arXiv subjects

Pengyue Hou

Publications and source records attributed to Pengyue Hou.

7 recordsLinked to original sources

arXiv2026

Covariant Multi-Scale Negative Coupling on Dynamic Riemannian Manifolds: A Geometric Framework for Topological Persistence in Infinite-Dimensional Systems

Dimensional reduction is a generic consequence of dissipation in nonlinear evolution equations, often leading to attractor collapse and the loss of dynamical richness. To counteract this, we introduce a geometric framework for Covariant Multi-Scale Negative Coupling Systems (C-MNCS), formulated intrinsically on smooth Riemannian manifolds for a broad class of semilinear dissipative PDEs. The proposed coupling redistributes energy across dynamically separated spectral bands, inducing a scale-balanced feedback that prevents finite-dimensional degeneration. We establish the short-time well-posedness of the coupled state-metric evolution system in Sobolev spaces and derive a priori estimates for phase-space contraction rates. Furthermore, under a global boundedness hypothesis, we prove that the global attractor possesses a strictly finite Hausdorff and Kaplan-Yorke dimension. To bridge abstract topological bounds with physical realizability, we isolate the core Adaptive Spectral Negative Coupling (ASNC) mechanism for numerical validation. High-resolution experiments, utilizing a fully coupled ETDRK4 scheme and continuous QR-based Lyapunov exponent computation on a conformally flat 2D dynamic scalar manifold, corroborate the theoretical predictions. These computations explicitly demonstrate the stabilization of high-dimensional attractors against severe macroscopic dissipation. This geometrically consistent mechanism offers a new paradigm for maintaining structural complexity and multiscale control in infinite-dimensional dynamical systems.

nlin.CD↗

arXiv2026

The "Robert Boulton" Singularity: Semantic Tunneling and Manifold Unfolding in Recursive AI

The stability of generative artificial intelligence trained on recursive synthetic data is conventionally monitored via Perplexity (PPL). We demonstrate that PPL is a deceptive metric in context-stabilized regimes (L=128). Using a rigorous sliding-window protocol (N=1500), we identify a novel failure mode termed "Semantic Tunneling." While the Baseline model maintains high grammatical fluency (PPL approx. 83.9), it suffers a catastrophic loss of semantic diversity, converging within seven generations to a single, low-entropy narrative attractor: the "Robert Boulton" Singularity. This phenomenon represents a total collapse of the latent manifold (Global Effective Rank 3.62 -> 2.22), where the model discards diverse world knowledge to optimize for statistically safe syntactic templates. To address this, we apply the Multi-Scale Negative Coupled Information Systems (MNCIS) framework recently established in Hou (2026) [arXiv:2601.11594]. We demonstrate that Adaptive Spectral Negative Coupling (ASNC) acts as a topological operator that actively induces "Manifold Unfolding." MNCIS forces the model to expand its effective rank from the anisotropic baseline of 3.62 to a hyper-diverse state of 5.35, effectively constructing an "Artificial Manifold" that resists the gravitational pull of semantic attractors and preserves the long-tail distribution of the training data.

cs.LG↗

arXiv2026

Multi-Scale Negative Coupled Information Systems (MNCIS): A Unified Spectral Topology Framework for Stability in Turbulence, AI, and Biology

Complex dynamical systems frequently encounter a recurrent structural instability: the collapse of the spectral gap, driving the system toward a low-dimensional "Zero-Mode Attractor" (e.g., spectral pile-up or over-smoothing). Building upon recent global well-posedness estimates [Hou, arXiv:2601.00638], this work generalizes the Multi-Scale Negative Coupled Information System (MNCIS) framework. We postulate that global stability requires an active topological operator - Adaptive Spectral Negative Coupling (ASNC) - functioning as a state-dependent high-pass filter that penalizes entropy accumulation at spectral boundaries. We validate this unified framework via three implementations: (1) Hydrodynamics: In 3D Navier-Stokes turbulence ($N=256^3$), ASNC acts as a global-enstrophy adaptive sub-grid scale (SGS) model, stabilizing the inviscid limit and preserving the Kolmogorov $-5/3$ inertial range without artificial hyper-viscosity. Crucially, we verify that the operator remains dormant ($γ\approx 0$) during the linear growth phase of physical instabilities, functioning strictly as a conditional topological clamp. (2) Artificial Intelligence: Addressing Over-smoothing in Graph Neural Networks (GNNs), we implement ASNC as a parameter-free topological constraint. Unlike baselines (e.g., DeepGCNs) relying on dense residual connections, our framework enables the training of ultra-deep 64-layer networks without residual connections, maintaining perfectly stationary feature variance ($σ^2 \equiv 1.0$) on the ogbn-arxiv benchmark. (3) Biological Physics: In reaction-diffusion morphogenesis, it stabilizes Turing patterns against diffusive washout in high-entropy regimes. Our results suggest that the MNCIS framework provides a base-independent topological condition for distinguishing viable complex systems from those collapsing into thermal equilibrium.

