arXiv subjects

Runze Wang

Publications and source records attributed to Runze Wang.

At least 19 recordsLinked to original sources

arXiv2026

A stronger upper bound on the D-chromatic index

For a graph $G$, a proper edge coloring of $G$ is called a D-coloring if every diamond subgraph of $G$ is rainbow. Let $\chi'_D(G)$ be the D-chromatic index of $G$, which is the smallest integer $k$ such that $G$ admits a D-coloring with $k$ colors. Let $\Delta$ be the maximum degree of $G$. The only known Brooks-type upper bound on $\chi'_D(G)$ is $\frac{9}{16}\Delta^2 + \frac{1}{2}\Delta$, given by a greedy coloring. In this paper, using a probabilistic method, we obtain the first improvement upon this upper bound by proving that $\chi'_D(G) \le (1-c)\frac{9}{16}\Delta^2$ for some $c > 0$ and sufficiently large $\Delta$.

math.CO↗

arXiv2026

Parallel Time-Band Mixing with Learned Observation-Adding for Robust ASR Front-Ends

Speech enhancement is often used as a front-end for robust ASR, yet recurrent temporal and cross-band modules introduce sequential dependencies that reduce parallel efficiency. In this paper, we present a sequence-parallel band-split enhancement front-end built on a Parallel Time-Band Mixer (PTBM) block that eliminates within-block recurrent unrolling. PTBM integrates intra-band temporal mixing and per-frame cross-band attention within a unified parallel architecture, enabling efficient contextual modeling across both time and frequency dimensions. The system retains the mask-plus-residual reconstruction interface and introduces learned Observation-Adding (LOA) to suppress ASR-sensitive artifacts without development-set tuning. Experiments on DNS Challenge and CHiME-4 with frozen Whisper back-ends show that the proposed front-end consistently reduces word error rate relative to recurrent band-split baselines while requiring only 0.96 M parameters and 0.58 GMAC/s for the front-end network.

cs.SD↗

arXiv2026

Zelevinsky Segments and Hyperspecial Branching Laws for All Depth-Zero Representations of GL_N(F)

For every irreducible depth-zero representation of the general linear group over a non-Archimedean local field, parameterized by multisets of segments in the sense of Zelevinsky, we determine the complete decomposition of the space of vectors fixed by the pro-unipotent radical of a hyperspecial maximal compact subgroup. The decomposition is described explicitly in terms of the Zelevinsky parameters: the irreducible constituents are governed by Kostka numbers and Zelevinsky decomposition numbers, and they are naturally bounded between two partitions arising from the Zelevinsky segments of the representation and of its Aubert dual. In the generic case the result is given entirely by Kostka numbers. For general depth-zero Bernstein blocks, the multiplicities are products of the corresponding single-block multiplicities. We first prove, for an arbitrary unramified connected reductive group, that the functor of taking pro-unipotent fixed vectors intertwines Zelevinsky--Aubert duality on the p-adic side with Alvis--Curtis duality on the finite side. The proof for general linear groups combines Bushnell--Kutzko types, finite Harish--Chandra series, Iwahori--Hecke algebras, and the Zelevinsky classification to provide a complete and effective hyperspecial branching law for all irreducible depth-zero representations.

math.RT↗

arXiv2026

NaLA: A 3D Native LLM Layout Agent for High-quality 3D Scene Generation

Recently, Large Language Models (LLMs) have emerged as promising layout agents for 3D scene generation. Existing layout agents still suffer from implausible layout generation because most of them convert 3D assets and 3D layouts into textual descriptions as inputs and outputs, which involves severe information loss due to the modality gap between texts and 3D assets and 3D layouts. We propose NaLA, a native 3D LLM layout Agent for high-quality 3D scene generation by placing 3D assets in the scene. For the inputs, NaLA encodes 3D scene boundaries and 3D assets directly into the LLM, preserving fine-grained geometry and enabling explicit reasoning over relationships like collisions, surface supporting, and containment. To accurately output the positions and orientations of assets, NaLA adopts a coarse-to-fine prediction mechanism that first predicts discrete poses in an autoregressive manner and then refines the discrete poses with a continuous regression. Trained on diverse layout datasets, NaLA attains strong geometric perception and layout coherence. Experiments demonstrate that NaLA outperforms prior layout agents in both generation quality and inference efficiency, with comprehensive ablation studies to verify each component's effectiveness.

