arXiv subjects

Guanghui Wang

Publications and source records attributed to Guanghui Wang.

At least 19 recordsLinked to original sources

arXiv2026

Fourier level inequalities on the discrete cube via complex hypercontractivity and Riesz transforms

Eldan's level-$1{:}3$ inequality is a central tool in his second-order correlation inequalities for increasing Boolean functions. His proof is going to Gaussian space and uses an entropy estimate for second Hermite tensors. We give a direct proof on the discrete hypercube. For increasing real-valued functions $f,g:\{0,1\}^n\to\mathbb R$, we prove $$ W_3[f,g]\ge -2W_1[f,g]\log\!\left(\frac{\sqrt{\mathrm{Var}(f)\mathrm{Var}(g)}}{W_1[f,g]}\right). $$ The proof combines complex hypercontractivity with the discrete Riesz transforms. We also give a short proof of a level-$1:d$ inequality obtained by Keller and Kindler. As an application, we recover Eldan's correlation inequality with a slight improvement. If $f,g:\{0,1\}^n\to\{0,1\}$ are increasing and $g$ is antipodal, then $$ \mathrm{Cov}(f,g)\ge \frac1{24}\,\frac{\sum_i\mathrm{Inf}_i[f]\mathrm{Inf}_i[g]}{\sqrt{\log\!\left(4e\sqrt{\mathrm{Var}(f)\mathrm{Var}(g)}/(\sum_i\mathrm{Inf}_i[f]\mathrm{Inf}_i[g])\right)}}, $$ where the square-root logarithm cannot be improved as shown in the OR--majority example.

math.CO↗

arXiv2026

Large tight components and Dirac thresholds for tight Hamilton cycles

For every odd integer $r\ge1$, let $q_r=1-2^{-r}\binom r{(r-1)/2}$. We show that, for every odd $r\ge3$ and sufficiently large $n$, every $n$-vertex $r$-uniform hypergraph with at least $q_r\binom nr$ edges contains a tight component with at least $(1/2-o(1))\binom nr$ edges. This confirms a conjecture posed by Lang and Sanhueza-Matamala in 2024. As an application, for every odd $r\ge1$ and every integer $k\ge\lceil r(3-2q_r)\rceil$, we prove that the asymptotic minimum $(k-r)$-degree threshold for a tight Hamilton cycle in a $k$-uniform hypergraph is $q_r$, which settles, in this range, another conjecture of Lang and Sanhueza-Matamala in 2022 stating that the lower-bound construction due to Han and Zhao is asymptotically optimal. Our proof combines an isoperimetric inequality for Johnson graphs with a Kruskal-Katona-type theorem, which is of independent interest.

math.CO↗

arXiv2026

Physical structure as an organizing principle for universal Hamiltonian learning

Density functional theory (DFT) gives the electronic structure of materials, but its cost limits large-supercell calculations and materials screening. Machine-learned Hamiltonians bypass the self-consistent cycle but are usually system-specific; universal ones could cover new compositions and disordered solids. Such models must generalize across chemistry and keep downstream properties physical, while staying inexpensive for large cells. Here we introduce UniTB, a universal E(3) equivariant Hamiltonian representation framework that integrates physical priors rooted in density-functional tight-binding theory with deep learning. UniTB's network, which corrects a prior Hamiltonian, generalizes across chemistry through a mixture of experts routed by that prior and a charge-equilibration head as in self-consistent-charge tight binding. A projection bounds band shifts from the prior, suppressing spurious states and keeping downstream properties physical. We provide the fastest SO(2) tensor-product GPU kernels for the network. The variant UniTB-Flash assembles its prior from two-center tables at $O(N)$ cost for $N$ atoms, against $O(N\log N)$ on a grid. Trained on 29,242 crystals, UniTB reaches a 0.48 meV matrix-element error on nonmagnetic test crystals spanning 68 elements. Without amorphous training data, both models agree with DFT optics and conductivity of amorphous Ge-Sb-Te. UniTB-Flash ranks candidates with no significant difference from UniTB, whose property values are more accurate; together they screen 16,195 crystals for five application domains of industrial relevance.

cond-mat.mtrl-sci↗

arXiv2026

From Debate to Decision: Conformal Social Choice for Safe Multi-Agent Deliberation

