A Feasible Conjugate Gradient Method for Calculating B\mathcal B-Eigenpairs of Symmetric Tensors

In this paper, we propose a feasible conjugate gradient (FCG) method for calculating ${\mathcal B}$-eigenpairs of a symmetric tensor ${\mathcal A}$. The method is an extension of the well-known conjugate gradient method for unconstrained optimization problems to some curve constrained optimization problems. The proposed FCG method can find a ${\mathcal B}$-eigenpair of a symmetric tensor ${\mathcal A}$ without the requirement that the orders of ${\mathcal A}$ and $\mathcal B$ are equal. We pay particular attention to the Polak-Rib\'ire-Polyak (PRP) type conjugate gradient method. We show that the FCG method with some Armijo-type line search is globally convergent. Our numerical experiments indicate the promising performance of the proposed method

Constructing Balance from Imbalance for Long-tailed Image Recognition

Long-tailed image recognition presents massive challenges to deep learning systems since the imbalance between majority (head) classes and minority (tail) classes severely skews the data-driven deep neural networks. Previous methods tackle with data imbalance from the viewpoints of data distribution, feature space, and model design, etc.In this work, instead of directly learning a recognition model, we suggest confronting the bottleneck of head-to-tail bias before classifier learning, from the previously omitted perspective of balancing label space. To alleviate the head-to-tail bias, we propose a concise paradigm by progressively adjusting label space and dividing the head classes and tail classes, dynamically constructing balance from imbalance to facilitate the classification. With flexible data filtering and label space mapping, we can easily embed our approach to most classification models, especially the decoupled training methods. Besides, we find the separability of head-tail classes varies among different features with different inductive biases. Hence, our proposed model also provides a feature evaluation method and paves the way for long-tailed feature learning. Extensive experiments show that our method can boost the performance of state-of-the-arts of different types on widely-used benchmarks. Code is available at https://github.com/silicx/DLSA.Comment: Accepted to ECCV 202

Finding the spectral radius of a nonnegative irreducible symmetric tensor via DC programming

The Perron-Frobenius theorem says that the spectral radius of an irreducible nonnegative tensor is the unique positive eigenvalue corresponding to a positive eigenvector. With this in mind, the purpose of this paper is to find the spectral radius and its corresponding positive eigenvector of an irreducible nonnegative symmetric tensor. By transferring the eigenvalue problem into an equivalent problem of minimizing a concave function on a closed convex set, which is typically a DC (difference of convex functions) programming, we derive a simpler and cheaper iterative method. The proposed method is well-defined. Furthermore, we show that both sequences of the eigenvalue estimates and the eigenvector evaluations generated by the method $Q$-linearly converge to the spectral radius and its corresponding eigenvector, respectively. To accelerate the method, we introduce a line search technique. The improved method retains the same convergence property as the original version. Preliminary numerical results show that the improved method performs quite well

Introgression of bacterial blight (BB) resistance genes Xa7 and Xa21 into popular restorer line and their hybrids by molecular marker-assisted backcross (MABC) selection scheme

Yihui1577 is an elite restorer line widely used in hybrid rice production in China, however, both the restorer and their derived hybrids are susceptible to bacterial blight (BB) caused by Xathomonas oryzae pv. oryzae (Xoo). In order to overcome this problem, we had introgressed two resistant genes Xa7 and Xa21 into Yihui1577 by marker-assisted backcross (MABC) with foreground selection scheme to speed up the process. Six breeding lines with different BB resistance genes: HH1202 (Xa7), HH1203 (Xa7), HH1204 (Xa21), HH1205 (Xa21), HH1206 (Xa7+Xa21) and HH1207 (Xa7+Xa21) were selected and crossed with four CMS and one TGMS lines. Seven most virulent and prevalent Xoo strains (PXO61, PXO99, ZHE173, GD1358, FuJ, YN24 and HeN11) from the Philippines and different provinces of China were inoculated for evaluating the BB-resistance of the selected lines and their derived hybrids. The results reveal that the two lines and their derived hybrids with single resistance gene Xa7 were resistant against six of the seven Xoo strains, except for PXO99. The lines with single resistance gene Xa21 were only susceptible to the Xoo strain FuJ, but some of their derived hybrids were susceptible to the Xoo strains FuJ and GD1358. Interestingly, the pyramiding lines carrying the two resistance genes Xa7 and Xa21 and also their derived hybrids were resistant against all the seven Xoo strains. The data of agronomic and grain quality characteristics demonstrated that the selected lines were similar to that of the recurrent parent Yihui1577. Corrective measures taken by way of introgression of BB-resistance genes: Xa7 and Xa21 into the popular restorer line, Yihui1577 through MABC approach for enhancing the BB-resistance level was effective and timely.Keywords: Bacterial blight, resistance gene, Xa7 and Xa21, MABC, inoculation and reaction, agronomic traits, grain qualit

D&D: Learning Human Dynamics from Dynamic Camera

3D human pose estimation from a monocular video has recently seen significant improvements. However, most state-of-the-art methods are kinematics-based, which are prone to physically implausible motions with pronounced artifacts. Current dynamics-based methods can predict physically plausible motion but are restricted to simple scenarios with static camera view. In this work, we present D&D (Learning Human Dynamics from Dynamic Camera), which leverages the laws of physics to reconstruct 3D human motion from the in-the-wild videos with a moving camera. D&D introduces inertial force control (IFC) to explain the 3D human motion in the non-inertial local frame by considering the inertial forces of the dynamic camera. To learn the ground contact with limited annotations, we develop probabilistic contact torque (PCT), which is computed by differentiable sampling from contact probabilities and used to generate motions. The contact state can be weakly supervised by encouraging the model to generate correct motions. Furthermore, we propose an attentive PD controller that adjusts target pose states using temporal information to obtain smooth and accurate pose control. Our approach is entirely neural-based and runs without offline optimization or simulation in physics engines. Experiments on large-scale 3D human motion benchmarks demonstrate the effectiveness of D&D, where we exhibit superior performance against both state-of-the-art kinematics-based and dynamics-based methods. Code is available at https://github.com/Jeffsjtu/DnDComment: ECCV 2022 (Oral