cs.CV↗

arXiv2026

Proper edge coloring with rainbow diamonds

Motivated by the B-coloring defined by Gy\'arf\'as and S\'ark\"ozy, we introduce a new edge coloring called \emph{D-coloring}. For a graph $G$, a D-coloring of $G$ is a proper edge coloring such that every diamond subgraph is rainbow. The \emph{D-chromatic index} of $G$, denoted by $\chi'_D(G)$, is the minimum number of colors needed for a D-coloring of $G$. Denote by $\Delta$ the maximum degree of $G$. We prove that $\chi'_D(G)\le \frac{9}{16}\Delta^2+\frac{1}{2}\Delta$, conjecture that $\chi'_D(G)\le \frac{1}{2}\Delta^2+\frac{1}{2}\Delta$, and verify this conjecture for $\Delta\le 5$.

math.CO↗

arXiv2026

Afford-VLA: Action-Aligned Visual Planning via Internalized Affordance

Vision-language-action (VLA) models have shown strong potential for generalist robot manipulation, yet they remain limited by insufficient spatial reasoning, particularly in determining where to interact in complex visual scenes. While recent efforts introduce various forms of visual planning to address this issue, existing approaches either rely on global geometric cues, symbolic intermediate representations, or externally generated visual signals, which are often weakly coupled with downstream action prediction. In this work, we revisit visual planning in VLA systems and argue that effective planning should be local, visually grounded, internally generated, and directly aligned with action. Based on this insight, we propose Afford-VLA, a unified framework that internalizes task-conditioned affordance as an explicit visual planning interface within VLA models. Concretely, we introduce learnable tokens to query task-relevant interaction regions, decode affordance masks from multimodal features, and convert them into compact embeddings that directly condition action generation. This design enables affordance to be both generated and utilized within the VLA, forming a tightly coupled perception-action pathway. To further support this integration, we adopt a training strategy that allows the affordance pathway to be jointly optimized with action prediction, improving its effectiveness for downstream control. We evaluate our method on multiple simulation benchmarks, including LIBERO, LIBERO-Plus, and SimplerEnv, achieving consistent state-of-the-art performance, along with strong real-world results. These findings demonstrate that internalizing affordance as action-aligned visual planning provides a powerful paradigm for improving VLA systems.

cs.RO↗

arXiv2026

Learning to Evolve: A Self-Improving Framework for Multi-Agent Systems via Textual Parameter Graph Optimization

Designing and optimizing multi-agent systems (MAS) is a complex, labor-intensive process of "Agent Engineering." Existing automatic optimization methods, primarily focused on flat prompt tuning, lack the structural awareness to debug the intricate web of interactions in MAS. More critically, these optimizers are static; they do not learn from experience to improve their own optimization strategies. To address these gaps, we introduce Textual Parameter Graph Optimization (TPGO), a framework that enables a multi-agent system to learn to evolve. TPGO first models the MAS as a Textual Parameter Graph (TPG), where agents, tools, and workflows are modular, optimizable nodes. To guide evolution, we derive "textual gradients," structured natural language feedback from execution traces, to pinpoint failures and suggest granular modifications. The core of our framework is Group Relative Agent Optimization (GRAO), a novel meta-learning strategy that learns from historical optimization experiences. By analyzing past successes and failures, GRAO becomes progressively better at proposing effective updates, allowing the system to learn how to optimize itself. Extensive experiments on complex benchmarks like GAIA and MCP-Universe show that TPGO significantly enhances the performance of state-of-the-art agent frameworks, achieving higher success rates through automated, self-improving optimization.

cs.AI↗

arXiv2026

The K_+-fixed vectors of Iwahori-spherical GL_n-representations: connections with Zelevinsky's segments

