arXiv subjects

Chao Liu

Publications and source records attributed to Chao Liu.

At least 19 recordsLinked to original sources

arXiv2026

A logarithmic error term for subset sums of zero-sum-free sets

For a positive integer $k$, let $f(k)$ be the minimum number of distinct nonempty subset sums of a zero-sum-free $k$-element set, where the minimum is taken over all finite abelian groups. We prove $f(k)\ge \frac{k^2}{2}-13k\log(k+1)-116k$. Together with the classical upper bound, this gives $f(k)=k^2/2+O(k\log k)$, with the optimal leading coefficient. As a consequence, the Olson constant of every finite abelian group $G$ satisfies $\mathrm{Ol}(G)\le\sqrt{2|G|}+O(\log|G|)$. The argument combines a triangular lower bound for repeated supports, a count using blocks of two and three copies, and a greedy expansion argument. No restriction is imposed on the order of the group or on the stabilizer of the set of subset sums.

math.CO↗

arXiv2026

Davenport constants with growing binary rank

We study the correction to the standard lower bound $D^*$ for Davenport constants of finite abelian groups with a growing elementary two-component. For every fixed nontrivial abelian $p$-group $H$ of odd order, we prove $D(H\oplus C_2^r)=D^*(H\oplus C_2^r)+(D(H)-1)\log_2 r+O_H(1)$, with a uniform version for varying $H$. For $C_3\oplus C_2^r$, we determine exact values on explicit infinite intervals of ranks. More generally, the correction is logarithmic or smaller precisely when the fixed group has at most one odd prime divisor. We show that the two-primary part affects the logarithmic coefficient: for $C_{24}\oplus C_2^r$, the ratio $(D-D^*)/\log_2 r$ has limsup at least $2.4933231\ldots>2$, whereas for $C_3\oplus C_2^r$ the limit is $2$. These upper limiting coefficients are unbounded even with the odd prime fixed. The proofs use binary codes and finite-field Fourier analysis.

math.CO↗

arXiv2026

Advancement or Acceleration? How Data Curation Improves LLM Training

While data curation is widely credited with improving large language model training, a basic question remains unresolved: does curation expand what a model can ultimately learn, or merely reach the same solution faster? In this paper, we formalize this distinction between advancement (improving the attainable performance) and acceleration (reaching the same performance with less data). Through an analytic characterization and real-world LLM experiments, we show that advancement requires a correctable train-target gap. When the baseline training and target objectives coincide, no curation policy improves the endpoint, although curation may still accelerate training. This reframes advancement as a property of the curation task rather than the curation method. Under a common gap-centric view of data mixture and selection, we operationalize this condition as the $Δ$-test, an observable discrepancy between the uncurated baseline's training and target losses that is computable prior to expensive curation. Across extensive experiments, an appreciably nonzero $Δ$ predicts persistent gains, whereas gains near $Δ=0$ tend to diminish as the training budget grows. Beyond individual methods, our findings recenter data curation on the task itself and point to target-set construction as a promising direction for shaping what curation can achieve.

cs.LG↗

arXiv2026

Yuvion VL: A Multimodal Foundation Model for Adversarial Content and AI Safety

General-purpose models often struggle to reliably identify and understand real-world multimodal risks, largely due to the inherent multimodal adversarial nature of content and AI safety. We present Yuvion VL, a family of multimodal large language models purpose-built for content and AI safety, with both instruction-tuned and reasoning-oriented variants. Yuvion VL addresses this gap by treating safety as an inherently adversarial and multimodal problem and designing the entire pipeline around adversarial robustness. For data construction, we develop an automated pipeline integrating adversarial-aware data synthesis with multi-stage quality control, producing large-scale, high-quality multimodal samples augmented with domain knowledge and reasoning annotations. For training, we adopt a three-stage pipeline that includes continued pretraining for risk-concept cross-modal alignment, instruct post-training for production-grade safety tasks, and reasoning post-training for enhanced interpretability and performance in complex tasks. We further introduce Confuse-then-Contrast Fine-Tuning, a contrastive framework that mines model-specific confusions and constructs multi-image contrastive groups to enforce explicit discrimination of fine-grained visual-semantic elements, enabling the model to distinguish between visually similar cases with different safety implications in adversarial safety tasks. To support rigorous evaluation, we further introduce Yuvion VL RiskEval (YVRE), a collection of benchmarks covering diverse open and internal evaluations, with a focus on content and AI safety, adversarial robustness, and real-world capability requirements. Experiments show that Yuvion VL-32B achieves industry-leading safety performance, surpassing comparably sized open-source models and best closed-source commercial models, while maintaining comparable general capabilities.

