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Polarimetric imaging, a technique that captures the invisible polarization-related properties of given materials, has broad applications from fundamental physics to advanced fields such as target recognition, stress detection, biomedical diagnosis and remote sensing. The introduction of quantum sources into classical imaging systems has demonstrated distinct advantages, yet few studies have explored their combination with polarimetric imaging. In this study, we present a quantum polarimetric imaging system that integrates polarization-entangled photon pairs into a polarizer-sample-compensator-analyzer (PSRA)-type polarimeter. Our system visualizes the birefringence properties of a periodical-distributed anisotropic material under decreasing illumination levels and diverse disturbing light sources. Compared to the classical system, the quantum approach reveals the superior sensitivity and robustness in low-light conditions, particularly useful in biomedical studies where the low illumination and non-destructive detection are urgently needed. The study also highlights the nonlocality of entangled photons in birefringence measurement, indicating the potential of quantum polarimetric system in the remote sensing domain.

Global Covariance Pooling (GCP) has been demonstrated to improve the performance of Deep Neural Networks (DNNs) by exploiting second-order statistics of high-level representations. GCP typically performs classification of the covariance matrices by applying matrix function normalization, such as matrix logarithm or power, followed by a Euclidean classifier. However, covariance matrices inherently lie in a Riemannian manifold, known as the Symmetric Positive Definite (SPD) manifold. The current literature does not provide a satisfactory explanation of why Euclidean classifiers can be applied directly to Riemannian features after the normalization of the matrix power. To mitigate this gap, this paper provides a comprehensive and unified understanding of the matrix logarithm and power from a Riemannian geometry perspective. The underlying mechanism of matrix functions in GCP is interpreted from two perspectives: one based on tangent classifiers (Euclidean classifiers on the tangent space) and the other based on Riemannian classifiers. Via theoretical analysis and empirical validation through extensive experiments on fine-grained and large-scale visual classification datasets, we conclude that the working mechanism of the matrix functions should be attributed to the Riemannian classifiers they implicitly respect., Comment: 24 pages, 3 figures

We propose a hidden convexity-based method to address distributed optimal energy flow (OEF) problems for transmission-level integrated electricity-gas systems. First, we develop a node-wise decoupling method to de-compose an OEF problem into multiple OEF subproblems. Then, we propose a hidden convexity-based method to equivalently reformulate nonconvex OEF subproblems as semi-definite programs. This method differs from any ap-proximation and convexification methods that may incur infeasible solutions. Since all OEF subproblems are origi-nally convex or equivalently convexified, we adopt an ADMM to solve the hidden convexity-based distributed OEF problem with convergence analysis. Test results validate the effectiveness of the proposed method, especially in handling a large number of agents., Comment: 7 pages

This paper presents two new metrics on the Symmetric Positive Definite (SPD) manifold via the Cholesky manifold, i.e., the space of lower triangular matrices with positive diagonal elements. We first unveil that the existing popular Riemannian metric on the Cholesky manifold can be generally characterized as the product metric of a Euclidean metric and a Riemannian metric on the space of n-dimensional positive vectors. Based on this analysis, we propose two novel metrics on the Cholesky manifolds, i.e., Diagonal Power Euclidean Metric and Diagonal Generalized Bures-Wasserstein Metric, which are numerically stabler than the existing Cholesky metric. We also discuss the gyro structures and deformed metrics associated with our metrics. The gyro structures connect the linear and geometric properties, while the deformed metrics interpolate between our proposed metrics and the existing metric. Further, by Cholesky decomposition, the proposed deformed metrics and gyro structures are pulled back to SPD manifolds. Compared with existing Riemannian metrics on SPD manifolds, our metrics are easy to use, computationally efficient, and numerically stable., Comment: 25 pages, 1 figures

