Searcharxiv⌕ Search

arXiv subjects

Zhiqi Chen

Publications and source records attributed to Zhiqi Chen.

At least 19 recordsLinked to original sources
arXiv2026

The decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness

In this paper, we discuss the decomposition of a Lie group with a left invariant pseudo-Riemannian metric and the uniqueness. The decomposition is defined by non-degenerate strong ideals of the Levi-Civita connection. Its factors are totally geodesic normal subgroups on the simply connected covering group. We explain its relation with the de Rham--Wu decomposition and with the usual decompositions of Lie algebras by explicit examples, including a non-flat Riemannian product which is indecomposable in the present sense. We also describe the possible mixed metric terms between strong factors. As applications, we obtain the factorwise reduction of the Einstein equation and of the geodesic equation. In particular, the strong factors are unique up to their order when the Ricci tensor is non-degenerate, and geodesic completeness reduces to completeness of the factors even when the strong decomposition is not orthogonal.

math.GR↗
arXiv2026

Positive biorthogonal curvature on $S^2\times T^2$

We construct explicit Riemannian metrics with positive biorthogonal curvature on $S^2\times T^2$, answering a question of Bettiol. In particular, positive biorthogonal curvature on a closed four-manifold does not force its fundamental group to be virtually free.

math.DG↗
arXiv2026

FeatureHospital: A Skill-Driven Multi-Agent Framework for Automated Algorithm Customization in Multi-View Multi-Label Feature Selection

Multi-view multi-label feature selection aims to identify a compact and informative feature subset from heterogeneous views while preserving discriminative information for multiple labels. Existing methods are generally developed from specific modeling perspectives and incorporate mechanisms tailored to particular data characteristics. Designing suitable feature selection algorithms across datasets with diverse and heterogeneous characteristics still relies heavily on expert knowledge and substantial manual effort, imposing considerable time and labor costs that severely hinder the practical adoption of feature selection. To address this problem, we propose FeatureHospital, a Skill-driven multi-agent framework for automated multi-view multi-label feature selection algorithm design. FeatureHospital first diagnoses the target dataset to identify its feature selection issues. Based on the diagnosis, specialist agents equipped with domain Skills then prescribe corresponding optimization strategies and Loss terms for different issues. After that, the resulting prescriptions are reconciled to remove overlaps and resolve conflicts before being integrated into a compact dataset-specific objective. Finally, the constructed objective is optimized to select the final feature subset. Experimental results demonstrate that FeatureHospital can construct effective feature selection algorithms for different datasets based on their individual characteristics.

cs.AI↗
arXiv2026

Drop-In Perceptual Optimization for 3D Gaussian Splatting

Despite their output being ultimately consumed by human viewers, 3D Gaussian Splatting (3DGS) methods often rely on ad-hoc combinations of pixel-level losses, resulting in blurry renderings. To address this, we systematically explore perceptual optimization strategies for 3DGS by searching over a diverse set of distortion losses. We conduct the first-of-its-kind large-scale human subjective study on 3DGS, involving 39,320 pairwise ratings across several datasets and 3DGS frameworks. A regularized version of Wasserstein Distortion, which we call WD-R, emerges as the clear winner, excelling at recovering fine textures without incurring a higher splat count. WD-R is preferred by raters more than $2.3\times$ over the original 3DGS loss, and $1.5\times$ over the current best method Perceptual-GS. WD-R also consistently achieves state-of-the-art LPIPS, DISTS, and FID scores across various datasets, and generalizes across recent frameworks, such as Mip-Splatting and Scaffold-GS, where replacing the original loss with WD-R consistently enhances perceptual quality within a similar resource budget (number of splats for Mip-Splatting, model size for Scaffold-GS), and leads to reconstructions being preferred by human raters $1.8\times$ and $3.6\times$, respectively. We also find that this carries over to the task of 3DGS scene compression, with $\approx 50\%$ bitrate savings for comparable perceptual metric performance.

