arXiv:2511.11927v1 Announce Type: new 
Abstract: We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica method from statistical physics, we analytically compute the typical value of the top eigenvalue, the top eigenvector component density, and the overlap between the signal vector and the top eigenvector. The solution is given in terms of recursive distributional equations for auxiliary probability density functions which can be efficiently solved using a population dynamics algorithm. Specialising the noise matrix to Poissonian and Random Regular degree distributions, the critical signal strength is analytically identified at which a transition happens for the recovery of the signal via the top eigenvector, thus generalising the celebrated BBP transition to the sparse noise case. In the large-connectivity limit, known results for dense noise are recovered. Analytical results are in agreement with numerical diagonalisation of large matrices.

تدرس هذه الدراسة استنتاج الإشارات ذات الرتبة الواحدة في الأبعاد العالية المتأثرة بالضوضاء المتناثرة، والتي تم نمذجتها كمصفوفة ارتباط لرسم بياني غير موجه ذو أوزان. باستخدام طريقة النسخ من الفيزياء الإحصائية، تحسب الدراسة القيم النموذجية لأعلى قيمة ذاتية وكثافة مكونات أعلى متجه ذاتي. يتم تحديد القوة الحرجة للإشارة لاستعادتها عبر أعلى متجه ذاتي، مما يعمم انتقال BBP إلى السيناريوهات ذات الضوضاء المتناثرة.

Este estudio investiga la inferencia de alta dimensión de una señal de rango uno afectada por ruido disperso, modelado como la matriz de adyacencia de un grafo no dirigido ponderado. Utilizando el método de réplicas de la física estadística, la investigación calcula los valores típicos del valor propio principal y la densidad de componentes del vector propio. Se identifica la fuerza crítica de la señal para la recuperación a través del vector propio principal, generalizando la transición BBP a escenarios con ruido disperso.

Cette étude examine l'inférence de signaux de rang un en haute dimension, affectés par un bruit épars, modélisé comme la matrice d'adjacence d'un graphe non dirigé pondéré. En utilisant la méthode des répliques de la physique statistique, la recherche calcule les valeurs typiques de la plus grande valeur propre et de la densité des composantes du vecteur propre. La force critique du signal pour la récupération via le vecteur propre principal est identifiée, généralisant la transition BBP aux scénarios de bruit épars.

This study investigates the high-dimensional inference of a rank-one signal affected by sparse noise, modeled as the adjacency matrix of a weighted undirected graph. Utilizing the replica method from statistical physics, the research computes the typical values of the top eigenvalue and eigenvector component density. The critical signal strength for recovery via the top eigenvector is identified, generalizing the BBP transition to scenarios with sparse noise.

PCA recovery thresholds in low-rank matrix inference with sparse noise

arXiv:2408.10901v4 Announce Type: replace 
Abstract: Recent advancements in Latent Diffusion Models (LDMs) have revolutionized image synthesis and manipulation, raising significant concerns about data misappropriation and intellectual property infringement. While adversarial attacks have been extensively explored as a protective measure against such misuse of generative AI, current approaches are severely limited by their heavy reliance on model-specific knowledge and substantial computational costs. Drawing inspiration from the posterior collapse phenomenon observed in VAE training, we propose the Posterior Collapse Attack (PCA), a novel framework for protecting images from unauthorized manipulation. Through comprehensive theoretical analysis and empirical validation, we identify two distinct collapse phenomena during VAE inference: diffusion collapse and concentration collapse. Based on this discovery, we design a unified loss function that can flexibly achieve both types of collapse through parameter adjustment, each corresponding to different protection objectives in preventing image manipulation. Our method significantly reduces dependence on model-specific knowledge by requiring access to only the VAE encoder, which constitutes less than 4\% of LDM parameters. Notably, PCA achieves prompt-invariant protection by operating on the VAE encoder before text conditioning occurs, eliminating the need for empty prompt optimization required by existing methods. This minimal requirement enables PCA to maintain adequate transferability across various VAE-based LDM architectures while effectively preventing unauthorized image editing. Extensive experiments show PCA outperforms existing techniques in protection effectiveness, computational efficiency (runtime and VRAM), and generalization across VAE-based LDM variants. Our code is available at https://github.com/ZhongliangGuo/PosteriorCollapseAttack.