Aligning large language models (LLMs) with human objectives is crucial for real-world applications. However, fine-tuning LLMs for alignment often suffers from unstable training and requires substantial computing resources. Test-time alignment techniques, such as prompting and guided decoding, do not modify the underlying model, and their performance remains dependent on the original model's capabilities. To address these challenges, we propose aligning LLMs through representation editing. The core of our method is to view a pre-trained autoregressive LLM as a discrete-time stochastic dynamical system. To achieve alignment for specific objectives, we introduce external control signals into the state space of this language dynamical system. We train a value function directly on the hidden states according to the Bellman equation, enabling gradient-based optimization to obtain the optimal control signals at test time. Our experiments demonstrate that our method outperforms existing test-time alignment techniques while requiring significantly fewer resources compared to fine-tuning methods., Comment: fix typos

Recent progress of deep generative models in the vision and language domain has stimulated significant interest in more structured data generation such as molecules. However, beyond generating new random molecules, efficient exploration and a comprehensive understanding of the vast chemical space are of great importance to molecular science and applications in drug design and materials discovery. In this paper, we propose a new framework, ChemFlow, to traverse chemical space through navigating the latent space learned by molecule generative models through flows. We introduce a dynamical system perspective that formulates the problem as learning a vector field that transports the mass of the molecular distribution to the region with desired molecular properties or structure diversity. Under this framework, we unify previous approaches on molecule latent space traversal and optimization and propose alternative competing methods incorporating different physical priors. We validate the efficacy of ChemFlow on molecule manipulation and single- and multi-objective molecule optimization tasks under both supervised and unsupervised molecular discovery settings. Codes and demos are publicly available on GitHub at https://github.com/garywei944/ChemFlow.

Manifold-valued measurements exist in numerous applications within computer vision and machine learning. Recent studies have extended Deep Neural Networks (DNNs) to manifolds, and concomitantly, normalization techniques have also been adapted to several manifolds, referred to as Riemannian normalization. Nonetheless, most of the existing Riemannian normalization methods have been derived in an ad hoc manner and only apply to specific manifolds. This paper establishes a unified framework for Riemannian Batch Normalization (RBN) techniques on Lie groups. Our framework offers the theoretical guarantee of controlling both the Riemannian mean and variance. Empirically, we focus on Symmetric Positive Definite (SPD) manifolds, which possess three distinct types of Lie group structures. Using the deformation concept, we generalize the existing Lie groups on SPD manifolds into three families of parameterized Lie groups. Specific normalization layers induced by these Lie groups are then proposed for SPD neural networks. We demonstrate the effectiveness of our approach through three sets of experiments: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/LieBN.git., Comment: Accepted by ICLR 2024

Four wave mixing (FWM) is an important way to generate supercontinuum and frequency combs in the mid-infrared band. Here, we obtain simultaneous synthetic FWM in the visible and mid-infrared bands by cascading quadratic nonlinear processes in a periodically poled lithium niobate crystal (PPLN), which has a 110dB(at 3000nm) higher conversion efficiency than the FWM directly generated by third-order susceptibilities in bulk PPLN crystals. A general model of this process is developed that is in full agreement with the experimental verifications. The frequency difference between the new frequency components can be freely tuned by changing the frequency difference of the dual pump lasers. Furthermore, by increasing the conversion bandwidth and efficiency of the cascaded processes, it is feasible to generate frequency combs in three bands the visible, near-infrared and mid-infrared bands simultaneously through high-order cascaded processes. This work opens up a new avenue toward free-tuning multiband frequency comb generation with multi-octaves frequency spanning, which will have significant applications in fields such as mid-infrared gas sensing, lidar and precision spectroscopy.

In this paper, we introduce a new post-training compression paradigm for Large Language Models (LLMs) to facilitate their wider adoption. We delve into LLM weight low-rank factorization, and find that the challenges of this task stem from the outlier phenomenon in the LLM activations and the sensitivity difference among various kinds of layers. To address these issues, we propose a training-free approach called Activation-aware Singular Value Decomposition (ASVD). Specifically, ASVD manages activation outliers by scaling the weight matrix based on the activation distribution, thereby enhancing decomposition accuracy. Additionally, we propose an efficient iterative calibration process to optimize layer-specific decomposition by addressing the varying sensitivity of different LLM layers. ASVD can compress a network by 10-20%, without compromising the performance of LLMs. Based on the success of the low-rank decomposition of projection matrices in the self-attention module, we further introduce ASVD to compress the KV cache. By reducing the channel dimension of KV activations, memory requirements for KV cache can be largely reduced. Thanks to the 50-75% reduction in the rank of the KV projection matrices, ASVD can further achieve 50% KV cache reductions without performance drop in a training-free manner.