We study the space of K_+-fixed vectors of Iwahori-spherical representations of GL_n over a non-archimedean local field. For a generic Iwahori-spherical representation, we show that its decomposition into irreducible modules of the finite Lie group K/K_+ is controlled by a partition determined by the representation: an irreducible module occurs only if its partition is dominated by that partition, and when it occurs the multiplicity is a Kostka number. For an arbitrary irreducible Iwahori-spherical representation, we attach a partition from its data and prove a necessary condition: any occurring module must correspond to a partition dominated by this one, and the module attached to the partition itself occurs exactly once. We also give a combinatorial algorithm which, by further computation, determines precisely which modules actually occur and with what multiplicities. This answers a question of Prasad.

math.RT↗

arXiv2026

Wavefront sets for genuine representations of $\rm GL$-covers of Kazhdan--Patterson or Savin types

First, we consider general Brylinski--Deligne covers of the $p$-adic general linear groups, and discuss the theory of Bernstein--Zelevinsky derivatives. We also recall the Zelevinsky-type classification of the irreducible genuine spectrum for the Kazhdan--Patterson and Savin covers. Following this, for these two special families of covers, we determine the wavefront sets of their irreducible genuine representations, expressed in terms of the iterated degrees of the highest Bernstein--Zelevinsky derivatives. Finally, for Kazhdan--Patterson covers, we reinterpret this result on the wavefront set using a version of the local Langlands correspondence and the covering Barbasch--Vogan duality.

math.RT↗

arXiv2026

Classify all representation which contains a Steinberg in its hyperspecial subgroup

This paper addresses Question 1 posed by Dipendra Prasad in his recent problem list: classify all irreducible smooth representations of an unramified reductive p-adic group such that the space of vectors fixed by the pro-unipotent radical of a hyperspecial maximal compact subgroup, viewed as a representation of the finite reductive group obtained as the quotient of that hyperspecial subgroup by its pro-unipotent radical, contains the Steinberg representation. We prove that any such representation must be Iwahori-spherical, hence a subquotient of some unramified principal series. By a detailed analysis of the action of the Iwahori--Hecke algebra on the Iwahori-fixed space, we show that in each principal series there exists exactly one irreducible subquotient containing the Steinberg representation, and we give an explicit construction of this subquotient. Hence this gives a bijection between Weyl group orbits of unramified characters and irreducible representations containing the Steinberg representation in their hyperspecial subgroup. This classification is richer than Prasad's expectation: besides twists of the Steinberg representation and generic unramified representations, every principal series contributes a unique subquotient with the required property. The proof relies on establishing an isomorphism between the finite Iwahori--Hecke algebra of the finite Lie group obtained as the quotient of the hyperspecial subgroup by its pro-unipotent radical and the finite Hecke algebra of the p-adic group consisting of compactly supported I-bi-invariant functions on the hyperspecial subgroup, and comparing their actions on the Iwahori-fixed vectors.

math.RT↗

arXiv2026

Observation of Resonance of Kagome Flat Band Doublet

The interplay between local and itinerant electrons underpins many correlated and topological quantum states. Kagome lattices provide an ideal platform by hosting both flat (localized states) and dispersive bands (itinerant states), yet direct spectroscopic evidence of their dynamical coupling has remained elusive. Here we report the long-sought flat band resonance in the quasi-two-dimensional kagome bilayer material CsCr6Sb6. Using angle-resolved photoemission spectroscopy, transport measurements, and combined density functional theory and dynamical mean-field theory, we identify coexisting flat band doublets and dispersive bands near the Fermi energy. Upon cooling, the flat and dispersive bands exhibit a pronounced enhancement of spectral weight and hybridization, directly evidencing flat band resonance. Crucially, this emergence coincides with the onset of short-range antiferromagnetic correlations, contrasting sharply with conventional Kondo lattice behavior. Our findings demonstrate not only the long-sought flat band resonance in kagome materials, but also its unconventional correlation with magnetism.

cond-mat.str-el↗

arXiv2026

STAC: Plug-and-Play Spatio-Temporal Aware Cache Compression for Streaming 3D Reconstruction

