arXiv subjects

Min Tang

Publications and source records attributed to Min Tang.

At least 19 recordsLinked to original sources

arXiv2026

The interface scattering law for run-and-tumble kinetic models

For microorganisms with run-and-tumble motility, kinetic models provide a well-established description of transport in smoothly varying environments. Sharp signal changes, however, can induce asymmetric interface responses. A motivating example is the response to dark-light boundaries: cells moving into the light largely maintain their direction, whereas those entering the dark are effectively scattered back. Through an interface-layer analysis of pathway-based kinetic equations, we formally derive effective interface conditions for the limiting run-and-tumble model. These velocity-nonlocal conditions capture non-adiabatic scattering near signal discontinuities, linking intracellular sensory dynamics to transport across sharp environmental boundaries. For a two-velocity model, they reduce to an explicit transmission matrix. We assess the interface law numerically using biologically motivated parameters for E. coli chemotaxis.

math.AP↗

arXiv2026

Beneath the Surface: What We Overlook When We Talk About Agent Evolution

Agent harness evolution enables recursive self-improvement (RSI) without updating model weights. We examine whether higher benchmark scores yield reliable, efficient, and transferable improvement. We evaluate four methods across harnesses, general and coding tasks. Repeated evaluations, controlled agent expansion, component interventions, and admission replays reveal recurring patterns. All sixteen evolved agents gain previously uncovered tasks while losing previously covered ones. In one general-task case, reliability rises by 5.2 points despite losing ten previously covered tasks. Most reliability gains also increase deployment cost. Specific changes usually outperform generic reminders, but their benefits can change when combined. The highest-scoring agent does not yield the largest mean improvement in any of our four pools, and stricter admission can discard useful alternatives. Transfer selectively preserves gains: coverage usually falls on the general-task target across both harness types and paradigms, but rises on the coding target with the outer-layer-only harness. These findings motivate preservation-aware evaluation, tested decision rules, and explicit applicability conditions. As a constructive follow-up, EvoAudit turns these diagnostics into revisions of select, analyze, mutate, and gate, achieving the best performance.

cs.AI↗

arXiv2026

TraceCAD: Trace-Guided Repair for Agentic CAD Generation

LLM-based CAD agents produce executable parametric programs, but their correction loops may lose evidence about satisfied requirements, faulty operations, and prior repairs. We introduce TraceCAD, a recovery layer that links requested features, modeling steps, failure evidence, and candidate outcomes as persistent state. TraceCAD diagnoses likely faulty operations, searches bounded edits in their dependency regions, validates candidates through execution and preservation checks, and retains successful and failed repair outcomes in reusable skill memory. On DeepCAD-derived benchmarks with 200-model ablations and a 1K-model comparison, TraceCAD achieves competitive geometric quality in terms of IoU, Chamfer distance, and Hausdorff distance. Removing persistent state nearly halves recovery score; removing localized search more than doubles geometric regression and doubles code-agent invocations. Initializing the skill store on disjoint training models further reduces retries, token cost, and latency. These results demonstrate that persistent, localized, and reusable recovery improves final CAD quality and repair reliability.

cs.AI↗

arXiv2026

Patient-specific rubric-based evaluation of large language models across longitudinal cancer care

Large language models (LLMs) show promise in specialty medicine, yet existing evaluations largely focus on isolated clinical encounters rather than tracking how clinical responsibilities evolve across a longitudinal care pathway. Here we introduce NPC-RubricBench, a phase-aware benchmark for evaluating multistage clinical reasoning across the cancer care continuum, using nasopharyngeal carcinoma as a defined disease context. Curated from longitudinal records of 405 patients across two cancer centers, the benchmark comprises 941 patient-phase units across six sequential care phases and 17,688 patient-specific atomic criteria spanning five evaluation dimensions, with each assessment strictly restricted to decision-time clinical evidence. Evaluating 30 general-purpose and medical LLMs revealed that strong diagnostic performance does not carry over to downstream care. We evaluated 30 general-purpose and medical LLMs, showing that high diagnostic performance did not translate into improved downstream care. Instead, the dominant failure modes reversed across phases. Explicit decision errors dominated anatomical staging at 48.2%, whereas decision omissions dominated initial work-up and post-treatment follow-up at 33.4% and 30.4%, respectively. In the evaluated model set, medically adapted models showed higher omission rates than general-purpose models. Moreover, varying query granularity exposes a critical specification trade-off: broad open-ended requests degrade Decision Quality across all 30 models, while more detailed, checklist-like prompts raise Decision Quality but reduce Evidence Faithfulness and Safety Adherence. Furthermore, NPC-RubricBench demonstrates that static diagnostic benchmarks are insufficient to ensure consistent clinical reliability over time, highlighting the importance of phase-adaptive safeguards in multistage medical AI.

