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Wenhui Chen

Publications and source records attributed to Wenhui Chen.

At least 19 recordsLinked to original sources
arXiv2026

The critical exponent for the two-dimensional semilinear wave equation with strong damping

In this manuscript, we determine the critical exponent for the two-dimensional semilinear wave equation with strong damping. A recent result in D'Abbicco (arXiv, 2026) gives global in-time small data solutions for $p>\frac{10}{3}$, whereas we in the paper prove finite-time blow-up for $2<p\leqslant\frac{10}{3}$ under an averaged sign condition on the initial velocity. Together with the previously known blow-up result for $1<p\leqslant3$, the threshold for the power nonlinearity $|u|^p$ is \begin{align*} p=p_{\mathrm{crit}}=\frac{10}{3}. \end{align*} We prove positivity of the full two-dimensional velocity fundamental solution and construct a positive averaged kernel, which allows us to establish a nonlinear lower-bound iteration in a parabolic region.

math.AP↗
arXiv2026

Train What You Deploy: Closing the MLP Reachability Gap in Low-Rank Clone Distillation

A compressed student has two shapes that need not agree: the weight it deploys at inference and the weight family its training can reach. We show that a state-of-the-art weight-inheritance distiller, Low-Rank Clone (LRC), deploys a full-width student MLP but ties training to a teacher-induced slice, leaving 62.5-81.4% of each deployed matrix's independent linear degrees of freedom unreachable-paid for at inference, never trainable. Our principle is one line: train what you deploy. From the identical LRC warm start, we make the training object the entire deployed matrix, with no change in deployed shape, deployed parameter count, or inference FLOPs, via two mergeable realizations (Dense-LRC and CORE-LRC) that both collapse to one deployed weight. This recovers stranded capacity: taking the stronger realization per teacher, +2.36/+2.71/+10.45 Avg9 over matched-budget plain-LRC baselines across three teachers (Llama3.2-3B, Llama3.1-8B, Qwen2.5-3B), with the largest gain on the widest teacher (Qwen), where it reaches the original recipe's approx. 20B-token accuracy at 10B tokens (2x token efficiency); there the strictly same-lineage arm still recovers +6.39, the fully controlled figure. Controls strongly support attributing the gain to the enlarged reachable set, rather than to added parameters or the recipe. From approx. 10B distillation tokens plus a short SFT, a half-parameter 1.5B student matches its approx. 9T-token teacher's 9-task macro-average, within evaluation noise and with a residual MMLU deficit, and a 2.7B student beats Meta's own official compression of Llama3.1-8B at ~900x fewer compression tokens (a token count under unmatched recipes, not a compute claim). All results are from single-seed runs on the LRC backbone.

cs.LG↗
arXiv2026

A Judge Should Know What Changed:Construct Validity for LLM-as-a-Judge Evaluation

LLM-as-a-judge evaluation is usually assessed by agreement and robustness to surface perturbations, but reliability does not establish construct validity. We formalize construct validity for an evaluator as a two-dimensional profile: invariance S, the probability that a verdict is unchanged under construct-preserving edits, and construct sensitivity R, the probability that it changes under minimal construct-changing edits. We show that S and R are independent and that no scalar summary preserves all relevant comparisons. We measure the profile across 7 judges and 4 domains using 7 construct-changing intervention types and 5 register-only controls, with intervention direction determined by human annotators and generation, verification, and judging assigned to disjoint model families. At matched invariance S >= 0.90, judges average S = 0.945 but R = 0.319. Sensitivity also differs between scope and strength edits: R_scope = 0.383 versus R_strength = 0.262, a +0.121 gap with the same sign for all 7 judges. We further audit five public label sets and find that surface-only predictors reproduce 55%-67% of labels in paired mode, including 67.4% of MT-Bench human votes. These results show that high judge agreement can coexist with weak sensitivity to changes in the construct being evaluated, motivating joint reporting of invariance and sensitivity and auditing the validation set itself.

cs.AI↗
arXiv2026

Budget-Constrained Embodied Perception: Four Resource Walls and a Pre-Registered Evaluation of Access-Structured Perception on Open Models at less than 31B