The task of out-of-distribution (OOD) detection is crucial for deploying machine learning models in real-world settings. In this paper, we observe that the singular value distributions of the in-distribution (ID) and OOD features are quite different: the OOD feature matrix tends to have a larger dominant singular value than the ID feature, and the class predictions of OOD samples are largely determined by it. This observation motivates us to propose \texttt{RankFeat}, a simple yet effective \emph{post hoc} approach for OOD detection by removing the rank-1 matrix composed of the largest singular value and the associated singular vectors from the high-level feature. \texttt{RankFeat} achieves \emph{state-of-the-art} performance and reduces the average false positive rate (FPR95) by 17.90\% compared with the previous best method. The success of \texttt{RankFeat} motivates us to investigate whether a similar phenomenon would exist in the parameter matrices of neural networks. We thus propose \texttt{RankWeight} which removes the rank-1 weight from the parameter matrices of a single deep layer. Our \texttt{RankWeight}is also \emph{post hoc} and only requires computing the rank-1 matrix once. As a standalone approach, \texttt{RankWeight} has very competitive performance against other methods across various backbones. Moreover, \texttt{RankWeight} enjoys flexible compatibility with a wide range of OOD detection methods. The combination of \texttt{RankWeight} and \texttt{RankFeat} refreshes the new \emph{state-of-the-art} performance, achieving the FPR95 as low as 16.13\% on the ImageNet-1k benchmark. Extensive ablation studies and comprehensive theoretical analyses are presented to support the empirical results., Comment: submitted to T-PAMI

A prominent goal of representation learning research is to achieve representations which are factorized in a useful manner with respect to the ground truth factors of variation. The fields of disentangled and equivariant representation learning have approached this ideal from a range of complimentary perspectives; however, to date, most approaches have proven to either be ill-specified or insufficiently flexible to effectively separate all realistic factors of interest in a learned latent space. In this work, we propose an alternative viewpoint on such structured representation learning which we call Flow Factorized Representation Learning, and demonstrate it to learn both more efficient and more usefully structured representations than existing frameworks. Specifically, we introduce a generative model which specifies a distinct set of latent probability paths that define different input transformations. Each latent flow is generated by the gradient field of a learned potential following dynamic optimal transport. Our novel setup brings new understandings to both \textit{disentanglement} and \textit{equivariance}. We show that our model achieves higher likelihoods on standard representation learning benchmarks while simultaneously being closer to approximately equivariant models. Furthermore, we demonstrate that the transformations learned by our model are flexibly composable and can also extrapolate to new data, implying a degree of robustness and generalizability approaching the ultimate goal of usefully factorized representation learning., Comment: NeurIPS23

Generative Adversarial Networks (GANs), especially the recent style-based generators (StyleGANs), have versatile semantics in the structured latent space. Latent semantics discovery methods emerge to move around the latent code such that only one factor varies during the traversal. Recently, an unsupervised method proposed a promising direction to directly use the eigenvectors of the projection matrix that maps latent codes to features as the interpretable directions. However, one overlooked fact is that the projection matrix is non-orthogonal and the number of eigenvectors is too large. The non-orthogonality would entangle semantic attributes in the top few eigenvectors, and the large dimensionality might result in meaningless variations among the directions even if the matrix is orthogonal. To avoid these issues, we propose Householder Projector, a flexible and general low-rank orthogonal matrix representation based on Householder transformations, to parameterize the projection matrix. The orthogonality guarantees that the eigenvectors correspond to disentangled interpretable semantics, while the low-rank property encourages that each identified direction has meaningful variations. We integrate our projector into pre-trained StyleGAN2/StyleGAN3 and evaluate the models on several benchmarks. Within only $1\%$ of the original training steps for fine-tuning, our projector helps StyleGANs to discover more disentangled and precise semantic attributes without sacrificing image fidelity., Comment: ICCV23

