Depth of powers of the edge ideal of an increasing weighted path
We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.
math.AC↗
arXiv subjects
Jiaxin Li
Publications and source records attributed to Jiaxin Li.
DualView: Adaptive Local-Global Fusion for Multi-Hop Document Reranking
Multi-hop question answering requires aggregating information from multiple documents, a critical capability for knowledge-intensive applications. A fundamental challenge lies in efficiently identifying the minimal relevant document set from retrieved candidates while maintaining high recall. We present an efficient dual-view cascaded reranking framework for multi-hop document reranking. Operating as a lightweight post-retrieval stage over E5-base-v2 candidates, our architecture comprises: (1) a Local Scorer employing stacked cross-attention for fine-grained query-document relevance; and (2) a Global Scorer modeling inter-document dependencies via Transformer-based context aggregation. These views are dynamically fused through an Adaptive Gate conditioned on query semantics. Under the fixed candidate set reranking setting with offline cached embeddings, our model achieves competitive results, particularly outstanding on MuSiQue with 99.4% Top-4 Recall and 97.8% Full Hit accuracy at 4.0 ms latency (249 QPS). It substantially outperforms 600M-parameter cross-encoders (BGE-Large: 92.0% Recall, Jina-v3: 90.1% Recall) while maintaining 5 to 6 times lower latency. Ablation studies validate that both Local and Global views contribute substantially to multi-hop performance.
cs.IR↗
Pansharpening for Thin-Cloud Contaminated Remote Sensing Images: A Unified Framework and Benchmark Dataset
Pansharpening under thin cloudy conditions is a practically significant yet rarely addressed task, challenged by simultaneous spatial resolution degradation and cloud-induced spectral distortions. Existing methods often address cloud removal and pansharpening sequentially, leading to cumulative errors and suboptimal performance due to the lack of joint degradation modeling. To address these challenges, we propose a Unified Pansharpening Model with Thin Cloud Removal (Pan-TCR), an end-to-end framework that integrates physical priors. Motivated by theoretical analysis in the frequency domain, we design a frequency-decoupled restoration (FDR) block that disentangles the restoration of multispectral image (MSI) features into amplitude and phase components, each guided by complementary degradation-robust prompts: the near-infrared (NIR) band amplitude for cloud-resilient restoration, and the panchromatic (PAN) phase for high-resolution structural enhancement. To ensure coherence between the two components, we further introduce an interactive inter-frequency consistency (IFC) module, enabling cross-modal refinement that enforces consistency and robustness across frequency cues. Furthermore, we introduce the first real-world thin-cloud contaminated pansharpening dataset (PanTCR-GF2), comprising paired clean and cloudy PAN-MSI images, to enable robust benchmarking under realistic conditions. Extensive experiments on real-world and synthetic datasets demonstrate the superiority and robustness of Pan-TCR, establishing a new benchmark for pansharpening under realistic atmospheric degradations.
cs.CV↗
Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems
Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving the GEPs in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. We demonstrate a method for evaluating both the loss function and its gradients on near-term quantum devices. We validate numerically the algorithm's performance through simulations, and demonstrate its application to GEPs in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.
quant-ph↗
OmniXtreme: Breaking the Generality Barrier in High-Dynamic Humanoid Control
High-fidelity motion tracking serves as the ultimate litmus test for generalizable, human-level motor skills. However, current policies often hit a "generality barrier": as motion libraries scale in diversity, tracking fidelity inevitably collapses - especially for real-world deployment of high-dynamic motions. We identify this failure as the result of two compounding factors: the learning bottleneck in scaling multi-motion optimization and the physical executability constraints that arise in real-world actuation. To overcome these challenges, we introduce OmniXtreme, a scalable framework that decouples general motor skill learning from sim-to-real physical skill refinement. Our approach uses a flow-matching policy with high-capacity architectures to scale representation capacity without interference-intensive multi-motion RL optimization, followed by an actuation-aware refinement phase that ensures robust performance on physical hardware. Extensive experiments demonstrate that OmniXtreme maintains high-fidelity tracking across diverse, high-difficulty datasets. On real robots, the unified policy successfully executes multiple extreme motions, effectively breaking the long-standing fidelity-scalability trade-off in high-dynamic humanoid control.