cs.CV↗

arXiv2026

A $\wedge$-like metallicity profile in the disk of the Sagittarius dwarf galaxy

Unveiling the properties of the progenitors that formed the tidal structures of the Milky Way (MW) is essential for exploring the MW's assembly history. Such studies further afford a unique opportunity to dissect the formation and evolution of dwarf galaxies by contrasting surviving and disrupted systems. However, reconstructing the intrinsic structure of progenitors solely from the positions and velocities of their tidal debris remains a formidable challenge. Here, we decode the chemo-kinematic signatures embedded in the stellar streams of the Sagittarius (Sgr) dwarf galaxy through N-body simulations. Our simulation reproduces a vertical metallicity gradient in the Sgr streams. We show that this feature is naturally explained if the stream originated from a disk component with a $\wedge$-like metallicity profile. Remarkably, similar metallicity profiles are identified in MaNGA survey data for a few (3/217) field dwarf galaxies, suggesting this feature is rare but not unique to Sgr. The vertical metallicity gradient of stellar streams preserves extra detailed galactic fossil records, enabling quantitative reconstruction of the peculiar structure of the satellite galaxy. The similar metallicity profiles of Sgr and MW raise the question of a possible special coevolution.

astro-ph.GA↗

arXiv2026

Star formation history of Draco revealed by DESI DR1: suppressed early star formation efficiency for Milky Way dwarf galaxies

Dwarf galaxies serve as fossils for understanding the early star formation history of the local Universe. In this work, we use stellar abundances for individual stars derived from the first data release of the Dark Energy Spectroscopic Instrument (DESI DR1) to investigate the star formation history of the dwarf spheroidal galaxy Draco. We simultaneously fit the stellar metallicity distribution function (MDF) and the [Mg/Fe]-[Fe/H] trend using the galactic chemical evolution (GCE) model flexCE. Our best-fit models imply a low star formation efficiency (SFE) of $0.003$ to $0.007\,\mathrm{Gyr}^{-1}$, which is about ten times lower than values reported in the literature, but consistent with recent SFE estimates for ultra-faint dwarf galaxies. By combining recent literature measurements, we find that the SFEs of Milky Way dwarf galaxies scale with stellar mass as $\mathrm{SFE}\propto M_\star^{0.24}$. A low star formation efficiency is associated with a strong outflow efficiency; we estimate a large wind mass-loading factor $η_{\mathrm{wind}}$ of approximately 172-260. This is well in line with the observed outflow-stellar mass relation and with the Feedback in Realistic Environment (FIRE) cosmological simulations. Our results demonstrate the power of large-scale, low-to-medium resolution stellar spectroscopic surveys to deliver robust constraints on the early formation history of galaxies in the local Universe.