Online 3D reconstruction from streaming inputs requires both long-term temporal consistency and efficient memory usage. Although causal variants of VGGT address this challenge through a key-value (KV) cache mechanism, the cache grows linearly with the stream length, creating a major memory bottleneck. Under limited memory budgets, early cache eviction significantly degrades reconstruction quality and temporal consistency. In this work, we observe that attention in causal transformers for 3D reconstruction exhibits intrinsic spatio-temporal sparsity. Based on this insight, we propose STAC, a Spatio-Temporally Aware Cache Compression framework for streaming 3D reconstruction with large causal transformers. STAC consists of three key components: (1) a Working Temporal Token Caching mechanism that preserves long-term informative tokens using decayed cumulative attention scores; (2) a Long-term Spatial Token Caching scheme that compresses spatially redundant tokens into voxel-aligned representations for memory-efficient storage; and (3) a Chunk-based Multi-frame Optimization strategy that jointly processes consecutive frames to improve temporal coherence and GPU efficiency. Extensive experiments show that STAC achieves state-of-the-art reconstruction quality while reducing memory consumption by nearly 10x and accelerating inference by 4x, substantially improving the scalability of real-time 3D reconstruction in streaming settings.

cs.CV↗

arXiv2026

Strong edge-coloring of sparse graphs with Ore-degree 7 or 8

In a strong edge-coloring of a graph $G=(V,E)$, any two edges of distance at most $2$ get distinct colors. The strong chromatic index of $G$, denoted by $\chi_s'(G)$, is the minimum number of colors needed in a strong edge-coloring of $G$. The Ore-degree of $G$ is defined by $\max\{d(u)+d(v):uv\in E\}$. In this paper, we apply the discharging method and make use of Hall's marriage theorem to prove two results toward a conjecture by Chen et al. First, we prove that if $G$ is a graph with Ore-degree $7$ and maximum average degree less than $\frac{34}{11}$, then $\chi_s'(G)\le 13$. This result improves the previous best bound from $\frac{40}{13}$ to $\frac{34}{11}$. Second, we prove that if $G$ is a graph with Ore-degree $8$ and maximum average degree less than $\frac{113}{31}$, then $\chi_s'(G)\le 20$.

math.CO↗

arXiv2026

Pollard's theorem in general abelian groups

We make further progress towards a Kneser-type generalization of Pollard's Theorem to general abelian groups. For two sets $A$ and $B$ in an abelian group $G$, the \emph{$t$-popular sumset} of $A$ and $B$, denoted by $A+_t B$, is the set of elements in $G$ each with at least $t$ representations of the form $a+b$, where $a\in A$ and $b\in B$. For $|A|,\, |B|\ge t\geq 2$, we prove that if \begin{align*} \sum_{i=1}^t |A+_i B|< t|A|+t|B|-\frac{4}{3}t^2+\frac{2}{3}t, \end{align*} then there exist $A'\subseteq A$ and $B'\subseteq B$ with $|A\setminus A'|+|B\setminus B'|\le t-1$, $A'+_t B'=A'+B'=A+_t B$, and $ \sum_{i=1}^t |A+_i B|\ge t|A|+t|B|-t|H|,$ where $H$ is the stabilizer of $A'+B'=A+_t B$. Our result improves the main quadratic term in the previous best bound from $-2t^2$ to $-\frac{4}{3}t^2$.

math.NT↗

arXiv2026

Geometric wavefront sets of genuine Iwahori-spherical representations

For Iwahori-spherical genuine representations of central covers with positive real Satake parameters, we prove the upper bound inequality for their geometric wavefront sets, formulated for general genuine representations in an earlier work by Gao--Liu--Lo--Shahidi. Meanwhile, we show the equality is attained for covers of type A groups and for some representations of covers of the exceptional groups. We also verify the equality for certain Iwahori-spherical representations occurring in regular unramified principal series; this uses and generalizes the earlier work of Karasiewicz--Okada--Wang on theta representations. Lastly, we determine the leading coefficients in the Harish-Chandra character expansion of a theta representation when its geometric wavefront set is of a special type.

math.RT↗

arXiv2025

Let It Flow: Agentic Crafting on Rock and Roll, Building the ROME Model within an Open Agentic Learning Ecosystem