cs.RO↗
Floor Plan-Guided Visual Navigation Incorporating Depth and Directional Cues
Current visual navigation strategies mainly follow an exploration-first and then goal-directed navigation paradigm. This exploratory phase inevitably compromises the overall efficiency of navigation. Recent studies propose leveraging floor plans alongside RGB inputs to guide agents, aiming for rapid navigation without prior exploration or mapping. Key issues persist despite early successes. The modal gap and content misalignment between floor plans and RGB images necessitate an efficient approach to extract the most salient and complementary features from both for reliable navigation. Here, we propose GlocDiff, a novel framework that employs a diffusion-based policy to continuously predict future waypoints. This policy is conditioned on two complementary information streams: (1) local depth cues derived from the current RGB observation, and (2) global directional guidance extracted from the floor plan. The former handles immediate navigation safety by capturing surrounding geometry, while the latter ensures goal-directed efficiency by offering definitive directional cues. Extensive evaluations on the FloNa benchmark demonstrate that GlocDiff achieves superior efficiency and effectiveness. Furthermore, its successful deployment in real-world scenarios underscores its strong potential for broad practical application.
cs.RO↗
The Great March 100: 100 Detail-oriented Tasks for Evaluating Embodied AI Agents
Recently, with the rapid development of robot learning and imitation learning, numerous datasets and methods have emerged. However, these datasets and their task designs often lack systematic consideration and principles. This raises important questions: Do the current datasets and task designs truly advance the capabilities of robotic agents? Do evaluations on a few common tasks accurately reflect the differentiated performance of various methods proposed by different teams and evaluated on different tasks? To address these issues, we introduce the Great March 100 (\textbf{GM-100}) as the first step towards a robot learning Olympics. GM-100 consists of 100 carefully designed tasks that cover a wide range of interactions and long-tail behaviors, aiming to provide a diverse and challenging set of tasks to comprehensively evaluate the capabilities of robotic agents and promote diversity and complexity in robot dataset task designs. These tasks are developed through systematic analysis and expansion of existing task designs, combined with insights from human-object interaction primitives and object affordances. We collect a large amount of trajectory data on different robotic platforms and evaluate several baseline models. Experimental results demonstrate that the GM-100 tasks are 1) feasible to execute and 2) sufficiently challenging to effectively differentiate the performance of current VLA models. Our data and code are available at https://rhos.ai/research/gm-100.
cs.RO↗
InfiniDepth: Arbitrary-Resolution and Fine-Grained Depth Estimation with Neural Implicit Fields
Existing depth estimation methods are fundamentally limited to predicting depth on discrete image grids. Such representations restrict their scalability to arbitrary output resolutions and hinder the geometric detail recovery. This paper introduces InfiniDepth, which represents depth as neural implicit fields. Through a simple yet effective local implicit decoder, we can query depth at continuous 2D coordinates, enabling arbitrary-resolution and fine-grained depth estimation. To better assess our method's capabilities, we curate a high-quality 4K synthetic benchmark from five different games, spanning diverse scenes with rich geometric and appearance details. Extensive experiments demonstrate that InfiniDepth achieves state-of-the-art performance on both synthetic and real-world benchmarks across relative and metric depth estimation tasks, particularly excelling in fine-detail regions. It also benefits the task of novel view synthesis under large viewpoint shifts, producing high-quality results with fewer holes and artifacts.
cs.CV↗
DensiCrafter: Physically-Constrained Generation and Fabrication of Self-Supporting Hollow Structures
The rise of 3D generative models has enabled automatic 3D geometry and texture synthesis from multimodal inputs (e.g., text or images). However, these methods often ignore physical constraints and manufacturability considerations. In this work, we address the challenge of producing 3D designs that are both lightweight and self-supporting. We present DensiCrafter, a framework for generating lightweight, self-supporting 3D hollow structures by optimizing the density field. Starting from coarse voxel grids produced by Trellis, we interpret these as continuous density fields to optimize and introduce three differentiable, physically constrained, and simulation-free loss terms. Additionally, a mass regularization penalizes unnecessary material, while a restricted optimization domain preserves the outer surface. Our method seamlessly integrates with pretrained Trellis-based models (e.g., Trellis, DSO) without any architectural changes. In extensive evaluations, we achieve up to 43% reduction in material mass on the text-to-3D task. Compared to state-of-the-art baselines, our method could improve the stability and maintain high geometric fidelity. Real-world 3D-printing experiments confirm that our hollow designs can be reliably fabricated and could be self-supporting.