astro-ph.GA↗

arXiv2026

On True Minimum Distances of Goppa Codes

Binary Goppa codes are important in coding theory and cryptography. It is well-known that the minimum distance of a binary Goppa code defined by a squarefree polynomial of degree $r$ is at least $2r+1$. Though from the classical results of C. J. Moreno, O. Moreno, F. Levy-dit-Vehel and S. Litsyn that the true minimum distances of binary Goppa codes are $2r+1$, when the extension field degree $m$ is larger than $(r-1)^{4r}$. There have only very few families of binary Goppa codes with determined true minimum distances. In this paper, we give necessary and sufficient conditions for binary Goppa codes such that their minimum distances are $2r+1$ and $2r+2$. Infinitely many infinite families of binary Goppa codes with minimum distance $2r+1$ are given. In particular, we construct such codes for every Goppa degree $r$ in the range $2^{h-1}<r<2^h$ over $\mathbb F_{2^{2h}}$. For every $2\le r\le\lfloor2^m/3\rfloor$, we also obtain at least $2^m-3r+1$ distinct monic squarefree Goppa polynomials of degree $r$ over $\mathbb F_{2^m}$, such that their related binary Goppa codes have minimum distance $2r+1$. We extend a criterion for $q$-ary Goppa codes to split auxiliary polynomials and obtain some infinite families of $q$-ary Goppa codes attaining their designed distances $r+1$. We also construct infinite families of binary Goppa codes with minimum distance exactly $2r+2$.

cs.IT↗

arXiv2026

IMF-aware N-body forward modelling of membership selection functions for young open clusters

We present an IMF-aware N-body forward-modelling framework, in which the stellar initial mass function (IMF) is an explicit input, to quantify the membership selection functions of open clusters, namely completeness and contamination as functions of magnitude. Accurate derivation of the IMF requires correcting for these selection effects, which otherwise distort the inferred present-day mass function. Our framework simulates clusters with IMF slopes $α_2 = -2.7, -2.3, -1.9$, converts them into synthetic Gaia observations, adds mock field populations, and recovers members with HDBSCAN to mimic observational membership selection. Applying this framework to 35 young open clusters (ages $\lesssim100$ Myr, distances $\lesssim600$ pc), we find declining completeness towards the faint limit; older, more expanded, and more diffuse models have lower completeness and higher contamination. For a given cluster, models with flatter IMFs yield modestly but systematically lower global completeness and higher contamination, despite initial cluster masses calibrated to the same observed member count. These models undergo more stellar evolution mass loss and expand more, resulting in lower projected stellar densities; their lower completeness is consistent with more diffuse clusters being harder to separate from field stars. Corrections derived from a mismatched IMF largely recover the total star counts but leave a larger distortion in the shape of the present-day luminosity function than those derived with the correct IMF. Because membership recovery is tied to a cluster's structural evolution and the specific membership algorithm used, our findings emphasize that selection functions should be inferred jointly with the IMF rather than assumed in advance.

astro-ph.GA↗

arXiv2026

GTSM: Gaussian Splatting with Thermal State-Space Dynamics for Spatio-Temporal Thermal Field Reconstruction and Prediction

Temperature-field reconstruction and prediction are important for condition monitoring, process analysis, and state assessment in industrial and dynamic environments. This work aims to recover a four-dimensional spatio-temporal thermal state field directly from two-dimensional observations, without requiring a predefined 3D model, prescribed thermodynamic equation, or predefined heating/cooling trajectory. To this end, we propose the Gaussian Thermal State-Space Model (GTSM), which represents thermal evolution through a shared scene-level latent process and Gaussian-specific local thermal states. The resulting continuous dynamics are propagated using differentiable RK2 integration, allowing thermal evolution to be inferred from multi-view and multi-temporal observations and continuously extrapolated beyond the observed interval. GTSM is designed as a backbone-agnostic thermal dynamics module for Gaussian representations and can be integrated with both static 3D Gaussian Splatting and dynamic 4D Gaussian Splatting, supporting thermal reconstruction and prediction under both static and time-varying target geometry. The reconstructed representation further enables novel-view thermal rendering and future-time thermal-state prediction. Experiments on real infrared sequences and synthetic dynamic thermal data demonstrate improved reconstruction accuracy and substantially stronger temporal extrapolation than representative baselines, while also validating the applicability of GTSM to deforming targets.

