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This paper proposes to develop a new variant of the two-time-scale stochastic approximation to find the roots of two coupled nonlinear operators, assuming only noisy samples of these operators can be observed. Our key idea is to leverage the classic Ruppert-Polyak averaging technique to dynamically estimate the operators through their samples. The estimated values of these averaging steps will then be used in the two-time-scale stochastic approximation updates to find the desired solution. Our main theoretical result is to show that under the strongly monotone condition of the underlying nonlinear operators the mean-squared errors of the iterates generated by the proposed method converge to zero at an optimal rate $\mathcal{O}(1/k)$, where $k$ is the number of iterations. Our result significantly improves the existing result of two-time-scale stochastic approximation, where the best known finite-time convergence rate is $\mathcal{O}(1/k^{2/3})$.

Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if regular monos are adhesive, then the existence of a regular join for any pair of regular subobjects entails quasiadhesivity. It is also known (quasi)adhesive categories can be embedded in a Grothendieck topos via a functor preserving pullbacks and pushouts along (regular) monomorphisms. In this paper we extend these results to $\mathcal{M}, \mathcal{N}$-adhesive categories, a concept recently introduced to generalize the notion of (quasi)adhesivity. We introduce the notion of $\mathcal{N}$-adhesive morphism, which allows us to express $\mathcal{M}, \mathcal{N}$-adhesivity as a condition on the subobjects's posets. Moreover, $\mathcal{N}$-adhesive morphisms allows us to show how an $\mathcal{M},\mathcal{N}$-adhesive category can be embedded into a Grothendieck topos, preserving pullbacks and $\mathcal{M}, \mathcal{N}$-pushouts.

Dynamic scene graph generation (SGG) focuses on detecting objects in a video and determining their pairwise relationships. Existing dynamic SGG methods usually suffer from several issues, including 1) Contextual noise, as some frames might contain occluded and blurred objects. 2) Label bias, primarily due to the high imbalance between a few positive relationship samples and numerous negative ones. Additionally, the distribution of relationships exhibits a long-tailed pattern. To address the above problems, in this paper, we introduce a network named TD$^2$-Net that aims at denoising and debiasing for dynamic SGG. Specifically, we first propose a denoising spatio-temporal transformer module that enhances object representation with robust contextual information. This is achieved by designing a differentiable Top-K object selector that utilizes the gumbel-softmax sampling strategy to select the relevant neighborhood for each object. Second, we introduce an asymmetrical reweighting loss to relieve the issue of label bias. This loss function integrates asymmetry focusing factors and the volume of samples to adjust the weights assigned to individual samples. Systematic experimental results demonstrate the superiority of our proposed TD$^2$-Net over existing state-of-the-art approaches on Action Genome databases. In more detail, TD$^2$-Net outperforms the second-best competitors by 12.7 \% on mean-Recall@10 for predicate classification.

Diffusion models have emerged as powerful generative tools, rivaling GANs in sample quality and mirroring the likelihood scores of autoregressive models. A subset of these models, exemplified by DDIMs, exhibit an inherent asymmetry: they are trained over $T$ steps but only sample from a subset of $T$ during generation. This selective sampling approach, though optimized for speed, inadvertently misses out on vital information from the unsampled steps, leading to potential compromises in sample quality. To address this issue, we present the S$^{2}$-DMs, which is a new training method by using an innovative $L_{skip}$, meticulously designed to reintegrate the information omitted during the selective sampling phase. The benefits of this approach are manifold: it notably enhances sample quality, is exceptionally simple to implement, requires minimal code modifications, and is flexible enough to be compatible with various sampling algorithms. On the CIFAR10 dataset, models trained using our algorithm showed an improvement of 3.27% to 14.06% over models trained with traditional methods across various sampling algorithms (DDIMs, PNDMs, DEIS) and different numbers of sampling steps (10, 20, ..., 1000). On the CELEBA dataset, the improvement ranged from 8.97% to 27.08%. Access to the code and additional resources is provided in the github.