cs.CV↗
arXiv2026

What Matters in Practical Learned Image Compression

One of the major differentiators unlocked by learned codecs relative to their hard-coded traditional counterparts is their ability to be optimized directly to appeal to the human visual system. Despite this potential, a perceptual yet practical image codec is yet to be proposed. In this work, we aim to close this gap. We conduct a comprehensive study of the key modeling choices that govern the design of a practical learned image codec, jointly optimized for perceptual quality and runtime -- including within the ablations several novel techniques. We then perform performance-aware neural architecture search over millions of backbone configurations to identify models that achieve the target on-device runtime while maximizing compression performance as captured by perceptual metrics. We combine the various optimizations to construct a new codec that achieves a significantly improved tradeoff between speed and perceptual quality. Based on rigorous subjective user studies, it provides 2.3-3x bitrate savings against AV1, AV2, VVC, ECM and JPEG-AI, and 20-40% bitrate savings against the best learned codec alternatives. At the same time, on an iPhone 17 Pro Max, it encodes 12MP images as fast as 230ms, and decodes them in 150ms -- faster than most top ML-based codecs run on a V100 GPU.

cs.CV↗
arXiv2025

Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?

Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning performance of large language models (LLMs), particularly on mathematics and programming tasks. Similar to how traditional RL helps agents explore and learn new strategies, RLVR is believed to enable LLMs to continuously self-improve, thus acquiring novel reasoning abilities beyond those of the corresponding base models. In this study we critically examine the current state of RLVR by systematically probing the reasoning capability boundaries of RLVR-trained LLMs across various model families, RL algorithms, and math, coding, and visual reasoning benchmarks, using pass@k at large k values as the evaluation metric. Surprisingly, we find that the current training setup does not elicit fundamentally new reasoning patterns. While RLVR-trained models outperform their base models at small k (e.g., k = 1), the base models achieve a higher pass@k score when k is large. Coverage and perplexity analyses show that the observed reasoning abilities originate from and are bounded by the base model. Treating the base model as an upper bound, our quantitative analysis shows that six popular RLVR algorithms perform similarly and remain far from optimal in leveraging the potential of the base model. By contrast, we find that distillation can introduce new reasoning patterns from the teacher and genuinely expand the model's reasoning capabilities. Overall, our findings suggest that current RLVR methods have not yet realized the potential of RL to elicit truly novel reasoning abilities in LLMs. This highlights the need for improved RL paradigms, such as continual scaling and multi-turn agent-environment interaction, to unlock this potential.

cs.AI↗
arXiv2025

Combining LLM Semantic Reasoning with GNN Structural Modeling for Multi-View Multi-Label Feature Selection

Multi-view multi-label feature selection aims to identify informative features from heterogeneous views, where each sample is associated with multiple interdependent labels. This problem is particularly important in machine learning involving high-dimensional, multimodal data such as social media, bioinformatics or recommendation systems. Existing Multi-View Multi-Label Feature Selection (MVMLFS) methods mainly focus on analyzing statistical information of data, but seldom consider semantic information. In this paper, we aim to use these two types of information jointly and propose a method that combines Large Language Models (LLMs) semantic reasoning with Graph Neural Networks (GNNs) structural modeling for MVMLFS. Specifically, the method consists of three main components. (1) LLM is first used as an evaluation agent to assess the latent semantic relevance among feature, view, and label descriptions. (2) A semantic-aware heterogeneous graph with two levels is designed to represent relations among features, views and labels: one is a semantic graph representing semantic relations, and the other is a statistical graph. (3) A lightweight Graph Attention Network (GAT) is applied to learn node embedding in the heterogeneous graph as feature saliency scores for ranking and selection. Experimental results on multiple benchmark datasets demonstrate the superiority of our method over state-of-the-art baselines, and it is still effective when applied to small-scale datasets, showcasing its robustness, flexibility, and generalization ability.

cs.AI↗
arXiv2024

Curvatures of metric Jordan algebras

In this paper, we investigate metric Jordan algebras, and follow the lines of the paper (J. Milnor: Curvatures of left invariant metrics on Lie groups. Adv. Math. (1976)). Firstly, we define the Jordan-Levi-Civita connection, then we show that every metric Jordan algebra admits a unique Jordan-Levi-Civita connection. Secondly, using the Jordan-Levi-Civita connection, we introduce three natural curvature tensors on metric Jordan algebras, and obtain the corresponding curvature formulas. Thirdly, based on these curvature formulas, we prove that every formally real Jordan algebra admits both a metric of non-positive Jordan curvature, and a Jordan-Einstein metric of negative Jordan scalar curvature. Besides, for nilpotent Jordan algebras, we prove that they admit no Jordan-Einstein metrics.