cs.CV↗

arXiv2026

LLMRec: Benchmarking Large Language Models on Recommendation Task

Recently, the fast development of Large Language Models (LLMs) such as ChatGPT has significantly advanced NLP tasks by enhancing the capabilities of conversational models. However, the application of LLMs in the recommendation domain has not been thoroughly investigated. To bridge this gap, we propose LLMRec, a LLM-based recommender system designed for benchmarking LLMs on various recommendation tasks. Specifically, we benchmark several popular off-the-shelf LLMs, such as ChatGPT, LLaMA, ChatGLM, on five recommendation tasks, including rating prediction, sequential recommendation, direct recommendation, explanation generation, and review summarization. Furthermore, we investigate the effectiveness of supervised finetuning to improve LLMs' instruction compliance ability. The benchmark results indicate that LLMs displayed only moderate proficiency in accuracy-based tasks such as sequential and direct recommendation. However, they demonstrated comparable performance to state-of-the-art methods in explainability-based tasks. We also conduct qualitative evaluations to further evaluate the quality of contents generated by different models, and the results show that LLMs can truly understand the provided information and generate clearer and more reasonable results. We aspire that this benchmark will serve as an inspiration for researchers to delve deeper into the potential of LLMs in enhancing recommendation performance. Our codes, processed data and benchmark results are available at https://github.com/williamliujl/LLMRec.

cs.IR↗

arXiv2026

Generalized Hamming Weights and Subcode Support Weight Distributions of Twisted Reed-Solomon Codes

In this paper, we determine the generalized Hamming weight hierarchies of two classes of twisted Reed--Solomon (TRS) codes. For TRS codes with one twist, we first determine all possible values of the generalized Hamming weights. We then give a complete characterization of the weight hierarchy in terms of the minimum distance of the dual code. Explicit conditions are derived for the minimum distances of the code and its dual, which make the whole weight hierarchy explicitly computable. As special cases, the obtained results recover several known characterizations for TRS codes to be MDS, NMDS codes, and $s$-gap AMDS codes. For TRS codes with two twists, we similarly determine the complete generalized Hamming weight hierarchy. In this case, the higher generalized Hamming weights are determined by the first two generalized Hamming weights of the dual code, for which explicit rank conditions are also obtained. In addition, we further determine the subcode support weight distributions of this class of single-twist TRS codes. More precisely, for each $1 \le r \le k$, we derive an explicit formula for the number of $r$-dimensional subcodes with a prescribed support size, thereby giving a complete description of the support distribution of subcodes.

cs.IT↗

arXiv2026

Agentic Real2Sim: Physics-based World Modeling with Vision-Language Agents

Real-to-sim conversion for robotic interaction with objects remains labor-intensive because it requires more than visual reconstruction: a streamlined real2sim process must recover scene geometries and object states, infer physical parameters, and assemble actors, objects, cameras, poses, and trajectories into a runnable physical simulation. Today this process still depends on brittle workflow glue across visual perception tools and simulators: manual tuning of visual foundation models, mesh cleanup, coordinate frame alignments, etc. We introduce \textit{Agentic Real2Sim}, a framework for generalized physical world modeling with vision-language agents that converts a real-world recording of object-robot interaction into a simulatable episodic twin, and connects the resulting twin to downstream policy fine-tuning and evaluation. We evaluate Agentic Real2Sim on rigid-object manipulation, deformable-object interaction, and humanoid motion scenes, spanning domains that are usually handled by separate Real2Sim pipelines. The framework's agentic decisions can be driven by an open-weight VLM backend at a small fraction of the cost of frontier models, while attaining a comparable conversion success rate. The framework further supports custom scene conversion, fine-tuning of a pretrained policy with data generated from converted episodes, and works effectively as a surrogate for real-world policy evaluation. The project site, including code is available at https://agentic-real2sim.github.io.