physics.comp-ph↗

arXiv2026

Global Dynamics and Stabilization of Zero-Mode Singularities in Multi-Scale Reaction-Diffusion Systems via Negative Coupling

This paper establishes a rigorous mathematical framework for the Multi-Scale Negative Coupled System (MNCS), a dynamical model describing hierarchical state spaces with directed, sign-structured interactions. We address the stabilization of reaction-diffusion systems on bounded domains $Ω\subset \mathbb{R}^d$ ($d \le 3$) subject to homogeneous Neumann boundary conditions. A critical feature of this setting is the "zero-mode singularity," where the Laplacian operator possesses a trivial zero eigenvalue ($λ_0=0$), providing no linear dissipation for the spatial mean. We rigorously prove the global well-posedness of the system and the existence of a compact global attractor $\mathcal{A}$ in the phase space $\mathbb{H}=(L^2(Ω))^N$. Utilizing the Moser-Alikakos iteration technique, we establish uniform $L^\infty(Ω)$ bounds, overcoming the lack of Sobolev embedding from $H^1$ into $L^\infty$ in three dimensions. These bounds enable the derivation of explicit upper estimates for the fractal dimension of the attractor via the Kaplan-Yorke trace formula. We show that the dimension scales as $d_F(\mathcal{A}) \sim \max\{0, \mathcal{K}_{\mathcal{A}}-γ\}^{d/2}$, confirming that the negative coupling strength $γ$ acts as a global regularizer that compresses the phase space. The theoretical results are validated using a stiff-stable Second-Order Exponential Time Differencing (ETD2) scheme with Discrete Cosine Transform (DCT) to strictly enforce no-flux boundary conditions.

math.AP↗

arXiv2023

Improving Contrastive Learning of Sentence Embeddings with Focal-InfoNCE

The recent success of SimCSE has greatly advanced state-of-the-art sentence representations. However, the original formulation of SimCSE does not fully exploit the potential of hard negative samples in contrastive learning. This study introduces an unsupervised contrastive learning framework that combines SimCSE with hard negative mining, aiming to enhance the quality of sentence embeddings. The proposed focal-InfoNCE function introduces self-paced modulation terms in the contrastive objective, downweighting the loss associated with easy negatives and encouraging the model focusing on hard negatives. Experimentation on various STS benchmarks shows that our method improves sentence embeddings in terms of Spearman's correlation and representation alignment and uniformity.

cs.CL↗

arXiv2022

Improving Adversarial Robustness with Self-Paced Hard-Class Pair Reweighting

Deep Neural Networks are vulnerable to adversarial attacks. Among many defense strategies, adversarial training with untargeted attacks is one of the most effective methods. Theoretically, adversarial perturbation in untargeted attacks can be added along arbitrary directions and the predicted labels of untargeted attacks should be unpredictable. However, we find that the naturally imbalanced inter-class semantic similarity makes those hard-class pairs become virtual targets of each other. This study investigates the impact of such closely-coupled classes on adversarial attacks and develops a self-paced reweighting strategy in adversarial training accordingly. Specifically, we propose to upweight hard-class pair losses in model optimization, which prompts learning discriminative features from hard classes. We further incorporate a term to quantify hard-class pair consistency in adversarial training, which greatly boosts model robustness. Extensive experiments show that the proposed adversarial training method achieves superior robustness performance over state-of-the-art defenses against a wide range of adversarial attacks.

cs.CV↗

arXiv2022

Adversarial Fine-tune with Dynamically Regulated Adversary

Adversarial training is an effective method to boost model robustness to malicious, adversarial attacks. However, such improvement in model robustness often leads to a significant sacrifice of standard performance on clean images. In many real-world applications such as health diagnosis and autonomous surgical robotics, the standard performance is more valued over model robustness against such extremely malicious attacks. This leads to the question: To what extent we can boost model robustness without sacrificing standard performance? This work tackles this problem and proposes a simple yet effective transfer learning-based adversarial training strategy that disentangles the negative effects of adversarial samples on model's standard performance. In addition, we introduce a training-friendly adversarial attack algorithm, which facilitates the boost of adversarial robustness without introducing significant training complexity. Extensive experimentation indicates that the proposed method outperforms previous adversarial training algorithms towards the target: to improve model robustness while preserving model's standard performance on clean data.

cs.LG↗