math.DG↗
arXiv2024

Topology-engineered orbital Hall effect in two-dimensional ferromagnets

Recent advances in manipulation of orbital angular momentum (OAM) within the paradigm of orbitronics present a promising avenue for the design of future electronic devices. In this context, the recently observed orbital Hall effect (OHE) occupies a special place. Here, focusing on both the second-order topological and quantum anomalous Hall insulators in two-dimensional ferromagnets, we demonstrate that topological phase transitions present an efficient and straightforward way to engineer the OHE, where the OAM distribution can be controlled by the nature of the band inversion. Using first-principles calculations, we identify Janus RuBrCl and three septuple layers of MnBi$_2$Te$_4$ as experimentally feasible examples of the proposed mechanism of OHE engineering by topology. With our work we open up new possibilities for innovative applications in topological spintronics and orbitronics.

cond-mat.mtrl-sci↗
arXiv2023

Pseudo-Riemannian geodesic orbit nilmanifolds of signature $\boldsymbol{(n-2,2)}$

The geodesic orbit property is useful and interesting in itself, and it plays a key role in Riemannian geometry. It implies homogeneity and has important classes of Riemannian manifolds as special cases. Those classes include weakly symmetric Riemannian manifolds and naturally reductive Riemannian manifolds. The corresponding results for indefinite metric manifolds are much more delicate than in Riemannian signature, but in the last few years important corresponding structural results were proved for geodesic orbit Lorentz manifolds. Here we extend Riemannian and Lorentz results to trans-Lorentz nilmanifolds. Those are the geodesic orbit pseudo Riemannian manifolds $M = G/H$ of signature $(n-2,2)$ such that a nilpotent analytic subgroup of $G$ is transitive on $M$. For that we suppose that there is a reductive decomposition $\g = \h \oplus \n \text{ (vector space direct sum) with } [\h,\n] \subset \n$ and $\n$ nilpotent. When the metric is nondegenerate on $[\n,\n]$ we show that $\n$ is abelian or 2-step nilpotent. That is the same result as for geodesic orbit Riemannian and Lorentz nilmanifolds. When the metric is degenerate on $[\n,\n]$ we show that $\n$ is a double extension of a geodesic orbit nilmanifold of either Riemannian or Lorentz signature.

math.DG↗
arXiv2023

The moment map for the variety of Leibniz algebras

We consider the moment map $m:\mathbb{P}V_n\rightarrow \text{i}\mathfrak{u}(n)$ for the action of $\text{GL}(n)$ on $V_n=\otimes^{2}(\mathbb{C}^{n})^{*}\otimes\mathbb{C}^{n}$, and study the functional $F_n=\|m\|^{2}$ restricted to the projectivizations of the algebraic varieties of all $n$-dimensional Leibniz algebras $L_n$ and all $n$-dimensional symmetric Leibniz algebras $S_n$, respectively. Firstly, we give a description of the maxima and minima of the functional $F_n: L_n \rightarrow \mathbb{R}$, proving that they are actually attained at the symmetric Leibniz algebras. Then, for an arbitrary critical point $[μ]$ of $F_n: S_n \rightarrow \mathbb{R}$, we characterize the structure of $[μ]$ by virtue of the nonnegative rationality. Finally, we classify the critical points of $F_n: S_n \rightarrow \mathbb{R}$ for $n=2$, $3$, respectively.

math.RA↗
arXiv2022

The classification of $ω$-Lie algebras

Zusmanovich gave a fundamental result on the structure of $ω$-Lie algebras. But up to now, the classification of $ω$-Lie algebras is still open. In this paper, we give a complete classification of $ω$-Lie algebras over $\mathbb C$.