cs.AI↗

arXiv2026

Curvature Effects on Boundary Accumulation of Self-Propelled Particles: A Fokker-Planck Approach

It is well known that self-propelled particles tend to accumulate near boundaries. Although the influence of boundary geometry on this accumulation has been extensively studied using individual-based models, a population-level PDE description becomes desirable when a large number of particles are involved. In this work, we investigate boundary accumulation of self-propelled particles confined in two-dimensional circular and annular domains. We develop Fokker--Planck models that qualitatively reproduce the behavior observed in individual-based simulations. The main contribution is the formulation of appropriate evolution equations for particles accumulated at the boundary, incorporating transitions between the interior free-swimming state and the boundary-contact state. Starting from a general spatial two-dimensional model, we simplify the associated boundary conditions by assuming radial symmetry and then design an exponentially weighted difference scheme that preserves the total mass of the coupled system. Because transitions between different particle states induce singular behavior near the boundary, establishing discrete mass conservation is nontrivial. In particular, the velocity space must be divided into two subdomains, with the resulting discontinuity treated explicitly. Stochastic simulations and numerical experiments are performed both to validate the proposed models and to investigate the effects of geometric and dynamical parameters on boundary accumulation.

math.AP↗

arXiv2026

Minimal asymptotic $g$-adic bases from arbitrary partitions

Let $g>h\ge2$ be integers. For a nonempty set $W\subseteq\N$, let $\mathcal F^*(W)$ denote the set of its finite nonempty subsets. Let $$A_g(W)=\left\{\sum_{f\in F}a_fg^f: 1\leq a_f \leq g-1,F \in \mathcal F^*(W)\right\},$$ and let $\N=W_1\sqcup\cdots\sqcup W_h$ be a partition into infinite sets. We prove that $A=\bigcup_{i=1}^h A_g(W_i)$ is a minimal asymptotic basis of order $h$ for every such partition.

math.NT↗

arXiv2026

Recovering the spatiotemporally dependent diffusion and advection coefficients in a pathway-based Keller--Segel model

We investigate an inverse coefficient problem for an augmented Keller--Segel model arising in the description of phototactic and chemotactic population dynamics. The spatiotemporal evolution of the population density is governed by an advection-diffusion equation in which both the diffusion coefficient and the advection coefficient depend on space and time. Due to the underlying intracellular adaptation mechanism, even in a time-independent external environment, the diffusion coefficient $D(x,t)$ and the scalar advection coefficient $K(x,t)$ remain time-dependent and relax exponentially toward their respective steady-state profiles. Importantly, their relaxation is governed by the same rate, determined by the intracellular adaptation dynamics. From internal measurements of the density, we establish conditional Lipschitz stability for recovering either coefficient when the other is known, and derive cross-sensitivity estimates quantifying the compensation between diffusion and advection perturbations that produce the same density data. We further identify a finite-time separation between the transient and steady regimes: the full dynamics admit an exponentially accurate frozen-coefficient approximation at late times. When the steady-state coefficients are known, we also prove unique identification of the relaxation rate from the long-time behavior of the solution. Finally, we derive an explicit linearization of the forward map and, motivated by the temporal separation above, develop a two-stage gradient-based reconstruction strategy. Numerical experiments demonstrate the feasibility of the proposed method.

math.AP↗

arXiv2026

MidSurfNet: Learning Face Pairing for Mid-surface Abstraction of Thin-walled CAD Models

