty functions to handle operational constraints, and (iii) a warm start algorithm accelerating convergence in high-dimensional convex optimization. Theoretical analysis proves that the derived policy achieves stability in probabilistic transitions through martingale convergence arguments, demonstrating structural invariance to initial distributions. Experimental validations on production processes reveal that our model reduces long-term maintenance costs by 36.17% compared to Monte Carlo simulations (1500 vs. 2350 average cost) and improves computational efficiency by 14.29% over Q-learning methods. Sensitivity analyses confirm robustness across Weibull-distributed failure regimes (shape parameter β∈ [1.2, 4.8]) and varying resource constraints.

Abstract In complex-valued coherent inverse problems such as synthetic aperture radar (SAR), one may often have prior information only on the magnitude image which shows the features of interest such as strength of reflectivity. In contrast, there may be no more prior knowledge of the phase beyond it being a uniform random variable. However, separately regularising the magnitude, via some function G := H ( | ⋅ | ) , would appear to lead to a potentially challenging non-linear phase fitting problem in each iteration of even a linear least-squares reconstruction problem. We show that under certain sufficient conditions the proximal map of such a function G may be calculated as a simple phase correction to that of H. Further, we provide proximal map of (almost) arbitrary G := H ( | ⋅ | ) which does not meet these sufficient conditions. This may be calculated through a simple numerical scheme making use of the proximal map of H itself, and thus we provide a means to apply practically arbitrary regularisation functions to the magnitude when solving coherent reconstruction problems via proximal optimisation algorithms. This is demonstrated using publicly available real SAR data for generalised Tikhonov regularisation applied to multi-channel SAR, and both a simple level set formulation and total generalised variation applied to the standard single-channel case.

Arterial diseases are a leading cause of morbidity worldwide, necessitating the development of robust simulation tools to understand their progression mechanisms. In this study, we present a finite volume solver based on the incompressible lattice Boltzmann method (iLBM) to model complex cardiovascular flows. Standard LBM suffers from compressibility errors and is constrained to uniform Cartesian meshes, limiting its applicability to realistic vascular geometries. To address these issues, we developed an incompressible LBM scheme that recovers the incompressible Navier–Stokes equations (NSEs) and integrated it into a finite volume (FV) framework to handle unstructured meshes while retaining the simplicity of the LBM algorithm. The FV-iLBM model with linear reconstruction (LR) scheme was then validated against benchmark cases, including Taylor–Green vortex flow, shear wave attenuation, Womersley flow, and lid-driven cavity flow, demonstrating improved accuracy in reducing compressibility errors. In simulating flow over National Advisory Committee for Aeronautics (NACA) 0012 airfoil, the FV-iLBM model accurately captured vortex shedding and aerodynamic forces. After validating the FV-iLBM solver for simulating non-Newtonian flows, pulsatile blood flow through an artery afflicted with multiple stenoses was simulated, accurately predicting wall shear stress and flow separation. The results establish FV-iLBM as an efficient and accurate method for modeling cardiovascular flows.

The hierarchical modular functional structure in the human brain has not been adequately depicted by conventional functional magnetic resonance imaging (fMRI) acquisition techniques and traditional functional connectivity reconstruction methods. Fortunately, rapid advancements in fMRI scanning techniques and deep learning methods open a novel frontier to map the spatial hierarchy within Brain Connectivity Networks (BCNs). The novel multiband multi-echo (MBME) fMRI technique has increased spatiotemporal resolution and peak functional sensitivity, while the advanced deep linear model (multilayer-stacked) named DEep Linear Matrix Approximate Reconstruction (DELMAR) enables the identification of hierarchical features without extensive hyperparameter tuning. We incorporate a multi-echo blood oxygenation level-dependent (BOLD) signal and DELMAR for denoising in its first layer, thereby eliminating the need for a separate multi-echo independent component analysis (ME-ICA) denoising step. Our results demonstrate that the DELMAR/Denoising/Mapping strategy produces more accurate and reproducible hierarchical BCNs than traditional ME-ICA denoising followed by DELMAR. Additionally, we showcase that MBME fMRI outperforms multiband (MB) fMRI in terms of hierarchical BCN mapping accuracy and precision. These reproducible spatial hierarchies in BCNs have significant potential for developing improved fMRI diagnostic and prognostic biomarkers of functional connectivity across a wide range of neurological and psychiatric disorders.

Multi-label metric learning, as an extension of metric learning to multi-label scenarios, aims to learn better similarity metrics for objects with rich semantics. Existing multi-label metric learning approaches employ the common assumption of equal labeling-importance, i.e., all associated labels are considered relevant to the training instance, while there is no differentiation in the relative importance of their semantics. However, this common assumption does not reflect the fact that the importance of each relevant label is generally different, even though such importance information is not directly accessible from the training examples. In this paper, we claim that it is beneficial to leverage the implicit Relative LabelingImportance (RLI) information to facilitate multi-label metric learning. Specifically, the manifold structure within the feature space is exploited by local linear reconstruction, and then the RLIs are recovered by transferring such structure to the label space. Subsequently, a discrimiative multi-label metric learning framework is introduced to align the predictive modeling outputs with the recovered RLIs, under which instances with similar RLI are implicitly pulled closer to each other, while those with dissimilar RLI are pushed further apart. Comprehensive experiments on benchmark multi-label datasets validate the superiority of our proposed approach in learning effective similarity metrics between multi-label examples.