Embodied multimodal agents must answer from growing observation streams under a fixed per-decision token budget. We formalize this constraint through four resource walls: a perceptual Shannon wall for bounded state, a horizon wall for query-independent frame selection, a round wall for non-adaptive retrieval, and a conditional composition wall for fixed-depth inference. We introduce ASP, a training-free wrapper for frozen multimodal models that combines a capped structured state, a verbatim episodic index, and query-conditioned budget allocation with iterative access. Following a pre-registered protocol, we evaluate seven open-weight models from 3B to 31B on SEW-Bench, a license-free synthetic long-horizon walkthrough benchmark constructed to instantiate these walls. The registered natural-video benchmarks were not run because their frames require dataset agreements; our evidence therefore concerns access mechanisms, not natural-scene perception. Under a 4,096-token decision budget, ASP reaches 75 to 94% episodic retrieval accuracy, compared with 3 to 19% for equal-budget query-independent sampling, and budget reallocation outperforms quadrupling the sampling budget on every backbone. However, the full three-component architecture does not validate channel duality: removing the compressive state raises the flagship mean from 35.4 to 58.0, ASP does not outperform the verbatim-only baseline on any backbone, and two of four pre-registered falsification criteria fire. These results show that query-conditioned access, rather than parameter count or context growth alone, is decisive under a fixed budget, while prompted online compression does not earn its cost in this setting.

cs.AI↗
arXiv2026

Blow-up criteria and lifespan estimates for semilinear wave equations with time-dependent damping and mass

We consider semilinear wave equations with time-dependent damping and mass and a derivative-type nonlinearity. By applying a Liouville transformation and solving a Volterra integral equation posed from infinity, we construct a positive exact solution to the adjoint equation without using an explicit representation of the linear propagator. This solution is used to derive a blow-up criterion for energy solutions with finite propagation, together with an upper bound for the lifespan. If the primitive of the damping coefficient grows at most logarithmically, we obtain the full shifted Glassey range, including the critical exponent, and the corresponding polynomial and exponential lifespan estimates. The result applies independently of the sign of the scale-invariant discriminant and therefore includes the mass-dominant regime. It also covers non-integrable oscillatory perturbations of the damping coefficient when their contributions are canceled by the corresponding mass terms.

math.AP↗
arXiv2026

The critical exponent for the three-dimensional semilinear wave equation with strong damping

In this manuscript, we determine the critical exponent for the three-dimensional semilinear wave equation with strong damping and thereby resolve an open problem posed in 2014. The threshold for the power nonlinearity $|u|^p$ is \begin{align*} p=p_{\mathrm{crit}}=\frac{7}{3}. \end{align*} Sufficiently small data generate global in-time solutions for $p>\frac{7}{3}$, whereas there exist arbitrarily small smooth compactly supported data whose solutions blow up in finite time for $1<p\leqslant\frac{7}{3}$. Positivity of the full velocity fundamental solution, combined with a dimension-descent formula, yields a positive half-line kernel and replaces the finite propagation property unavailable for strongly damped waves. This leads to a nonlinear lower-bound parabolic iteration without radial symmetry or pointwise sign assumptions on the initial data. At the critical power, a refined slicing argument on moving shells converts the borderline logarithmic gain into the growth required for blow-up.

math.AP↗
arXiv2026

Auditing Discovery Claims: A Two-Sided Criterion for Agentic Science, with the Negative Side Decidable

When a self-improving AI-for-science system claims a new capability, the evidence is usually a benchmark delta, a description-length gate, or a p-value. None separates a real gain from extra search, from a changed verifier, or from adaptation to a fallible oracle. We build a two-sided audit whose negative side is a formal fact: a pseudoknot-free oracle provably cannot represent a crossing base pair, so the prior verifier's range is bounded exactly, offline, before any run. "New" is relative to the agent's prior self, never to the base model. First, how far a single fallible oracle can inflate a capability claim. An invented, solver-free operator solves 43/60 crossing RNA targets under the predictor it optimizes, above a context-free floor of 0/60; under three predictors, 1/60 survives. Paired on the same 43 targets, a predictor the operator never saw confirms 2 of its designs against 26 for a minimum-free-energy solver (p = 8e-7). No statistic computed from the system and its own oracle sees that gap. Second, agent-written procedures can beat a human-written one under a judge no objective can flatter, at a fraction of the compute. Of six frontier models, the two whose operators ran without timeouts carry over at 0.293 against our 0.095 (n = 951 paired units, target-clustered [+0.108, +0.297], p = 5e-5) while spending 4.6-10x fewer oracle calls. Three rungs: difference under an outside adjudicator (reached), not bought with compute (reached, both directions), mechanism identified and transferable (not reached; seven candidates tested, none moves the statistic). The ceiling is the panel itself: its three predictors share nearest-neighbour thermodynamic parameters, two agreeing at kappa = 0.673. The audit is as unsparing about our own system: matched undirected search is an exact zero, and a search-free probe puts 84% of our headline effect on targets a random sequence already solves.