Recently, conjectures have been made that there is a correlation between thermodynamic instability and super-entropy~\cite{{Johnson:2019mdp},{Cong:2019bud}}. In this paper, we started with torus-like black holes and verified the correlation mentioned above. After solving the specific analytical solutions of the specific heat capacity at constant volume $C_{V}$, the specific heat capacity at constant pressure $C_{P}$ and plotting the figures, we obtained the results which are consistent with the hypothesis from Ref. \cite{Cong:2019bud}. To further verify the generality of conjectures, we explored the BTZ black hole in nonlinear electrodynamics and phantom AdS black hole. And then the results are summarized via a table. Ultimately, the comparison among these three black holes leads us to the conclusion that there is no essential connection between thermodynamic instability and super-entropy., Comment: 14 pages, 5 figures, 1 table

Deep neural networks for learning Symmetric Positive Definite (SPD) matrices are gaining increasing attention in machine learning. Despite the significant progress, most existing SPD networks use traditional Euclidean classifiers on an approximated space rather than intrinsic classifiers that accurately capture the geometry of SPD manifolds. Inspired by Hyperbolic Neural Networks (HNNs), we propose Riemannian Multinomial Logistics Regression (RMLR) for the classification layers in SPD networks. We introduce a unified framework for building Riemannian classifiers under the metrics pulled back from the Euclidean space, and showcase our framework under the parameterized Log-Euclidean Metric (LEM) and Log-Cholesky Metric (LCM). Besides, our framework offers a novel intrinsic explanation for the most popular LogEig classifier in existing SPD networks. The effectiveness of our method is demonstrated in three applications: radar recognition, human action recognition, and electroencephalography (EEG) classification. The code is available at https://github.com/GitZH-Chen/SPDMLR.git., Comment: Accepted to CVPR 2024

This paper focuses on the N-k security-constrained optimal transmission switching (OTS) problem for variable renewable energy (VRE) penetrated power grids. A new three-stage stochastic and distributionally robust OTS model is proposed. The first stage has the primary purpose to schedule the power generation and network topology based on the forecast of VRE. The second stage controls the power generation and voltage magnitudes of voltage-controlled buses in response to VRE uncertainty, and the third stage reacts to N-k contingencies additionally by line switching and load shedding. The VRE and N-k contingencies, considering different availability of their probability distributions, are tackled by stochastic and distributionally robust optimization, respectively. By adopting stage-wise realization of uncertainties in VRE and contingencies, the associated corrective controls with different mechanisms can be handled separately and properly, which makes the proposed OTS model more realistic than existing two-stage ones. For solving the proposed OTS model, its tractable reformulation is derived, and a solution approach that combines the nested column-and-constraint generation algorithm and Dantzig-Wolfe procedure is developed. Finally, case studies include a simple IEEE network for illustrative purposes and then real system networks to demonstrate the efficacy of the proposed approach.

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data., Comment: ICML 2023

Recently, a conjecture has been proposed, which indicates a correlation between super-entropy black holes and the thermodynamic instability \cite{Cong:2019bud}. W.Cong et al. suggested that the $C_{V}$ (specific heat capacity at constant volume) and $C_{P}$ (specific heat capacity at constant pressure) of a super-entropy black hole could not be greater than zero simultaneously as set in the extended phase space, which implies that the black hole is unstable in extended thermodynamics. This conjecture is intriguing and meaningful. Therefore, we did a study on that. After deriving the equations of specific heat capacities as well as plotting the relevant curves of the four-dimensional conformal black holes (a kind of super-entropy black hole), we obtained regions on the graphs where $C_{V}$ and $C_{P}$ are simultaneously greater than zero, which contradicts the conjecture that super-entropy black hole corresponds to its thermodynamic instability. Thus far, we have provided a counterexample to the hypothesis in \cite{Cong:2019bud}., Comment: 13 pages, 3 figures