Multi-agent debate improves LLM reasoning, yet agreement is not evidence of correctness. When agents converge on a wrong answer through social reinforcement, consensus stopping commits that error to automated action with no recourse. We introduce Conformal Social Choice, a post-hoc layer that converts debate outputs into calibrated act-versus-escalate decisions. Verbalized probability distributions from heterogeneous agents are aggregated via a linear opinion pool and calibrated with split conformal prediction, yielding fixed-round marginal coverage: at any pre-specified round, the correct answer is included with probability ${\geq}\,1{-}α$, without assumptions on individual model calibration. A hierarchical action policy maps singletons to autonomous action and larger sets to human escalation. Across eight MMLU-Pro domains and two additional benchmarks, fixed-round coverage stays close to target. The key finding is not that debate becomes more accurate, but that the conformal layer makes its failures actionable: at the final round, 81.9\% of wrong-consensus cases are flagged by non-singleton sets at $α{=}0.05$. Separately, among cases that reach a singleton before the final round, accuracy reaches 90.0--96.8\% on MMLU-Pro (up to 22.1pp above consensus stopping): a selection effect, not a reasoning improvement. Simple probability- and entropy-threshold rules attain comparable interception; conformal's distinct value is a finite-sample fixed-round coverage guarantee together with explicit candidate sets for escalation. Adaptive first-singleton stopping is evaluated empirically and not covered by this guarantee.

cs.AI↗

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

Progressive Subset Selection and Cascaded Consistency for Unsupervised Vision-Language Model Adaptation

Pretrained Vision-Language Models (PVLMs) achieve strong zero-shot recognition but often suffer performance degradation under target-domain shift. Unsupervised adaptation provides a practical way to improve target-domain performance without labeled data, but it remains challenging because pseudo-labels generated by the model can be unreliable and no labeled validation set is available for model selection or early stopping. We propose a simple framework for unsupervised PVLM adaptation that combines progressive margin-based subset selection with cascaded consistency learning. The subset selection strategy constructs a class-balanced pseudo-labeled set using prediction margins and gradually expands it during training, enabling adaptation to start from reliable supervision anchors before incorporating broader target-domain data. Cascaded consistency learning further exploits unlabeled samples by using temporally smoothed teacher predictions on weakly augmented views to supervise student predictions on strongly augmented views, with confidence filtering to reduce the influence of uncertain pseudo-labels. To preserve the pretrained embedding structure, the framework updates only normalization parameters in the visual encoder and class prototypes initialized from text prompts. Experiments across multiple recognition benchmarks with both CLIP and SigLIP backbones show consistent improvements over zero-shot baselines and competitive performance against recent unsupervised PVLM adaptation methods. These results suggest that progressive pseudo-label selection and teacher-guided consistency provide an effective and lightweight strategy for adapting PVLM classifiers without labeled target data.

cs.CV↗

arXiv2026

Moment-Calibrated Conformal Prediction with Side Information

For a fixed conformal score function, standard split conformal prediction calibrates a prediction set using the empirical distribution of the conformal scores, without using available side information about the data. We propose a moment-calibrated approach that uses such information to reduce variability across calibration data sets. Side information involving the covariates, the response, or both is expressed as moment restrictions, which are enforced through empirical likelihood weights on the calibration data points. The resulting weighted empirical distribution of the scores determines the weighted empirical quantile without changing the score function. We establish finite-sample bounds on training-conditional and marginal coverage of the moment-calibrated prediction set. We derive asymptotic distributions for training-conditional coverage and average prediction-set size, show that their asymptotic variances are no larger than the corresponding variances under standard split conformal prediction, and characterize when the reductions are strict. In the semi-supervised setting, we identify an optimal moment function of a given covariate representation, develop implementations using prespecified moment functions or a function learned by cross-fitting, and quantify the effect of the unlabeled sample size. We also extend the method to coverage conditions indexed by a class of functions of the covariates through weighted quantile regression. Numerical studies demonstrate the effectiveness of the proposed methods.

stat.ME↗

arXiv2026

Who Verifies the Verifier? Co-Evolving Inspectable Graders with Self-Improving Agents