cs.AI↗
arXiv2026

Judging Is Not Enumerating: Silent Omissions in LLM-Authored Acceptable Sets

Language models are increasingly promoted from examinees to examiners: they write the test suites, answer keys, rubrics, and reward functions that define correctness for other systems. We measure the capability that role assumes and find it lacking under the protocol the role is usually deployed with, one-shot greedy authoring with no test-time reasoning. Across four reference constructions - two with complete finite truth, one with a hardened executable reference (HumanEval+/MBPP+), one with an explicitly incomplete lexical reference (WordNet) - models judge whether a candidate belongs far better than they author the set itself. On the incompleteness-proof algorithmic construction the gap is +0.34 to +0.29 F1 over a 24x parameter range and does not close; on executable code, models judging at F1 0.74-0.90 author suites admitting only 19-42% of oracle-correct solutions. A control locates the deficit: asked to emit the predicate rather than its extension, the same models reach F1 about 0.99. The failure is not missing knowledge or an inability to specify, but an inability to materialise the region a specification induces. The dominant error is omission, which resists audit: an over-inclusion is a token a reviewer can challenge, a missing member an absence whose discovery is the authoring problem itself. Models detect planted over-inclusions 6-7x more often than planted omissions, and a production deployment of 43,227 items fails omission-first at 10:1. Wired into RLVR, an authored key costs 1.9 points of accuracy against an exact oracle and 18.5 WordNet-relative (six paired seeds, p=0.031). Gating authored verifiers on a known-correct probe cuts false rejection from 58-92% to at most 5%, but keeps only 5-39% of suites. Repairing them instead, by rewriting each wrong expected value to what a reference execution returns, raises yield 3.3-10.6x across four author families.

cs.AI↗
arXiv2026

Semilinear damped wave equation on a compact Lie group with a non-autonomous forcing term

In the present note, we consider a semilinear damped wave equation on a compact Lie group with a non-autonomous nonlinearity $\varphi(t)|u|^p$. We are interested in describing how the nonnegative time-dependent factor $\varphi$ affects the global in time prolongability of a local solution. In particular, the summability of the function $\varphi$ provides a criterion to distinguish between the blow-up in finite time and global existence of small data. Finally, we derive sharp lifespan estimates for local in time solutions when $\varphi\not\in L^1([0,+\infty)))$ and satisfies a certain scaling condition, that we named uniform upper scaling condition.

math.AP↗
arXiv2026

Sharp lifespan estimates and a Huygens-type effect for one-dimensional Nakao's problem

We study the lifespan of small data solutions to the one-dimensional Nakao's problem, which weakly couples a semilinear damped wave equation and a semilinear wave equation. For compactly supported initial data in a natural energy and integrability class, we establish lower lifespan bounds. Under the standard integral positivity assumptions, these bounds match the known upper estimates in a large region of the $(p,q)$-plane, including every $p>1$ when $q\geqslant3$. We further exploit a Huygens-type cancellation effect. Namely, the condition $\int_{\mathbb{R}}v_1(x)\,\mathrm{d}x=0$ eliminates the constant interior profile of the homogeneous free wave and yields a strictly improved lower bound for the lifespan in a nonempty parameter region. The proof combines diffusion-type $L^m-L^r$ estimates for the damped component with the one-dimensional d'Alembert formula within a time-dependent continuation framework.

math.AP↗
arXiv2026

The Capability Convergence Hypothesis: Capability from Access Structure, Not Scale