Symmetric Positive Definite (SPD) matrices have received wide attention in machine learning due to their intrinsic capacity to encode underlying structural correlation in data. Many successful Riemannian metrics have been proposed to reflect the non-Euclidean geometry of SPD manifolds. However, most existing metric tensors are fixed, which might lead to sub-optimal performance for SPD matrix learning, especially for deep SPD neural networks. To remedy this limitation, we leverage the commonly encountered pullback techniques and propose Adaptive Log-Euclidean Metrics (ALEMs), which extend the widely used Log-Euclidean Metric (LEM). Compared with the previous Riemannian metrics, our metrics contain learnable parameters, which can better adapt to the complex dynamics of Riemannian neural networks with minor extra computations. We also present a complete theoretical analysis to support our ALEMs, including algebraic and Riemannian properties. The experimental and theoretical results demonstrate the merit of the proposed metrics in improving the performance of SPD neural networks. The efficacy of our metrics is further showcased on a set of recently developed Riemannian building blocks, including Riemannian batch normalization, Riemannian Residual blocks, and Riemannian classifiers., Comment: Accepted by TIP 2024

False data injection (FDI) cyber-attacks on power systems can be prevented by strategically selecting and protecting a sufficiently large measurement subset, which, however, requires adequate cyber-defense resources for measurement protection. With any given cyber-defense resource, this paper proposes a preventive-corrective cyber-defense strategy, which minimizes the FDI attack-induced region in a preventive manner, followed by maximizing the cybersecurity margin in a corrective manner. First, this paper proposes a preventive cyber-defense strategy that minimizes the volume of the FDI attack-induced region via preventive allocation of any given measurement protection resource. Particularly, a sufficient condition for constructing the FDI unattackable lines is proposed, indicating that the FDI cyber-attack could be locally rather than globally prevented. Then, given a non-empty FDI attack-induced region, this paper proposes a corrective cyber-defense strategy that maximizes the cybersecurity margin, leading to a trade-off between the safest-but-expensive operation point (i.e., Euclidean Chebyshev center) and the cheapest-but-dangerous operation point. Simulation results on a modified IEEE 14 bus system verify the effectiveness and cost-effectiveness of the proposed preventive-corrective cyber-defense strategy.

To figure out the stability issues brought by renewable energy sources (RES) with non-Gaussian uncertainties in isolated microgrids, this paper proposes a chance constrained stability constrained optimal power flow (CC-SC-OPF) model. Firstly, we propose a bi-level optimization problem, of which the upper level aims to minimize the expected generation cost without violating the stability chance constraint; the lower level concerns about the stability index given by a semi-definite program (SDP). Secondly, we apply the Gaussian mixture model (GMM) to handle the non-Gaussian RES uncertainties and introduce analytical sensitivity analysis to reformulate chance constraints with respect to stability index and operational variables into linear deter-ministic versions. By incorporating linearized constraints, the bi-level model can be efficiently solved by Benders decomposition-based approach. Thirdly, we design a supplementary corrective countermeasure to compensate the possible control error caused by the linear approximation. Simulation results on the 33-bus microgrid reveal that compared to benchmarking approaches, the proposed model converges 30 times faster with more accurate solutions.

In this letter, we analytically investigate the sensitivity of stability index to its dependent variables in general power systems. Firstly, we give a small-signal model, the stability index is defined as the solution to a semidefinite program (SDP) based on the related Lyapunov equation. In case of stability, the stability index also characterizes the convergence rate of the system after disturbances. Then, by leveraging the duality of SDP, we deduce an analytical formula of the stability sensitivity to any entries of the system Jacobian matrix in terms of the SDP primal and dual variables. Unlike the traditional numerical perturbation method, the proposed sensitivity evaluation method is more accurate with a much lower computational burden. This letter applies a modified microgrid for comparative case studies. The results reveal the significant improvements on the accuracy and computational efficiency of stability sensitivity evaluation.