cs.CV↗
Time-Varying Network Driver Estimation (TNDE) Quantifies Stage-Specific Regulatory Effects From Single-Cell Snapshots
Identifying key driver genes governing biological processes such as development and disease progression remains a challenge. While existing methods can reconstruct cellular trajectories or infer static gene regulatory networks (GRNs), they often fail to quantify time-resolved regulatory effects within specific temporal windows. Here, we present Time-varying Network Driver Estimation (TNDE), a computational framework quantifying dynamic gene driver effects from single-cell snapshot data under a linear Markov assumption. TNDE leverages a shared graph attention encoder to preserve the local topological structure of the data. Furthermore, by incorporating partial optimal transport, TNDE accounts for unmatched cells arising from proliferation or apoptosis, thereby enabling trajectory alignment in non-equilibrium processes. Benchmarking on simulated datasets demonstrates that TNDE outperforms existing baseline methods across diverse complex regulatory scenarios. Applied to mouse erythropoiesis data, TNDE identifies stage-specific driver genes, the functional relevance of which is corroborated by biological validation. TNDE offers an effective quantitative tool for dissecting dynamic regulatory mechanisms underlying complex biological processes.
q-bio.MN↗
PrefixKV: Adaptive Prefix KV Cache is What Vision Instruction-Following Models Need for Efficient Generation
Recently, large vision-language models (LVLMs) have rapidly gained popularity for their strong generation and reasoning capabilities given diverse multimodal inputs. However, these models incur significant computational and memory overhead during inference, which greatly hinders the efficient deployment in practical scenarios. The extensive key-value (KV) cache, necessitated by the lengthy input and output sequences, notably contributes to the high inference cost. Based on this, recent works have investigated ways to reduce the KV cache size for higher efficiency. Although effective, they generally overlook the distinct importance distributions of KV vectors across layers and maintain the same cache size for each layer during the next token prediction. This results in the significant contextual information loss for certain layers, leading to notable performance decline. To address this, we present PrefixKV, where "Prefix" means the top-ranked KV based on importance rather than position in the original sequence. It reframes the challenge of determining KV cache sizes for all layers into the task of searching for the optimal global prefix configuration. With an adaptive layer-wise KV retention recipe based on binary search, the maximum contextual information can thus be preserved in each layer, facilitating the generation. Extensive experiments demonstrate that our method achieves the state-of-the-art performance compared with others. It exhibits superior inference efficiency and generation quality trade-offs, showing promising potential for practical applications. Code is available at https://github.com/THU-MIG/PrefixKV.
cs.CV↗
Depth of powers of integrally closed edge ideals of edge-weighted paths
We compute the depth of powers of edge ideals of integrally closed edge-weighted paths.
math.AC↗
Spatial-Spectral Binarized Neural Network for Panchromatic and Multi-spectral Images Fusion
Remote sensing pansharpening aims to reconstruct spatial-spectral properties during the fusion of panchromatic (PAN) images and low-resolution multi-spectral (LR-MS) images, finally generating the high-resolution multi-spectral (HR-MS) images. Although deep learning-based models have achieved excellent performance, they often come with high computational complexity, which hinder their applications on resource-limited devices. In this paper, we explore the feasibility of applying the binary neural network (BNN) to pan-sharpening. Nevertheless, there are two main issues with binarizing pan-sharpening models: (i) the binarization will cause serious spectral distortion due to the inconsistent spectral distribution of the PAN/LR-MS images; (ii) the common binary convolution kernel is difficult to adapt to the multi-scale and anisotropic spatial features of remote sensing objects, resulting in serious degradation of contours. To address the above issues, we design the customized spatial-spectral binarized convolution (S2B-Conv), which is composed of the Spectral-Redistribution Mechanism (SRM) and Gabor Spatial Feature Amplifier (GSFA). Specifically, SRM employs an affine transformation, generating its scaling and bias parameters through a dynamic learning process. GSFA, which randomly selects different frequencies and angles within a preset range, enables to better handle multi-scale and-directional spatial features. A series of S2B-Conv form a brand-new binary network for pan-sharpening, dubbed as S2BNet. Extensive quantitative and qualitative experiments have shown our high-efficiency binarized pan-sharpening method can attain a promising performance.