The Platonic Representation Hypothesis (PRH) holds that as models scale, representations of heterogeneous networks converge toward a shared model of reality. We propose its sequel and boundary, the Capability Convergence Hypothesis (CCH): under a fixed per-token inference budget, representational convergence does not entail capability convergence. Capability instead converges toward a class, the access-complete hybrid: any architecture holding both a compressive O(1)-state channel and a scalable verbatim-index channel. We anchor it on a witness task, the Newton's-apple problem in an infinite stream, and name three resource walls: a Shannon wall barring any o(Nb)-state architecture, a horizon wall barring any fixed window, and a circuit wall barring fixed-depth attention-only composition (conditional on TC0 != NC1). Under an explicit separability assumption a hybrid crosses all three by paying each wall's price, so capability is strictly super-additive under composition. We separate what we prove from what we conjecture: the access-completeness principle rests on information-theoretic lower bounds and pre-registered experiments, while the field-level convergence trend is an economics-motivated conjecture. We report the first pre-registered small-scale tests under criteria frozen before the data: the predicted scissors gap is measured (exact-retrieval error 0.994 vs. 0.000 once a 64-scalar state gains one global-attention layer), the state-tracking bifurcation lands at the registered boundary, and a conjunction witness shows an irreducibly two-channel solution; one prediction failed with its direction reversed and is reported as such. Representational convergence is given freely by scale; capability convergence must be purchased by access structure.

cs.AI↗
arXiv2026

Small data global in-time existence for Nakao's problem in two and three space dimensions

We study Nakao's problem in two and three space dimensions, a weakly coupled system consisting of a semilinear damped wave equation and a semilinear undamped wave equation. We establish the global in-time existence and uniqueness of small data mild Sobolev solutions in new admissible ranges, together with time-dependent estimates matching those for the corresponding linearized problems. The proof combines diffusion-type $L^m-L^r$ estimates for the damped component with the Poisson and Kirchhoff formulas for the undamped component. Dimension-dependent solution spaces are introduced to incorporate the weaker wave decay and logarithmic $L^2$ growth in two space dimensions. In three space dimensions, a two-level fixed point argument avoids an artificial restriction on $p$ by establishing the self-map property in a strong space and the contraction in a weaker metric. Furthermore, the undamped component scatters to a free wave in $H^2\times H^1$.

math.AP↗
arXiv2026

Large time intrinsic growth and asymptotic behavior for the classical Timoshenko system

In this paper, we investigate the large time behavior of solutions to the classical Timoshenko system in the whole space $\mathbb{R}$. Although the system is conservative and its natural energy is conserved in time, the transversal displacement $\varphi$ and the rotation angle $\psi$ exhibit intrinsic polynomial growths. We establish sharp $L^p-L^q$ estimates for the solutions and show that the growth mechanism originates from the interaction between quadratic oscillations and singular low-frequency amplitudes of different orders. Furthermore, we prove the optimality of the obtained growth rates under a nontrivial zeroth-moment condition on the initial data, while additional moment cancellations with a nontrivial first-moment condition lead to lower-order growth regimes. As a consequence, we derive large time asymptotic profiles related to an effective plate-type dispersive structure hidden in the low-frequency regime of the classical Timoshenko system. We also discuss the relation with the dissipative Timoshenko system through a large time vanishing dissipation limit for time-normalized solutions.

math.AP↗
arXiv2026

Large time asymptotic behavior for the weakly damped Jordan-Moore-Gibson-Thompson equation

This manuscript considers the Jordan-Moore-Gibson-Thompson (JMGT) equation and its linearized equation with an additional weak damping term (proposed by [B. Kaltenbacher, \emph{Inverse Problems} (2025)] firstly) in the whole space $\mathbb{R}^n$. We mainly study the unique existence and large time behavior, including optimal decay estimates and asymptotic profiles, of global in-time Sobolev solutions for any $n\geqslant 1$. This weak damping term leads to diffusion profiles in the sub-critical case $\delta>0$ and regularity-loss decay properties in the critical case $\delta=0$, which are greatly different from the results for the corresponding classical models without the weak damping term.

math.AP↗
arXiv2025

Sharp behavior of semilinear damped wave equations driven by mixed local-nonlocal operators