We changed the agent: did it actually get better? Every self-improving agent loop answers this hundreds of times, and every answer comes from a verifier. On open-ended tasks none exists, so the loop is handed a hand-written rubric or a bare LLM judge grading output from a model like itself, inviting reward hacking and shared blind spots. We make the verifier the evolving object: an inspectable expression over small, mostly deterministic drawback detectors, synthesized from clustered failures, gated at birth, and selected for agreement with a ten-item anchored reference set plus consensus over unlabeled outputs, never for the agent's score. On MBPP+ it gains +0.21 held-out agreement over the hand-authored seed composition, on every seed, and ends ahead of the bare LLM judge it contains. One finding should change how co-evolved verifiers are validated: removing the anchor guards collapses the verifier into a vacuous always-pass grader, yet that collapsed verifier trains skills just as well. Downstream task score cannot certify a self-evolved verifier. Score does answer sufficiency, and there an evolved verifier can substitute: Double Ratchet, pairing the verifier with a lifecycle-managed skill loop, retains 88-110% of the lift that ground truth or a rubric buys the same loop, across code generation, enterprise text-to-SQL, and reference-free report generation. When evolved skills gamed the report rubric, an outer judge caught it and one added detector repaired it; the judge itself was wrong until given the task contract.

cs.AI↗

arXiv2026

An asymptotic bound for the Bermond--Thomassen Conjecture

The Bermond--Thomassen Conjecture asserts that every digraph with minimum out-degree at least $2k-1$ contains $k$ disjoint directed cycles; it remains open in general. We asymptotically resolve it: there exist an absolute constant $K$ and a function $g(k)=o(k)$, independent of $n$, such that every $n$-vertex finite simple loopless digraph with minimum out-degree at least $2k+g(k)$ contains $k$ disjoint directed cycles for all integers $k\ge K$ and $n\ge1$. In fact we obtain the explicit error term $g(k)=O(k^{3/4}\sqrt{\log k})$.

math.CO↗

arXiv2026

UnitBoost: Managing Compound LLM Systems with a Merge Operator, Not a Model

Compound LLM systems often solve a coordination problem by adding a higher-level LLM. The resulting meta-agent reads workers' outputs, writes the final answer, allocates later calls, and decides when to stop. It is expressive, but it also concentrates three control decisions in an opaque, order-sensitive model call. We ask whether the manager needs to be generative at all. UnitBoost replaces that model with a defined meta-level operator: a task-given unit map turns worker outputs into slot-value proposals, a constrained argmax assembles the output, and the slots left unfilled or unsupported become an explicit residual for the next round. The operator is order-free, records unit provenance, and gives a simple guarantee: without coupling constraints, unit-wise maximization under the same admission score dominates selection of any complete candidate. On three held-out benchmarks, it exceeds the best single candidate chosen with gold labels by 0.060-0.195 absolute task-score points and input-matched generative managers by 0.048-0.076. Replacing only the management step improves six compound-system configurations by 0.013-0.182. Residual-directed rounds raise FanOutQA cell F1 from 0.4778 to 0.5524; matched controls show that the true residual outperforms random targets and ordinary rereading, while a label-free supply signal flags exhaustion after one unproductive round. The same analysis measures three conditions in which no such gain is available (one indivisible unit, unavailable unit identity, and an endpoint that charges for every emitted unit) and quantifies cross-unit coupling as a repair cost. The manager gives up semantic freedom and gains order invariance, unit provenance, and testable failure conditions.

cs.AI↗

arXiv2026

Metrics That Write Themselves: Evolving an Evaluator from Its Own Blind Spots

Agents improve quickly against a reliable automatic metric and stall without one, and the applications that need them most, report generation among them, are the ones nobody knows how to score. Can the metric write itself? Saying what makes an answer good is hard; pointing at something wrong with one is easier, so the metric we evolve is a pool of small Python operators that each flag a candidate for one named defect, or abstain, and vote. Asking a model for operators directly does not work: 183 candidates realise only 96 distinct behaviours, from one narrow region of an enormous space. EvalCEGAR instead borrows counterexample-guided abstraction refinement from program verification. It reads the pool as an abstraction and searches for a collision, two answers the operators score identically, one correct and one not. That pair, not a prompt, is the authoring request, and when a collision defeats every attempt the loop widens what an operator may read rather than resampling. On MBPP+ and HumanEval+, a sandbox whose hidden unit tests give exact ground truth, the loop writes a 55-line operator that closes 15.4% of the gap between flagging nothing and a perfect filter on 428 unseen tasks (+0.0065, p=0.0010) at a quarter of our best hand-written operator's flags. On the benchmark it never saw it matches that operator's effect exactly on a third of the flags. Six of eight runs admit such an operator and all six help out of sample; our 15 hand-written operators applied together as one filter lose accuracy. An LLM judge on the same information ties that delta on a nearly disjoint set of candidates, and charges a model call per candidate forever where the operator charges none.

