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Wenhui Chen

Publications and source records attributed to Wenhui Chen.

At least 37 records · Page 2Linked to original sources
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

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

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 $φ(t)|u|^p$. We are interested in describing how the nonnegative time-dependent factor $φ$ affects the global in time prolongability of a local solution. In particular, the summability of the function $φ$ 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 $φ\not\in L^1([0,+\infty)))$ and satisfies a certain scaling condition, that we named uniform upper scaling condition.

math.AP↗
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 $φ$ and the rotation angle $ψ$ 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 $δ>0$ and regularity-loss decay properties in the critical case $δ=0$, 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 $\mathcal{L}_{a,b}:=-aΔ+b(-Δ)^σ$, where $a,b\in\mathbb{R}_+$ and $σ\in(0,1)\cup (1,+\infty)$. We determine the critical exponent for this problem being $p_{\mathrm{crit}}=1+\frac{2\min\{1,σ\}}{n}$, 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 $σ\in(0,1)$ and the classical diffusion when $σ\in(1,+\infty)$, 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 $\max\{1,σ\}$ or $\min\{1,σ\}$.

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*} τ\partial_t^3ψ+\partial_t^2ψ+\mathcal{A}ψ+(δ+τ)\mathcal{A}\partial_tψ=(1+\tfrac{B}{2A})\partial_t[(\partial_tψ)^2] \end{align*} in the whole space $\mathbb{R}^n$, with $τ,δ,\frac{B}{A}\in\mathbb{R}_+$ and the fractional Laplacian $\mathcal{A}:=(-Δ)^σ$ equipping $σ\in\mathbb{R}_+$. 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↗
arXiv2025

The Tenth NTIRE 2025 Efficient Super-Resolution Challenge Report

This paper presents a comprehensive review of the NTIRE 2025 Challenge on Single-Image Efficient Super-Resolution (ESR). The challenge aimed to advance the development of deep models that optimize key computational metrics, i.e., runtime, parameters, and FLOPs, while achieving a PSNR of at least 26.90 dB on the $\operatorname{DIV2K\_LSDIR\_valid}$ dataset and 26.99 dB on the $\operatorname{DIV2K\_LSDIR\_test}$ dataset. A robust participation saw \textbf{244} registered entrants, with \textbf{43} teams submitting valid entries. This report meticulously analyzes these methods and results, emphasizing groundbreaking advancements in state-of-the-art single-image ESR techniques. The analysis highlights innovative approaches and establishes benchmarks for future research in the field.

cs.CV↗
arXiv2025

Sharp lifespan estimates for semilinear fractional evolution equations with critical nonlinearity

In this paper we consider semilinear wave equation and other second order $σ$-evolution equations with different (effective or non-effective) damping mechanisms driven by fractional Laplace operators; in particular, the nonlinear term is the product of a power nonlinearity $|u|^p$ with the critical exponent $p=p_{\mathrm{c}}(n)$ and a modulus of continuity $μ(|u|)$. We derive a critical condition on the nonlinearity by proving a global in time existence result under the Dini condition on $μ$ and a blow-up result when $μ$ does not satisfy the Dini condition. Especially, in this latter case we determine new sharp estimates for the lifespan of local solutions, obtaining coincident upper and lower bounds of the lifespan. In particular, we derive a new sharp estimate for the wave equation with structural damping and classical power nonlinearity $|u|^p$ in the critical case $p=p_c(n)$, not yet determined in previous literature. The proof of the blow-up results and the upper bound estimates of the lifespan require the introduction of new test functions which allows to overcome some new difficulties due to the presence of both non-local differential operators and general nonlinearities.

math.AP↗
arXiv2025

$L^p-L^q$ estimates for the dissipative and conservative Moore-Gibson-Thompson equations

This paper studies some $L^p-L^q$ estimates for the dissipative or conservative Moore-Gibson-Thompson (MGT) equations in the whole space $\mathbb{R}^n$. Our contributions are twofold. By applying the Fourier analysis associated with the modified Bessel function in the dissipative case, we derive some $L^p-L^q$ estimates of solutions. Then, introducing a good unknown related to the free wave equation in the conservative case, some $L^p-L^q$ estimates of solutions with the admissible closed triangle range of exponents are deduced. These results show some essential influences of dissipation from the MGT equations in the $L^q$ framework.

math.AP↗
arXiv2025

Large time behavior for the classical wave equation with different regular data and its applications