Inserting an SVD meta-layer into neural networks is prone to make the covariance ill-conditioned, which could harm the model in the training stability and generalization abilities. In this paper, we systematically study how to improve the covariance conditioning by enforcing orthogonality to the Pre-SVD layer. Existing orthogonal treatments on the weights are first investigated. However, these techniques can improve the conditioning but would hurt the performance. To avoid such a side effect, we propose the Nearest Orthogonal Gradient (NOG) and Optimal Learning Rate (OLR). The effectiveness of our methods is validated in two applications: decorrelated Batch Normalization (BN) and Global Covariance Pooling (GCP). Extensive experiments on visual recognition demonstrate that our methods can simultaneously improve covariance conditioning and generalization. The combinations with orthogonal weight can further boost the performance. Moreover, we show that our orthogonality techniques can benefit generative models for better latent disentanglement through a series of experiments on various benchmarks. Code is available at: \href{https://github.com/KingJamesSong/OrthoImproveCond}{https://github.com/KingJamesSong/OrthoImproveCond}., Comment: Accepted by IEEE T-PAMI. arXiv admin note: substantial text overlap with arXiv:2207.02119

In this paper, we investigated the chaos of the phantom AdS black hole in near-horizon regions and at a certain distance from the black hole, where the Lyapunov exponent was calculated by the Jacobian determinant. We found that the angular momenta of charged particles nearby the black hole affect the position of the equilibrium orbit as well as the Lyapunov exponent. When the charge is large enough and the angular momenta take particular values, the bound is violated at a certain distance from the event horizon. Concurrently, we compared the differences by analyzing tables and figures after taking different values of $\eta$, where $\eta$ is a constant indicating the nature of the electromagnetic field. When $\eta=1$, it corresponds to the Reissner-Nordstr$\ddot{o}$m-AdS black hole (RN-AdS black hole) and it represents the phantom AdS black hole when $\eta=-1$. In this way, we can draw the following conclusions. Under different values of $\eta$, the variation trends of curves related to $\lambda^{2}-\kappa^{2}$ could be different, where it can be judged whether the constraint is violated by determining if $\lambda^{2}-\kappa^{2}$ is greater than zero. In addition, the corresponding numerical values of angular momenta violating the bound in the phantom AdS black hole are much smaller than the case of RN-AdS black hole. But cases in these different black holes have the same rules to violate the bound. The large absolute values of charge and $\Lambda$ are more likely to violate the bound., Comment: 13 pages, 3 figures, 5 tables

The task of out-of-distribution (OOD) detection is crucial for deploying machine learning models in real-world settings. In this paper, we observe that the singular value distributions of the in-distribution (ID) and OOD features are quite different: the OOD feature matrix tends to have a larger dominant singular value than the ID feature, and the class predictions of OOD samples are largely determined by it. This observation motivates us to propose \texttt{RankFeat}, a simple yet effective \texttt{post hoc} approach for OOD detection by removing the rank-1 matrix composed of the largest singular value and the associated singular vectors from the high-level feature (\emph{i.e.,} $\mathbf{X}{-} \mathbf{s}_{1}\mathbf{u}_{1}\mathbf{v}_{1}^{T}$). \texttt{RankFeat} achieves the \emph{state-of-the-art} performance and reduces the average false positive rate (FPR95) by 17.90\% compared with the previous best method. Extensive ablation studies and comprehensive theoretical analyses are presented to support the empirical results., Comment: NeurIPS22

The topology transition problem of transmission networks is becoming increasingly crucial with topological flexibility more widely leveraged to promote high renewable penetration. This paper proposes a novel methodology to address this problem. Aiming at achieving a bumpless topology transition regarding both static and dynamic performance, this methodology utilizes various eligible control resources in transmission networks to cooperate with the optimization of line-switching sequence. Mathematically, a composite formulation is developed to efficiently yield bumpless transition schemes with AC feasibility and stability both ensured. With linearization of all non-convexities involved and tractable bumpiness metrics, a convex mixed-integer program firstly optimizes the line-switching sequence and partial control resources. Then, two nonlinear programs recover AC feasibility, and optimize the remaining control resources by minimizing the $\mathcal{H}_2$-norm of associated linearized systems, respectively. The final transition scheme is selected by accurate evaluation including stability verification using time-domain simulations. Finally, numerical studies demonstrate the effectiveness and superiority of the proposed methodology to achieve bumpless topology transition., Comment: Accepted by TPWRS