cs.AI↗

arXiv2026

The Erdős--Hajnal hypergraph Ramsey problem for $r_4(6,n)$

The Ramsey number $r_k(s,n)$ is the smallest integer $N$ such that every $N$-vertex $k$-graph contains either a copy of $K_s^{(k)}$ or an independent set of size $n$. Erdős and Hajnal conjectured that for every fixed $s>k\ge 4$, one has $r_k(s,n)\ge \operatorname{twr}_{k-1}(Ω(n))$. This conjecture was independently verified by Mubayi and Suk, and by Conlon, Fox and Sudakov, for $k\ge4$ and $s\ge k+3$. In this paper, we prove that $r_4(6,n)\ge 2^{2^{cn}}$ for some absolute constant $c>0$, improving upon our previous bound. Consequently, we confirm the Erdős--Hajnal conjecture for $r_k(k+2,n)$ for all fixed $k\ge4$.

math.CO↗

arXiv2026

Limiting Pointwise Decay for the compressible isentropic Navier-Stokes equations

We study the long-time pointwise behavior of small localized perturbations of a constant state for the one-dimensional compressible isentropic Navier-Stokes equations. After subtracting the two Burgers diffusion waves, the convergent sum of all higher-order diffusion waves, and the cross-family viscous corrections, we prove a cone-preserving pointwise estimate for the exact physical remainder and, in particular, \[ |R_i(x,t)|\leq C E_N\log(2+t)Ψ_i(x,t), \qquad \sup_{x\in\mathbb R}Ψ_i(x,t)\leq C(1+t)^{-1}. \] Here $E_N$ measures the size of the initial data and $Ψ_i$ is the cone-resolved weight; both are defined precisely in the main theorem below. Thus $\|R_i(t)\|_{L^\infty}\leq C E_N(1+t)^{-1}\log(2+t)$. The key new idea is to apply a familywise Cole--Hopf transformation to the spatial antiderivative of the remainder, which exactly eliminates the critical same-family first-order feedback. We further construct an approximate Green function adapted to the two characteristic families and combine it with Gaussian-mode extraction and a Kawashima-type energy argument. This yields a cone-preserving estimate at the limiting decay rate, up to a logarithmic loss.

math.AP↗

arXiv2026

A Finite-Entropy Criterion for the Entropic Conditional Central Limit Theorem

We prove a finite-entropy criterion for the entropic conditional central limit theorem. Let $(ξ_i,η_i)_{i\geq 1}$ be independent copies of a pair $(ξ,η)$, and set $W_n=n^{-1/2}\sum_{i=1}^n ξ_i$ and $\boldsymbolη_n=(η_1,\ldots,η_n)$. Under the assumptions that $\mathbb{E}\operatorname{Var}(ξ\midη)<\infty$ and that the conditional law of $ξ$ given $η$ is absolutely continuous almost surely, we show that $\mathbb{E}h(W_n\mid\boldsymbolη_n)$ converges to the Gaussian entropy $\frac12\log(2πeσ^2)$, where $σ^2=\mathbb{E}\operatorname{Var}(ξ\midη)$, if and only if $\mathbb{E}h(W_{n_0}\mid\boldsymbolη_{n_0})>-\infty$ for some $n_0$. The main technical ingredient is a continuity theorem for Fisher information under Gaussian smoothing, which allows us to replace the finite expected conditional Fisher-information assumption by a necessary and sufficient finite-entropy condition.

math.PR↗

arXiv2026

Beyond Isolated Heads: Multi-Overlapped-Head Self-Attention for Vision Transformers

Multi-Head Self-Attention (MHSA) is the cornerstone of Vision Transformers, allowing models to capture diverse feature representations by projecting tokens into independent subspaces. However, the standard MHSA strictly isolates these heads, preventing any information exchange during the attention computation itself. In this paper, we propose Multi-Overlapped-Head Self-Attention (MOHSA), a novel mechanism that replaces the hard division of attention heads with a soft, overlapping division. By allowing queries, keys, and values to partially overlap with those of adjacent heads, MOHSA fosters rich inter-head communication directly within the attention mechanism. We extensively investigate various overlap dimension scheduling strategies to identify optimal configurations. Comprehensive experiments in several Transformer architectures demonstrate that MOHSA outperforms standard MHSA on the CIFAR-10, CIFAR-100, Tiny-ImageNet, and ImageNet-1k datasets, offering a significant performance boost with negligible computational overhead. Code link: https://github.com/ZTX-100/MOHSA.

cs.CV↗

arXiv2026

The Blind Curator: How a Biased Judge Silently Disables Skill Retirement in Self-Evolving Agents