cs.RO↗

arXiv2026

Decomposing the Kinematics of SNR G180.0-01.7 with Medium-Resolution Spectra

The exceptionally large angular diameter and intrinsic optical faintness of the Galactic supernova remnant (SNR) G180.0-01.7 (S147) have historically hindered a comprehensive spectroscopic census of its filamentary structure. We present the first dedicated medium-resolution (R ~ 7500) spectroscopic study of S147 using the LAMOST Medium-Resolution Spectroscopic survey of Galactic Nebulae (MRS-N). By implementing multi-Gaussian decomposition on the H$α$, [NII], and [SII] emission complexes and applying combined spectroscopic and spatial criteria, we disentangle the shock-ionized filaments of the SNR from the pervasive foreground and background Diffuse Ionized Gas (DIG). Our analysis reveals a distinct bimodal radial velocity distribution for the SNR: a low-velocity population tracing the decelerated forward shock at a dense cavity wall, and a high-velocity population (with absolute radial velocities of ~ 70 $\pm$ 30 km/s) corresponding to ejecta within a low-density cavity. The co-existence of these populations provides kinematic evidence for the "supernova-in-a-cavity" scenario. Furthermore, we detect enhanced [SII]/H$α$ ratios in the DIG along the eastern and northern boundaries of the remnant, signaling shock compression of the ambient interstellar medium and highlighting remnant's multifaceted feedback.

astro-ph.GA↗

arXiv2026

Memorize, Adapt, Ignore: Diagnosing Robot Learning Mechanisms under Training Data Variation

Training data variation, whether through designing a domain randomization (DR) scheme in simulation or curating demonstrations for imitation learning, is a primary lever for improving the robustness of robotic manipulation policies. Yet its underlying mechanisms remain poorly understood, and practitioners typically select randomization parameters through expensive trial and error. We investigate these mechanisms through a series of case studies, randomizing object size, color, and type as well as scene lighting and linguistic prompts across settings including pick-and-place RL in ManiSkill and fine-tuning of vision-language-action (VLA) models on LIBERO and RoboTwin. We examine both model behavior and internal representations, using the empirical neural tangent kernel (NTK) as our primary diagnostic tool. We show that the NTK distinguishes a shift in the internal learning mechanism from \textit{memorizing} different situations with insufficient variation (e.g.\ learning what to do for a large cube, and what to do for a small cube) to \textit{adapting} to the situation at hand with sufficient variation. An NTK-based signal-to-noise ratio also helps distinguish when policies have learned to \emph{ignore} task-irrelevant factors (e.g.\ treating blue and red cubes identically, instead of learning a blue sub-policy and a red sub-policy). We use these diagnostics to develop practical guidance for designing DR schemes, selecting models, and detecting shortcut learning. We further compare different kinds of representations and validate our findings with real-world hardware experiments using ACT-based imitation learning.

cs.RO↗

arXiv2026

Kasner critical scaling in Einstein--Maxwell--scalar black holes with nonlinear collapse and scalarization

A critical scaling exponent of $1/2$ was numerically observed for the Kasner parameter of asymptotically flat scalarized black holes and conjectured to be universal [Phys.\ Rev.\ Lett.\ \textbf{136}, 251402 (2026)]. In the same static, spherically symmetric Einstein--Maxwell--scalar setting, we show that this exponent is not universal. We develop a rigorous mathematical framework and construct couplings realizing exponents $1/(2m)$ for any integer $m\ge1$ by tuning higher-order terms at fixed quadratic coupling parameter $μ$. Nonlinear interior collapse produces a spacelike Kasner singularity with $β_{\rm K}\propto\varepsilon^{-1}$, where $\varepsilon$ is the value of scalar field at the event horizon. An exterior branch satisfying $q/q_\star-1\propto\varepsilon^{2m}$, therefore, yields $β_{\rm K}\propto|q/q_\star-1|^{-1/(2m)}$, where $q$ is the charge-to-mass ratio and $q_\star$ its critical value. We also determine the prefactor explicitly. This recovers the $1/2$ law and establishes a hierarchy including $1/4$ and $1/6$.