Network topology has significant impacts on operational performance of power systems. While extensive research efforts have been devoted to optimization of network topology for improving various system performances, the problem of how to transition from the initial topology to the desired optimal topology requires study. To address this problem, we propose the concept of optimal topology transition (OTT). This aims to find the topology transition trajectory from an initial topology to a desired terminal topology, which optimizes certain transition performance and satisfies operational constraints. The OTT problem is further formulated as a mixed-integer program under certain assumptions. Next, we propose the formulation of transition-embedded topology optimization that is capable of optimizing network topology and its transition trajectory simultaneously. Considering the time complexity of directly solving the mixed-integer programs, an efficient problem-specific solution algorithm is developed. Finally, numerical studies demonstrate the effectiveness of the proposed OTT and transition-embedded topology optimization models, as well as the superiority of the obtained optimal transition trajectories compared to ad hoc transition trajectories., Comment: 13 page, accepted by TPWRS

When analyzing data from randomized clinical trials, covariate adjustment can be used to account for chance imbalance in baseline covariates and to increase precision of the treatment effect estimate. A practical barrier to covariate adjustment is the presence of missing data. In this paper, in the light of recent theoretical advancement, we first review several covariate adjustment methods with incomplete covariate data. We investigate the implications of the missing data mechanism on estimating the average treatment effect in randomized clinical trials with continuous or binary outcomes. In parallel, we consider settings where the outcome data are fully observed or are missing at random; in the latter setting, we propose a full weighting approach that combines inverse probability weighting for adjusting missing outcomes and overlap weighting for covariate adjustment. We highlight the importance of including the interaction terms between the missingness indicators and covariates as predictors in the models. We conduct comprehensive simulation studies to examine the finite-sample performance of the proposed methods and compare with a range of common alternatives. We find that conducting the proposed adjustment methods generally improves the precision of treatment effect estimates regardless of the imputation methods when the adjusted covariate is associated with the outcome. We apply the methods to the Childhood Adenotonsillectomy Trial to assess the effect of adenotonsillectomy on neurocognitive functioning scores.

EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in the deep neural networks. In this paper, we propose a QR-based ED method dedicated to the application scenarios of computer vision. Our proposed method performs the ED entirely by batched matrix/vector multiplication, which processes all the matrices simultaneously and thus fully utilizes the power of GPUs. Our technique is based on the explicit QR iterations by Givens rotation with double Wilkinson shifts. With several acceleration techniques, the time complexity of QR iterations is reduced from $O{(}n^5{)}$ to $O{(}n^3{)}$. The numerical test shows that for small and medium batched matrices (\emph{e.g.,} $dim{<}32$) our method can be much faster than the Pytorch SVD function. Experimental results on visual recognition and image generation demonstrate that our methods also achieve competitive performances., Comment: Accepted by ECCV22

Inserting an SVD meta-layer into neural networks is prone to make the covariance ill-conditioned, which could harm the model in the training stability and generalization abilities. In this paper, we systematically study how to improve the covariance conditioning by enforcing orthogonality to the Pre-SVD layer. Existing orthogonal treatments on the weights are first investigated. However, these techniques can improve the conditioning but would hurt the performance. To avoid such a side effect, we propose the Nearest Orthogonal Gradient (NOG) and Optimal Learning Rate (OLR). The effectiveness of our methods is validated in two applications: decorrelated Batch Normalization (BN) and Global Covariance Pooling (GCP). Extensive experiments on visual recognition demonstrate that our methods can simultaneously improve the covariance conditioning and generalization. Moreover, the combinations with orthogonal weight can further boost the performances., Comment: Accepted by ECCV22