A self-evolving agent retires its bad skills by watching them fail, so what happens when the judge cannot see the failures? Skill retirement is the structural constraint that keeps a growing library from drifting below the no-skill baseline, but its guarantee assumes an unbiased reward, which is false for the LLM judges that reference-free tasks require. We show that a biased judge does not merely add noise; it \emph{silently switches off the curator}. We make this precise with a corrupted-reward analysis, then a behavioral study on a reference-free report-writing testbed with a code-generation cross-check, injecting corruption on top of a deterministic reward to isolate the causal channel. Symmetric noise leaves retirement intact, but \emph{false-pass} bias (failures slipping through as passes) disables contribution-based retirement past a sharp threshold (here a false-pass rate of $0.45$) that no amount of data can cross. Separating genuine retirement from cap-eviction churn shows this \emph{mechanism} failure is universal, holding across domains and failure rates and sparing only near-zero-false-pass, verifier-like graders. The downstream \emph{outcome}, though, is regime-dependent: eval quality degrades only where the same corruption also starves skill synthesis, and otherwise holds steady, so the disabled curator is \emph{silent}, surfacing in no aggregate metric. The contribution is a behavioral safety result, not a performance one. A cheap defect-injection audit then tells an operator, before deployment, which side of the threshold their judge occupies.

cs.AI↗

arXiv2026

Extracting a nitrile-centered, ether-assisted motif hierarchy for lithium-battery electrolyte design from billion-scale molecular space

Designing electrolyte molecules for lithium batteries requires balancing electronic stability with appropriate Li+ solvation, yet the structural basis remains unclear across chemically diverse molecules. High-throughput screening expands the searchable space, but ranked candidates alone do not reveal recurring motifs or their applicability limits. We searched nearly one billion GDB13 structures using electronic--solvation descriptors without explicit functional-group preferences or scaffold constraints. Across descriptor weights, high-ranking populations separated into a nitrile-dominant regime and a coexistence regime containing substantial fractions of both nitrile- and ether-containing molecules. These regimes together define a nitrile-centered, ether-assisted motif hierarchy: nitrile remains favored across broad weight ranges, whereas ether becomes prominent under stronger electrostatic and polarity constraints. Encoding this hierarchy in a generative model expands the candidate space beyond GDB13 and yields high-scoring fluorinated structures without an explicit fluorination reward. Explicit-solvent molecular dynamics simulations show weak, exchangeable coordination of representative candidates without displacing ethylene carbonate from the dominant first solvation shell around Li+; effects on ion association and transport depend on molecular structure and concentration. These results establish a quantitative, interpretable and physically bounded motif hierarchy that systematizes established nitrile and ether chemistry for lithium-battery electrolyte design.

physics.chem-ph↗

arXiv2026

Reconcile Once, Write Anytime: A Trust-Tiered Librarian and a Multi-Agent Writer for Drift-Free, Point-in-Time Research

Long-form research reports generated by large language models drift, contradict themselves, and lose provenance: the same metric appears with different values, and rumor is quoted as confidently as an audited filing. We present a two-tier agentic system that separates a maintained, point-in-time knowledge library from report writing. A deterministic "librarian" ingests timestamped sources into a trust-tiered ontology, layering evidence cards, an authoritative metric ledger, and a claim graph into an always-current source of truth, not per-query RAG over raw chunks. A portable multi-agent "writer" runtime then composes a contradiction-free, evidence-grounded report at any knowledge cutoff T, reading only evidence with as_of <= T (no look-ahead); red-team verdicts flow back into the librarian. We evaluate on a self-collected, public corpus of 6,130 sources yielding 555,926 evidence cards (SEC EDGAR filings across 295 issuers and 11 sectors, U.S. Bureau of Labor Statistics releases, and Wikipedia). From the one library we compose four point-in-time reports on distinct theses and run eight reproducible experiments, whose headline metrics come from a deterministic quality-control gate, itself validated by defect-injection meta-evaluation at recall 1.0 and precision 1.0. A shared metric ledger removes 6,845 cross-section contradictions to zero. Tier-first selection is correct on 22/22 gold cases where a popularity-first baseline scores only 9/22; trust tiering leaks zero media-sourced numbers, and no government statistic displaces a company's own filing. A red-team refutation propagates back and self-corrects a later run with zero manual edits. Replay exhibits zero look-ahead violations across seven cutoffs while the library grows from 235,373 to 555,312 cards. Difficulty-tiered model routing exceeds the all-Opus quality ceiling while running 3.7x faster than serial.

cs.MA↗