This paper investigates the Cauchy problem for the semilinear damped wave equation $u_{tt}+\mathcal{L}_{a,b}u+u_t=|u|^p$ with the mixed local-nonlocal operator $\mathcal{L}_{a,b}:=-a\Delta+b(-\Delta)^{\sigma}$, where $a,b\in\mathbb{R}_+$ and $\sigma\in(0,1)\cup (1,+\infty)$. We determine the critical exponent for this problem being $p_{\mathrm{crit}}=1+\frac{2\min\{1,\sigma\}}{n}$, which sharply separates global in-time existence and finite-time blow-up of solutions. Furthermore, for the super-critical case $p>p_{\mathrm{crit}}$, we establish the asymptotic profiles of global in-time solutions, showing the anomalous diffusion when $\sigma\in(0,1)$ and the classical diffusion when $\sigma\in(1,+\infty)$, together with the sharp decay estimates. For solutions blowing up in finite time when $1<p\leqslant p_{\mathrm{crit}}$, we derive the sharp estimates for upper and lower bounds of lifespan. Our results reveal the crucial influence of mixed operators on the qualitative properties of solutions, fundamentally governing their critical phenomena, large-time behavior and blow-up dynamics, via $\max\{1,\sigma\}$ or $\min\{1,\sigma\}$.

math.AP↗
arXiv2025

Global in-time rough large data solution to complex-valued semilinear damped evolution equations

We study the semilinear Cauchy problem for complex-valued damped evolution equations \begin{align*} \partial_t^2u+(-\Delta)^{\sigma}u+(-\Delta)^{\delta}\partial_tu=u^p,\ \ u(0,x)=u_0(x),\ \partial_tu(0,x)=u_1(x), \end{align*} with $\delta\in[0,\sigma]$, $\sigma\in\mathbb{R}_+$ and $p\in\mathbb{N}_+\backslash\{1\}$, where the initial data belong to the rough space $E^{\alpha}_s$ endowed with the norm \begin{align*} \|f\|_{E^{\alpha}_s}=\big\|\langle\xi\rangle^s\,2^{\alpha|\xi|}\widehat{f}(\xi)\big\|_{L^2}\ \ \mbox{with}\ \ \alpha<0, \ s\in\mathbb{R}. \end{align*} Concerning $(u_0,u_1)\in E^{\alpha}_{s+\bar{\kappa}}\times E^{\alpha}_s$ when $s\geqslant\frac{n}{2}-\frac{2\kappa+\bar{\kappa}-2\delta}{p-1}-\bar{\kappa}$ with $\kappa=\min\{2\delta,\sigma\}$ and $\bar{\kappa}=\max\{2\delta,\sigma\}$ whose Fourier transforms are supported in a suitable subset of first octant, we prove a global in-time existence result without requiring the smallness of rough initial data.

math.AP↗
arXiv2025

Global in-time existence of solutions for the complex-valued Jordan-Moore-Gibson-Thompson equations of Westervelt-type under different conditions on initial data

We are interested in the global in-time existence of solutions for the complex-valued Jordan-Moore-Gibson-Thompson (JMGT) equations of Westervelt-type, namely, \begin{align*} \tau\partial_t^3\psi+\partial_t^2\psi+\mathcal{A}\psi+(\delta+\tau)\mathcal{A}\partial_t\psi=(1+\tfrac{B}{2A})\partial_t[(\partial_t\psi)^2] \end{align*} in the whole space $\mathbb{R}^n$, with $\tau,\delta,\frac{B}{A}\in\mathbb{R}_+$ and the fractional Laplacian $\mathcal{A}:=(-\Delta)^{\sigma}$ equipping $\sigma\in\mathbb{R}_+$. Our aims are twofold. For one thing, by considering the rough initial data with their Fourier support restrictions in a suitable subset of first octant, we demonstrate a global in-time existence result without requiring the smallness of initial data. For another, by removing these Fourier support restrictions, we prove another global in-time existence result for the equivalent strongly coupled JMGT systems, where the real and imaginary parts of initial data, respectively, belong to regular Sobolev spaces with different additional Lebesgue integrabilities.

math.AP↗