In this paper, we mainly consider large time behavior for the classical free wave equation $u_{tt}-Δu=0$ in $\mathbb{R}^n$. We derive some large time optimal estimates for the quantity of solution $\|u(t,\cdot)\|_{L^2}$ with initial data belonging to $L^2$ or with additional weighted $L^1$ integrabilities. Particularly, some thresholds are discovered for the (local or global in time) stabilization of this quantity. We also apply these results to the wave equation with scale-invariant terms, the undamped $σ$-evolution equation, the critical Moore-Gibson-Thompson equation, and the linearized compressible Euler system.

math.AP↗
arXiv2024

Sharp large time asymptotic behavior for the multi-dimensional thermoelastic systems of type II and type III

In this paper, we study large time asymptotic behavior of the elastic displacement $u$ and the temperature difference $θ$ for the thermoelastic systems of type II and type III in the whole space $\mathbb{R}^n$ without using the thermal displacement transformation. For the type III model with hyperbolic thermal effect, we derive optimal growth/decay estimates and the novel double diffusion waves profiles for the solutions $u,θ$ with the $L^1$ integrable initial data as large time, which improve the results in [32,26,31,17]. This hyperbolic thermal law produces a stronger singularity than the classical Fourier law in thermoelastic systems. For the type II model lacking of dissipation mechanism, we obtain optimal growth estimates and the new double waves profiles for the solutions $u,θ$ as large time in low dimensions. Particularly, these results on the type II/III models show the infinite time blowup phenomena for $u$ if $n\leqslant 4$ and $θ$ if $n\leqslant 2$ in the $L^2$ norm due to the hyperbolic influence. We also clarify competitions between the elastic waves effect and the hyperbolic thermal effect for the thermoelastic systems via the critical dimensions.

math.AP↗
arXiv2024

On the Cauchy problem for semilinear thermoelastic plate systems in the $L^q$ framework

We mainly consider semilinear thermoelastic plate systems with general power nonlinearities in the whole space $\mathbb{R}^n$. By applying the Fourier analysis, some sharp $(L^q\cap L^m)-L^q$ estimates of solutions (with any $1\leqslant m\leqslant q\leqslant +\infty$) to the classical thermoelastic plate system are derived, which cover all known results in $\mathbb{R}^n$. Then, we investigate global in time existence of small data $L^q$ solutions (with any $q\in[1,+\infty]$) and blow-up of weak solutions for the semilinear thermoelastic plate systems under suitable conditions on the power exponents, which justify critical exponents for several classes of nonlinearities.

math.AP↗
arXiv2024

Large time asymptotic behavior for the dissipative Timoshenko system and its application

In this paper, we study large time behavior for the dissipative Timoshenko system in the whole space $\mathbb{R}$, particularly, on the transversal displacement $w$ and the rotation angle $ψ$ of the filament for the beam. Different from decay properties of the energy term derived by Ide-Haramoto-Kawashima (2008), we discover new optimal growth $L^2$ estimates for the solutions themselves. Under the non-trivial mean condition on the initial data $w_1$, the unknowns $w$ and $ψ$ grow polynomially with the optimal rates $t^{3/4}$ and $t^{1/4}$, respectively, as large time. Furthermore, asymptotic profiles of them are introduced by the diffusion plate function, which explains a hidden cancellation mechanism in the shear stress $\partial_x w-ψ$. As an application of our results, we study the semilinear dissipative Timoshenko system with a power nonlinearity. Precisely, if the power is greater than the Fujita exponent, then the global in time existence of Sobolev solution is proved for the case of equal wave speeds, which partly gives a positive answer to the open problem in Racke-Said-Houari (2013).

math.AP↗
arXiv2024

On the threshold nature of the Dini continuity for a Glassey derivative-type nonlinearity in a critical semilinear wave equation

In the present manuscript, we determine the critical condition for the nonlinearity in a semilinear wave equation with a derivative-type nonlinearity. More precisely, we consider a nonlinear term depending on the time derivative of the solution, which is the product of a power nonlinearity with critical Glassey exponent and a modulus of continuity. By employing Zhou's approach along a certain characteristic line, we prove the blow-up in finite time for classical solutions (under a suitable sign condition for the Cauchy data) and we derive upper bound estimates for the lifespan for a not Dini continuous modulus of continuity. Furthermore, in the 3-dimensional and radially symmetric case, by using weighted $L^{\infty}$ estimates, we establish the global existence of small data solutions for a Dini continuous modulus of continuity, and lower bound estimates for the lifespan in the not Dini continuous case. These results provide the regularity threshold (i.e. the Dini condition) for the modulus of continuity in the nonlinearity.

math.AP↗