cs.CV↗
StreamForest: Efficient Online Video Understanding with Persistent Event Memory
Multimodal Large Language Models (MLLMs) have recently achieved remarkable progress in video understanding. However, their effectiveness in real-time streaming scenarios remains limited due to storage constraints of historical visual features and insufficient real-time spatiotemporal reasoning. To address these challenges, we propose StreamForest, a novel architecture specifically designed for streaming video understanding. Central to StreamForest is the Persistent Event Memory Forest, a memory mechanism that adaptively organizes video frames into multiple event-level tree structures. This process is guided by penalty functions based on temporal distance, content similarity, and merge frequency, enabling efficient long-term memory retention under limited computational resources. To enhance real-time perception, we introduce a Fine-grained Spatiotemporal Window, which captures detailed short-term visual cues to improve current scene perception. Additionally, we present OnlineIT, an instruction-tuning dataset tailored for streaming video tasks. OnlineIT significantly boosts MLLM performance in both real-time perception and future prediction. To evaluate generalization in practical applications, we introduce ODV-Bench, a new benchmark focused on real-time streaming video understanding in autonomous driving scenarios. Experimental results demonstrate that StreamForest achieves the state-of-the-art performance, with accuracies of 77.3% on StreamingBench, 60.5% on OVBench, and 55.6% on OVO-Bench. In particular, even under extreme visual token compression (limited to 1024 tokens), the model retains 96.8% of its average accuracy in eight benchmarks relative to the default setting. These results underscore the robustness, efficiency, and generalizability of StreamForest for streaming video understanding.
cs.CV↗
Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs
For the edge ideal $I(\D)$ of a weighted oriented graph $\D$, we prove that its symbolic powers $I(\D)^{(t)}$ are Cohen-Macaulay for all $t\geqslant 1$ if and only if the underlying graph $G$ is composed of a disjoint union of some complete graphs. We also completely characterize the Cohen-Macaulayness of the ordinary powers $I(\D)^t$ for all $t\geqslant 2$. Furthermore, we provide a criterion for determining whether $I(\D)^t=I(\D)^{(t)}$.
math.AC↗
Depth and regularity of powers of edge ideals of edge-weighted trees
For an increasing weighted tree $G_ω$, we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal $I(G_ω)$. Moreover, if $G_ω$ is a strictly increasing weighted tree, we provide the minimal free resolution of $I(G_ω)$ and an exact formula for the regularity of all powers of $I(G_ω)$.
math.AC↗
Associated primes of powers of edge ideals of edge-weighted trees
In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.
math.AC↗
GAN decoder on a quantum toric code for noise-robust quantum teleportation
We propose a generative adversarial network (GAN)-based decoder for quantum topological codes and apply it to enhance a quantum teleportation protocol under depolarizing noise. By constructing and training the GAN's generator and discriminator networks using eigenvalue datasets from the code, we obtain a decoder with a significantly improved decoding pseudo-threshold. Simulation results show that our GAN decoder achieves a pseudo-threshold of approximately $p=0.2108$, estimated from the crossing point of logical error rate curves for code distances $d=3$ and $d=5$, nearly double that of a classical decoder under the same conditions ($p \approx 0.1099$). Moreover, at the same target logical error rate, the GAN decoder consistently achieves higher logical fidelity compared to the classical decoder. When applied to quantum teleportation, the protocol optimized using our decoder demonstrates enhanced fidelity across noise regimes. Specifically, for code distance $d=3$, fidelity improves within the depolarizing noise threshold range $P<0.06503$; for $d=5$, the range extends to $P<0.07512$. Moreover, with appropriate training, our GAN decoder can generalize to other error models. This work positions GANs as powerful tools for decoding in topological quantum error correction, offering a flexible and noise-resilient framework for fault-tolerant quantum information processing.
quant-ph↗