Mid-surface abstraction is an important preprocessing step for finite element analysis of thin-walled CAD models, and face pairing is its central subproblem. Existing face-pairing methods rely on handcrafted geometric criteria whose thresholds are hard to tune when a model has multiple local wall thicknesses; their groupings depend on threshold settings and processing order, so the same model can yield inconsistent results. We present MidSurfNet, a learning-based face-pairing method that couples a learned face-pair scorer with a deterministic face-group composition. The scorer evaluates every unordered face pair with two separately learned evidence streams: a geometry stream combining continuous pairing criteria with a conditional shape correction, and an attributed-topology stream over the B-Rep face-adjacency graph. A pair-conditioned gate fuses the two streams, and independent per-pair decisions retain opposing-face support relations at one operating threshold selected once on validation data, replacing rather than adding to the per-model thresholds of rule-based pipelines. Under a connected-and-bipartite condition, the composition stage organizes the retained relations into variable-cardinality m-to-n face groups, each independent of processing order for a fixed support graph and unique up to its two side labels. We also construct the MidSurf dataset, a benchmark of 1,575 manually annotated CAD models. On the test set, MidSurfNet attains a pair-level F1-Score of 87.32%, 23.22 percentage points above the strongest rule-based baseline, and an end-to-end Completion Rate of 75.42%, including 61.90% on the multi-wall-thickness category the evaluated rule-based implementations do not support. We demonstrate practical utility by generating mid-surfaces from the composed face groups through an industrial mid-surface API and running finite element analyses on the resulting shell models.

cs.GR↗

arXiv2026

Deriving subdiffusion equations from general Renewal--Jump dynamics

Subdiffusion occurs when long trapping or residence times of particles slow down spatial transport and produce a mean squared displacement proportional to $t^α$, with~$0<α<1$. We develop a general renewal--jump framework that combines the internal trapping dynamics with the reinjection of particles with spatial jumps. The internal trapping dynamics enters the macroscopic limit through the small-frequency behavior of a resolvent which limiting solution is not integrable. A growth mass condition determines the parameter~$α$. Then the spatial density converges on the time scale~$\eps^{-2/α}$ to a time-fractional diffusion equation. This criterion provides a common derivation for models with very different internal mechanisms. We first establish the abstract limit by Laplace transform in a general setting. We then show that the classical age-structured renewal model is a direct instance of the framework and apply the same criterion to an internal pathway model governed by a degenerate elliptic operator. Both yield the subdiffusion equation and its correct initial condition. The approach clarifies which microscopic property produces subdiffusion, how the anomalous exponent determines the macroscopic scaling, and why the initial distribution enters the limit through the initial spatial mass under the stated preparation assumptions.

math.AP↗

arXiv2026

A proof of the Freiman-Lev conjecture

Let $A=\{a_{0}, a_{1}, \ldots, a_{k-1}\}$ be a set of $k>7$ integers such that $0=a_{0}<a_1<\cdots<a_{k-1}$ and $\gcd(A)=1$. The set $2^{\wedge}A=\{a+b: a, b\in A, a\neq b\}$ is called the restricted sumsets of $A$. Freiman-Lev conjecture is a well-known conjecture which related to restricted sumsets [V.F. Lev, Restricted set addition in groups, I. The classical setting, J. London Math. Soc. 62(2000), 27-40]. Up to now, Freiman-Lev conjecture is still open for all $a_{k-2}\geqslant 2k-4$ and $a_{k-1}\geqslant 2k-2$. In this paper, we complete the proof of the Freiman-Lev conjecture by resolving this final and most challenging case.

math.NT↗

arXiv2026

Denoising-Aware Inversion: Revealing Privacy Risks in Noise-Protected Text Embeddings