Accurate 3D object detection in large-scale outdoor scenes, characterized by considerable variations in object scales, necessitates features rich in both long-range and fine-grained information. While recent detectors have utilized window-based transformers to model long-range dependencies, they tend to overlook fine-grained details. To bridge this gap, we propose MsSVT++, an innovative Mixed-scale Sparse Voxel Transformer that simultaneously captures both types of information through a divide-and-conquer approach. This approach involves explicitly dividing attention heads into multiple groups, each responsible for attending to information within a specific range. The outputs of these groups are subsequently merged to obtain final mixed-scale features. To mitigate the computational complexity associated with applying a window-based transformer in 3D voxel space, we introduce a novel Chessboard Sampling strategy and implement voxel sampling and gathering operations sparsely using a hash map. Moreover, an important challenge stems from the observation that non-empty voxels are primarily located on the surface of objects, which impedes the accurate estimation of bounding boxes. To overcome this challenge, we introduce a Center Voting module that integrates newly voted voxels enriched with mixed-scale contextual information towards the centers of the objects, thereby improving precise object localization. Extensive experiments demonstrate that our single-stage detector, built upon the foundation of MsSVT++, consistently delivers exceptional performance across diverse datasets.

This paper addresses the challenges of real-time, large-scale, and near-optimal multi-agent pathfinding (MAPF) through enhancements to the recently proposed LaCAM* algorithm. LaCAM* is a scalable search-based algorithm that guarantees the eventual finding of optimal solutions for cumulative transition costs. While it has demonstrated remarkable planning success rates, surpassing various state-of-the-art MAPF methods, its initial solution quality is far from optimal, and its convergence speed to the optimum is slow. To overcome these limitations, this paper introduces several improvement techniques, partly drawing inspiration from other MAPF methods. We provide empirical evidence that the fusion of these techniques significantly improves the solution quality of LaCAM*, thus further pushing the boundaries of MAPF algorithms.

Covariate shift is a common transfer learning scenario where the marginal distributions of input variables vary between source and target data while the conditional distribution of the output variable remains consistent. The existing notions describing differences between marginal distributions face limitations in handling scenarios with unbounded support, particularly when the target distribution has a heavier tail. To overcome these challenges, we introduce a new concept called density ratio exponent to quantify the relative decay rates of marginal distributions' tails under covariate shift. Furthermore, we propose the local k-nearest neighbour regressor for transfer learning, which adapts the number of nearest neighbours based on the marginal likelihood of each test sample. From a theoretical perspective, convergence rates with and without supervision information on the target domain are established. Those rates indicate that our estimator achieves faster convergence rates when the density ratio exponent satisfies certain conditions, highlighting the benefits of using density estimation for determining different numbers of nearest neighbours for each test sample. Our contributions enhance the understanding and applicability of transfer learning under covariate shift, especially in scenarios with unbounded support and heavy-tailed distributions.

We study the edge-coloring problem in simple $n$-vertex $m$-edge graphs with maximum degree $\Delta$. This is one of the most classical and fundamental graph-algorithmic problems. Vizing's celebrated theorem provides $(\Delta+1)$-edge-coloring in $O(m\cdot n)$ deterministic time. This running time was improved to $O\left(m\cdot\min\left\{\Delta\cdot\log n, \sqrt{n}\right\}\right)$. It is also well-known that $3\left\lceil\frac{\Delta}{2}\right\rceil$-edge-coloring can be computed in $O(m\cdot\log\Delta)$ time deterministically. Duan et al. devised a randomized $(1+\varepsilon)\Delta$-edge-coloring algorithm with running time $O\left(m\cdot\frac{\log^6 n}{\varepsilon^2}\right)$. It was however open if there exists a deterministic near-linear time algorithm for this basic problem. We devise a simple deterministic $(1+\varepsilon)\Delta$-edge-coloring algorithm with running time $O\left(m\cdot\frac{\log n}{\varepsilon}\right)$. We also devise a randomized $(1+\varepsilon)\Delta$-edge-coloring algorithm with running time $O(m\cdot(\varepsilon^{-18}+\log(\varepsilon\cdot\Delta)))$. For $\varepsilon\geq\frac{1}{\log^{1/18}\Delta}$, this running time is $O(m\cdot\log\Delta)$.

In data-driven control and machine learning, a common requirement involves breaking down large matrices into smaller, low-rank factors that possess specific levels of sparsity. This paper introduces an innovative solution to the orthogonal nonnegative matrix factorization (ONMF) problem. The objective is to approximate input data by using two low-rank nonnegative matrices, adhering to both orthogonality and $\ell_0$-norm sparsity constraints. the proposed maximum-entropy-principle based framework ensures orthogonality and sparsity of features or the mixing matrix, while maintaining nonnegativity in both. Additionally, the methodology offers a quantitative determination of the ``true'' number of underlying features, a crucial hyperparameter for ONMF. Experimental evaluation on synthetic and a standard datasets highlights the method's superiority in terms of sparsity, orthogonality, and computational speed compared to existing approaches. Notably, the proposed method achieves comparable or improved reconstruction errors in line with the literature.