gr-qc↗

arXiv2026

Photonics-GCCE: group collaborative-competitive evolution multi-agent framework for universal and autonomous optical design

Large language model (LLM)-empowered photonic agents connect natural-language intents to executable solvers, showing significant advantages over conventional optical design approaches. However, current multi-agent frameworks operate within a collaborative paradigm without extrinsic selective pressure, which could inherit shared blind spots, converge prematurely, and fail to accumulate transferable experience for intricate tasks. Here, we introduce a group photonics collaboration-compete evolution (GCCE) framework and its LLM instantiation, termed Photonics-GCCE. Two independent agent groups pursue the same design target and undergo structured competitive evaluation across refractive-index fidelity, fabrication sensitivity, algorithmic adequacy, and physical consistency. Each group comprises a leader and three specialist agents dedicated to materials, optimization, and code validation. Agents refine their skills through competitive evaluation across design rounds. Benchmarking across six device categories against single-agent and multi-agent baselines shows that Photonics-GCCE elevates composite scores into the high 90s, improves fabrication robustness by 15 to 17 points, and reduces solver iterations to roughly 40 rounds. A representative quasi?BIC demonstration achieves a practically fabricable design with a quality factor of 13120. Our results demonstrate Photonics-GCCE as a general-purpose and closed-loop framework for autonomous optical design, capable of producing high-performance, fabrication-ready devices across diverse nanophotonic tasks.

physics.optics↗

arXiv2026

Beyond Endpoint Performance: Process-Level Evaluation of Self-Evolving Agents

Self-evolving agents convert interaction feedback into persistent artifacts, such as memories or skills, which in turn guide subsequent decisions. As these artifacts are iteratively updated throughout an experience stream, the capabilities they support may evolve. Consequently, endpoint performance alone offers an incomplete view of self-evolution. Process-level evaluation is therefore essential to identify when a target capability emerges and whether later updates strengthen, preserve, or weaken it. Motivated by this, we propose \textsc{EvoPathBench}, a benchmark that tracks individual capabilities during artifact-level self-evolution. EvoPathBench fixes the base model, tools, freezes evolving artifacts at successive checkpoints, and evaluates the target capability on held-out episodes. This benchmark evaluates agent self-evolution using public trading data and calibrated trajectories. It tests three capabilities: generalization to unseen tasks, retention after unrelated learning, and rule adaptation to new evidence. Experimental results show that gains on similar unseen tasks often weaken under distribution shift, retention losses are concentrated in a minority of evolution paths, and no method achieves reliable rule adaptation. Moreover, while self-evolution enables agents to generate candidate artifacts with substantial held-out gains, the selected updates consistently fall short of realizing this potential. Together, these findings establish capability-level process evaluation as a foundation for analyzing self-evolution, identifying candidate evaluation and selection as key targets for improvement.

cs.AI↗

arXiv2026

DiagGen: Agentic Generation of Deformable Assets with Sim-based Diagnostics for Robotic Simulation

While simulation-ready deformable assets are essential for in-silico robotic manipulation tasks, existing generation frameworks typically assess physical plausibility after generation, leaving an object's simulated response unused as feedback for repairing upstream errors. We present DiagGen, an agentic framework that turns a single in-the-wild image into a simulation-ready deformable asset through a generate--simulate--diagnose--refine loop. DiagGen constructs part-aware geometry and material parameters, then uses a VLM (vision-language model)-based agent to select semantically informative regions, probe them in a physics simulator, observe material responses, and route evidence-backed repair cues to the responsible generation stage. Experiments on 40 assets show that diagnostics provides useful repair cues and can moderately improve the quality of generated deformable assets. Finally, we show that unlike assets generated from visual foundation models which may not be simulatable, DiagGen-generated deformables can be directly dropped into a high-fidelity physical simulator for the planning and simulation of contact-rich pick-and-place tasks. The project's website is https://diaggen.github.io/.

cs.RO↗