Dense text embeddings are widely used in data mining, retrieval, and downstream machine learning systems due to their compact and semantically rich representations, but recent embedding inversion attacks have shown that they can expose substantial information about the original text, leading to serious privacy leakage risks. A common defense is to release perturbed embeddings by adding Gaussian noise, which is simple yet effective against standard inversion attacks and does not significantly degrade embedding utility for downstream tasks. However, it remains unclear whether such noise-protected embeddings are sufficiently safe against adaptive attackers that explicitly account for the perturbation process. In this paper, we study text embedding inversion in a noise-protected setting, where the attacker can observe only noisy embeddings and has no access to clean embedding targets. We first analyze why existing generative inversion methods fail under this setting and identify a "Double Noise Trap", which fundamentally prevents standard generative inversion models from achieving high-quality reconstruction. To address this challenge, we propose DAEI, a denoising-aware embedding inversion pipeline that combines a residual denoising autoencoder with generative text inversion where the denoiser is trained in an unsupervised manner using Stein's unbiased risk estimate to enable denoising from noisy observations alone. Extensive experiments show that DAEI achieves approximately 154\% relative improvement in BLEU over the existing generative inversion baseline, while also improving token-level F1 and ROUGE-L by 32--60\%. The promising inversion performance of DAEI challenges the prevailing assumption that simple Gaussian perturbation is sufficient to prevent sensitive information leakage from embedding representations.

cs.LG↗

arXiv2026

CADIR: A Cross-Backend Editable Intermediate Representation for Agentic CAD Generation

Large language models have made it possible to generate executable computer-aided design (CAD) programs from natural-language descriptions or images. However, existing methods represent modeling processes as backend-specific sequential scripts with implicit dependencies or as static geometry, making it difficult to simultaneously preserve construction history, stable topological references, and feature-level editability across different CAD systems. We present CADIR, an agent-friendly executable intermediate representation for CAD generation and cross-backend editing. Built on the OCCT geometry kernel via OCP, CADIR provides explicit, compositional modeling operations and fine-grained execution diagnostics. During program execution, CADIR records modeling operations, parameter dependencies, constraints, and topology selections in a construction graph. To enable reliable cross-backend reconstruction, we introduce Geometric Signature Matching, which identifies corresponding edges and faces despite parameter changes and backend differences, allowing adapters to reconstruct native editable feature histories in FreeCAD, SolidWorks, and Fusion 360. Building on this representation, we further propose a construction-graph retrieval method for text and image queries that supports both full-graph and subgraph retrieval, enabling agents to leverage complete models and modeling substructures. Extensive experiments demonstrate that CADIR achieves higher geometric fidelity and execution reliability than existing CAD representations, that construction-graph retrieval further improves model generation quality, and that cross-backend editing enables reliable model reconstruction and post-reconstruction editing across multiple CAD environments.

cs.AI↗

arXiv2026

On a problem of minimal additive complements for not eventually periodic $S$-difference sets

Let $C$ and $W$ be two integer sets. If $C+W=\mathbb{Z}$, then we say that $C$ is an additive complement to $W$. If no proper subset of $C$ is an additive complement to $W$, then we say that $C$ is a minimal additive complement to $W$. In this paper, we give an affirmative answer to one problem of Ma and Chen [On a problem of minimal additive complements of integers, J. Number Theory 284(2026), 178-187.]

math.NT↗

arXiv2026

Bridging Scales in Chemotaxis: Scale-Uniform Forward Stability for Run-and-Tumble Kernel Estimation

Chemotactic motion is described by run-and-tumble kinetic models at microscopic scales and by Keller--Segel equations at macroscopic scales. We develop variational loss functionals for estimating the two components $T_0(x)$ and $T_1(x)$ of a turning kernel $T_ε=T_0+εT_1$, where $T_0$ determines the leading-order turning rate and diffusion, while $T_1$ governs the macroscopic chemotactic drift. Under suitable regularity and data-informativeness assumptions, we establish conditional scale-uniform forward-stability estimates showing that a small loss leads to a small discrepancy between the forward solutions generated by the true and estimated kernels across the kinetic and diffusive regimes. Combined with sparse inversion, the method accurately recovers smooth, nonsmooth, and strongly heterogeneous kernels and remains robust under measurement noise.

math.AP↗

arXiv2026

WarpagePINN: Thermal Warpage Prediction in Advanced Packaging via a Two-Stage Physics-Informed Neural Networks