أدت التطورات الأخيرة في نماذج الانتشار الكامنة (LDM) إلى تقديم هجوم الانهيار اللاحق (PCA)، وهو إطار مبتكر يهدف إلى حماية الصور من التلاعب غير المصرح به. تستند هذه الطريقة إلى ظاهرة الانهيار اللاحق التي لوحظت في تدريب المشفرات التلقائية المتغيرة (VAE)، مما يبرز نوعين متميزين من الانهيار: انهيار الانتشار والانهيار المركّز.

Los recientes avances en los Modelos de Difusión Latente (LDM) han llevado a la introducción del Ataque de Colapso Posterior (PCA), un marco novedoso destinado a proteger las imágenes de manipulaciones no autorizadas. Este enfoque se basa en el fenómeno de colapso posterior observado en el entrenamiento de Autoencoders Variacionales (VAE), destacando dos tipos de colapso distintos: colapso de difusión y colapso de concentración.

Les avancées récentes dans les modèles de diffusion latente (LDM) ont conduit à l'introduction de l'attaque de collapse postérieur (PCA), un cadre novateur visant à protéger les images contre la manipulation non autorisée. Cette approche s'inspire du phénomène de collapse postérieur observé dans l'entraînement des autoencodeurs variationnels (VAE), mettant en évidence deux types de collapse distincts : le collapse de diffusion et le collapse de concentration.

Recent advancements in Latent Diffusion Models (LDMs) have prompted the introduction of the Posterior Collapse Attack (PCA), a novel framework aimed at protecting images from unauthorized manipulation. This approach draws on the posterior collapse phenomenon observed in Variational Autoencoder (VAE) training, highlighting two distinct collapse types: diffusion collapse and concentration collapse.

A Gray-box Attack against Latent Diffusion Model-based Image Editing by Posterior Collapse

arXiv:2509.25228v2 Announce Type: replace 
Abstract: We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn from Haar-distributed orthogonal ensembles via QR decomposition of Gaussian matrices, to project data into lower-dimensional latent spaces for the base distribution. Unlike PCA-based flows or learned injective maps, RPFs are plug-and-play, efficient, and yield closed-form expressions for the Riemannian volume correction term. We demonstrate that RPFs are both theoretically grounded and practically effective, providing a strong baseline for generative modeling and a bridge between random projection theory and normalizing flows.

تم تقديم تدفقات الإسقاط العشوائي (RPFs) كإطار جديد لتدفقات التطبيع القابلة للحقن، باستخدام نظرية المصفوفات العشوائية والهندسة لإسقاط البيانات في فضاءات ذات أبعاد أقل. تستخدم هذه الطريقة مصفوفات شبه متعامدة عشوائية مستمدة من المصفوفات الغاوسية، مما يوفر نهجًا أكثر كفاءة وقائمًا على الأسس النظرية مقارنة بالتدفقات التقليدية المعتمدة على PCA.

Se han introducido los Random Projection Flows (RPFs) como un nuevo marco para los flujos normalizantes inyectivos, utilizando la teoría de matrices aleatorias y la geometría para proyectar datos en espacios de menor dimensión. Este método emplea matrices semi-ortogonales aleatorias derivadas de matrices gaussianas, ofreciendo un enfoque más eficiente y teóricamente fundamentado en comparación con los flujos basados en PCA tradicionales.

Les Random Projection Flows (RPFs) ont été introduits comme un nouveau cadre pour les flux normalisants injectifs, utilisant la théorie des matrices aléatoires et la géométrie pour projeter les données dans des espaces de dimension inférieure. Cette méthode emploie des matrices semi-orthogonales aléatoires dérivées de matrices gaussiennes, offrant une approche plus efficace et théoriquement fondée par rapport aux flux basés sur PCA traditionnels.

Random Projection Flows (RPFs) have been introduced as a new framework for injective normalizing flows, utilizing random matrix theory and geometry to project data into lower-dimensional spaces. This method employs random semi-orthogonal matrices derived from Gaussian matrices, offering a more efficient and theoretically grounded approach compared to traditional PCA-based flows.

PCA recovery thresholds in low-rank matrix inference with sparse noise

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