Agentic crafting requires LLMs to operate in real-world environments over multiple turns by taking actions, observing outcomes, and iteratively refining artifacts. Despite its importance, the open-source community lacks a principled, end-to-end ecosystem to streamline agent development. We introduce the Agentic Learning Ecosystem (ALE), a foundational infrastructure that optimizes the production pipeline for agentic model. ALE consists of three components: ROLL, a post-training framework for weight optimization; ROCK, a sandbox environment manager for trajectory generation; and iFlow CLI, an agent framework for efficient context engineering. We release ROME, an open-source agent grounded by ALE and trained on over one million trajectories. Our approach includes data composition protocols for synthesizing complex behaviors and a novel policy optimization algorithm, Interaction-Perceptive Agentic Policy Optimization (IPA), which assigns credit over semantic interaction chunks rather than individual tokens to improve long-horizon training stability. Empirically, we evaluate ROME within a structured setting and introduce Terminal Bench Pro, a benchmark with improved scale and contamination control. ROME demonstrates strong performance across benchmarks like SWE-bench Verified and Terminal Bench, proving the effectiveness of ALE.

cs.AI↗

arXiv2025

Stoichiometry-Controlled Structural Order and Tunable Antiferromagnetism in $\mathrm{Fe}_{x}\mathrm{NbSe_2}$ ($0.05 \le x \le 0.38$)

Transition metal dichalcogenides (TMDs) enable magnetic property engineering via intercalation, but stoichiometry-structure-magnetism correlations remain poorly defined for Fe-intercalated $\mathrm{NbSe_2}$. Here, we report a systematic study of $\mathrm{Fe}_{x}\mathrm{NbSe_2}$ across an extended composition range $0.05 \le x \le 0.38$, synthesized via chemical vapor transport and verified by rigorous energy-dispersive x-ray spectroscopy (EDS) microanalysis. X-ray diffraction, magnetic, and transport measurements reveal an intrinsic correlation between Fe content, structural ordering, and magnetic ground states. With increasing $x$, the system undergoes a successive transition from paramagnetism to a spin-glass state, then to long-range antiferromagnetism (AFM), and ultimately to a reentrant spin-glass phase, with the transition temperatures exhibiting a nonmonotonic dependence on Fe content. The maximum N\'eel temperature ($T_{\mathrm{N}}$ = $\mathrm{175K}$) and strongest AFM coupling occur at $x=0.25$, where Fe atoms form a well-ordered $2a_0 \times 2a_0 $ superlattice within van der Waals gaps. Beyond $x = 0.25$, the superlattice transforms or disorders, weakening Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions and significantly reducing $T_{\mathrm{N}}$. Electrical transport exhibits distinct anomalies at magnetic transition temperatures, corroborating the magnetic state evolution. Our work extends the compositional boundary of Fe-intercalated $\mathrm{NbSe_2}$, establishes precise stoichiometry-structure-magnetism correlations, and identifies structural ordering as a key tuning parameter for AFM. These findings provide a quantitative framework for engineering altermagnetic or switchable antiferromagnetic states in van der Waals materials.

cond-mat.mtrl-sci↗

arXiv2025

Online-PVLM: Advancing Personalized VLMs with Online Concept Learning

Personalized Visual Language Models (VLMs) are gaining increasing attention for their formidable ability in user-specific concepts aligned interactions (e.g., identifying a user's bike). Existing methods typically require the learning of separate embeddings for each new concept, which fails to support real-time adaptation during testing. This limitation becomes particularly pronounced in large-scale scenarios, where efficient retrieval of concept embeddings is not achievable. To alleviate this gap, we propose Online-PVLM, a framework for online concept learning by leveraging hyperbolic representations. Our approach makes a train-free paradigm for concept embeddings generation at test time, making the use of personalized VLMs both scalable and efficient. In addition, we develop OP-Eval, a comprehensive and large-scale benchmark comprising 1,292 concepts and over 30K high-quality instances with diverse question types, designed to rigorously assess online concept learning in realistic scenarios. Extensive experiments demonstrate the state-of-the-art performance of our proposed framework. Our source code and dataset will be made available.

cs.CL↗