Thermal warpage has become a critical issue in advanced packaging, primarily caused by the mismatch in coefficients of thermal expansion (CTE) among heterogeneously integrated materials. However, only a limited number of studies have focused on developing computational methods for coupled thermal-warpage prediction in the chiplet. This paper proposes a two-stage physics-informed neural network (WarpagePINN) framework to compute both temperature profile and warpage deformation of chiplets. The neural networks are trained without relying on labeled datasets generated by conventional simulators. In the first stage, the temperature field is modeled using a Fourier series representation that inherently satisfies boundary conditions, and the network is trained solely through a loss function derived from the governing equation. In the second stage, a multilayer perceptron (MLP) is employed for warpage prediction, utilizing a novel hybrid supervisory strategy to optimize the energy-based loss function instead of residual loss. A parametric WarpagePINN is also developed to quantify uncertainties associated with the CTE. Numerical results show that the proposed WarpagePINN framework achieves excellent agreement with conventional finite element methods, with a mean absolute error (MAE) of 0.2 μm, while achieving a speedup of approximately 1000 {\times} in CTE parameterization studies.

math.NA↗

arXiv2026

The Flip Side of RLHF: On-Policy Feedback for Reward Model Self-Supervised Improvement

Building strong reward models (RMs) for language model alignment is bottlenecked by the cost and difficulty of acquiring diverse and reliable preference data from human annotation or judge models. It is dramatically worse as the policy evolves beyond the static RM training. Therefore, we propose SAVE (Self-supervised reward model improvement via Value-Anchored On-policy feedback), a framework that grades on-policy responses as feedback by using the value function for on-policy RM training. SAVE naturally converts the reward-graded on-policy responses into supervision with a prompt-specific value head as an adaptive anchor. It computes RM advantages and filters ambiguous samples to update the RM via a contrastive objective. The effectiveness of SAVE for enhancing RM training is strongly validated through rigorous empirical evaluation across six diverse benchmarks. It achieves outperforming results across all datasets while maintaining consistent improvements across three RL algorithms (GRPO, RLOO, GSPO) and different policy backbones.

cs.CL↗

arXiv2026

Adaptive Punishment for Cooperation in Mixed-Motive Games

Mixed-motive scenarios are ubiquitous in real-world multi-agent interactions, where self-interested agents often defect for immediate rewards, overlooking the potential of altruistic cooperation to improve long-term gains and collective welfare. Peer punishment can deter defection, but as costly second-order altruism, its persistent imposition may undermine the punisher's interests. Existing approaches often struggle to effectively implement punishment to promote cooperation. To balance the efficacy and cost of punishment, we propose Adaptive Punishment for Cooperation (APC), a distributed method that determines punishment intensity based on both a dynamic punishment probability and the severity of defection. This dynamic probability substantially reduces costly and ineffective punishment while also promotes cooperation. To accurately assess defection and its severity, we use a defection awareness module, whose learning is guided by game reward. Theoretical analysis and empirical results show APC performs effectively in iterated public goods game. Empirically, APC also significantly outperforms existing baselines across sequential social dilemmas, learning rational and effective punishment policies that foster cooperation by strategically deterring defection.

cs.MA↗

arXiv2026

AirfoilGen: A valid-by-construction and performance-aware latent diffusion model for airfoil generation

Airfoil shape design is a fundamental task in aerospace engineering, with a direct impact on flight stability and fuel consumption. Deep learning has recently emerged as a promising tool for this task, but existing deep generative approaches remain limited in both geometric validity and physical controllability. They offer little control over the generated shapes, yielding invalid geometries, and they typically do not condition effectively on aerodynamic performance. To address these issues, this paper proposes AirfoilGen, a valid-by-construction and performance-aware latent diffusion model for airfoil. It first introduces a novel airfoil representation scheme, the circle sweeping representation, to constrain the generative process so that output shapes respect essential airfoil characteristics. It then enables explicit control over aerodynamic performance (e.g., lift and drag coefficients) by operating in a learned latent space: a transformer model encodes airfoil shapes into vector embeddings, and a conditional diffusion model denoises Gaussian noise into these latent embeddings while incorporating target aerodynamic performance. In addition, this paper presents a new dataset of over 200,000 airfoils, which is substantially larger than the widely used UIUC airfoil dataset (1,650 airfoils) and more suitable for training modern deep generative models. Experiments demonstrate that AirfoilGen enables airfoil generation with far greater geometric validity and aerodynamic performance controllability than previously achievable, with an average performance-conditioning accuracy of 98.41%.

cs.LG↗