math.RA↗
arXiv2021

On the Geometric Orbit Property for Lorentz Manifolds

The geodesic orbit property has been studied intensively for Riemannian manifolds. Geodesic orbit spaces are homogeneous and allow simplifications of many structural questions using the Lie algebra of the isometry group. Weakly symmetric Riemannian manifolds are geodesic orbit spaces. Here we define "naturally reductive" for pseudo-Riemannian manifolds and note that they are geodesic orbit spaces. A few years ago two of the authors proved that weakly symmetric pseudo-Riemannian manifolds are geodesic orbit spaces. In particular these results apply to pseudo-Riemannian Lorentz manifolds. There our main results are Theorems 4.2 and 5.1. In the Riemannian case the nilpotent isometry group for a geodesic orbit nilmanifold is abelian or $2$-step nilpotent. Examples show that this fails dramatically in the pseudo-Riemannian case. Here we concentrate on the geodesic orbit property for Lorentz nilmanifolds $G/H$ with $G = N \rtimes H$ and $N$ nilpotent. When the metric is nondegenerate on $[\mathfrak{n},\mathfrak{n}]$, Theorem 4.2 shows that $N$ either is at most $2$-step nilpotent as in the Riemannian situation, or is $4$-step nilpotent, but cannot be $3$-step nilpotent. Examples show that these bounds are the best possible. Surprisingly, Theorem 5.1 shows that $N$ is at most $2$-step nilpotent when the metric is degenerate on $[\mathfrak{n},\mathfrak{n}]$. Both theorems give additional structural information and specialize to naturally reductive and to weakly symmetric Lorentz nilmanifolds. Key Words: Geodesic Orbit Space; Lorentz nilmanifold; Weakly Symmetric Space; Naturally Reductive Space; Pseudo-Riemannian Manifold.

math.DG↗
arXiv2021

End-to-end Neural Video Coding Using a Compound Spatiotemporal Representation

Recent years have witnessed rapid advances in learnt video coding. Most algorithms have solely relied on the vector-based motion representation and resampling (e.g., optical flow based bilinear sampling) for exploiting the inter frame redundancy. In spite of the great success of adaptive kernel-based resampling (e.g., adaptive convolutions and deformable convolutions) in video prediction for uncompressed videos, integrating such approaches with rate-distortion optimization for inter frame coding has been less successful. Recognizing that each resampling solution offers unique advantages in regions with different motion and texture characteristics, we propose a hybrid motion compensation (HMC) method that adaptively combines the predictions generated by these two approaches. Specifically, we generate a compound spatiotemporal representation (CSTR) through a recurrent information aggregation (RIA) module using information from the current and multiple past frames. We further design a one-to-many decoder pipeline to generate multiple predictions from the CSTR, including vector-based resampling, adaptive kernel-based resampling, compensation mode selection maps and texture enhancements, and combines them adaptively to achieve more accurate inter prediction. Experiments show that our proposed inter coding system can provide better motion-compensated prediction and is more robust to occlusions and complex motions. Together with jointly trained intra coder and residual coder, the overall learnt hybrid coder yields the state-of-the-art coding efficiency in low-delay scenario, compared to the traditional H.264/AVC and H.265/HEVC, as well as recently published learning-based methods, in terms of both PSNR and MS-SSIM metrics.

eess.IV↗
arXiv2021

PDWN: Pyramid Deformable Warping Network for Video Interpolation

Video interpolation aims to generate a non-existent intermediate frame given the past and future frames. Many state-of-the-art methods achieve promising results by estimating the optical flow between the known frames and then generating the backward flows between the middle frame and the known frames. However, these methods usually suffer from the inaccuracy of estimated optical flows and require additional models or information to compensate for flow estimation errors. Following the recent development in using deformable convolution (DConv) for video interpolation, we propose a light but effective model, called Pyramid Deformable Warping Network (PDWN). PDWN uses a pyramid structure to generate DConv offsets of the unknown middle frame with respect to the known frames through coarse-to-fine successive refinements. Cost volumes between warped features are calculated at every pyramid level to help the offset inference. At the finest scale, the two warped frames are adaptively blended to generate the middle frame. Lastly, a context enhancement network further enhances the contextual detail of the final output. Ablation studies demonstrate the effectiveness of the coarse-to-fine offset refinement, cost volumes, and DConv. Our method achieves better or on-par accuracy compared to state-of-the-art models on multiple datasets while the number of model parameters and the inference time are substantially less than previous models. Moreover, we present an extension of the proposed framework to use four input frames, which can achieve significant improvement over using only two input frames, with only a slight increase in the model size and inference time.

cs.CV↗