arXiv:2507.05550v4 Announce Type: replace 
Abstract: Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the target data distribution via deterministic or stochastic differential equations (SDEs). The score function is typically estimated from data using a variety of approximation techniques, such as denoising or sliced score matching, Hyv\"arien's method, or Schr\"odinger bridges. In this paper, we derive an exact, closed-form, expression for the score function for a broad class of nonlinear diffusion generative models. Our approach combines modern stochastic analysis tools such as Malliavin derivatives and their adjoint operators (Skorokhod integrals or Malliavin Divergence) with a new Bismut-type formula. The resulting expression for the score function can be written entirely in terms of the first and second variation processes, with all Malliavin derivatives systematically eliminated, thereby enhancing its practical applicability. The theoretical framework presented in this work offers a principled foundation for advancing score estimation methods in generative modelling, enabling the design of new sampling algorithms for complex probability distributions. Our results can be extended to broader classes of stochastic differential equations, opening new directions for the development of score-based diffusion generative models.

تقدم ورقة جديدة تعبيرًا مغلقًا عن دالة الدرجة في نماذج التوليد الانتشاري، مما يعزز طرق التقدير المستخدمة في توزيعات البيانات المعقدة. هذه الخطوة مهمة لأنها تبسط تطبيق دوال الدرجة، التي تعتبر حاسمة لرسم خرائط توزيعات الاحتمال المعروفة إلى توزيعات البيانات المستهدفة من خلال المعادلات التفاضلية العشوائية.

Un nuevo artículo presenta una expresión en forma cerrada para la función de puntuación en modelos generativos de difusión, mejorando los métodos de estimación utilizados en distribuciones de datos complejas. Este avance es significativo ya que simplifica la aplicación de funciones de puntuación, que son cruciales para mapear distribuciones de probabilidad conocidas a distribuciones de datos objetivo a través de ecuaciones diferenciales estocásticas.

Un nouvel article présente une expression sous forme fermée pour la fonction de score dans les modèles génératifs de diffusion, améliorant les méthodes d'estimation utilisées dans les distributions de données complexes. Cette avancée est significative car elle simplifie l'application des fonctions de score, qui sont cruciales pour mapper les distributions de probabilité connues aux distributions de données cibles via des équations différentielles stochastiques.

A new paper presents a closed-form expression for the score function in diffusion generative models, enhancing the estimation methods used in complex data distributions. This advancement is significant as it simplifies the application of score functions, which are crucial for mapping known probability distributions to target data distributions through stochastic differential equations.

A Malliavin calculus approach to score functions in diffusion generative models

Although Black Friday is still two weeks away, you can find great Nintendo Switch and Switch 2 deals now. I've collected the best from Walmart, Best Buy, and more.

مع اقتراب يوم الجمعة السوداء بعد أسبوعين، تتوفر بالفعل عروض مبكرة على أجهزة نينتندو سويتش وسويتش 2. تقدم متاجر كبيرة مثل وول مارت وبيست باي أكثر من 20 عرضًا، مما يوفر للمستهلكين فرصة لتوفير المال على منتجات الألعاب الشهيرة قبل موسم التسوق للعطلات.

A medida que se acerca el Black Friday en dos semanas, ya están disponibles ofertas anticipadas en las consolas Nintendo Switch y Switch 2. Grandes minoristas como Walmart y Best Buy están ofreciendo más de 20 ventas, brindando a los consumidores la oportunidad de ahorrar en productos de videojuegos populares antes de la locura de compras navideñas.

À l'approche de Black Friday dans deux semaines, des offres anticipées sur les consoles Nintendo Switch et Switch 2 sont déjà disponibles. Des détaillants majeurs comme Walmart et Best Buy proposent plus de 20 ventes, offrant aux consommateurs l'occasion d'économiser sur des produits de jeu populaires avant la ruée des achats de vacances.

As Black Friday approaches in two weeks, early deals on Nintendo Switch and Switch 2 consoles are already available. Major retailers like Walmart and Best Buy are offering over 20 sales, providing consumers with an opportunity to save on popular gaming products ahead of the holiday shopping rush.

Best early Black Friday Nintendo Switch deals 2025: 20+ sales out early

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Black Friday is just over one week away, but you can get a jump on your holiday shopping list with great deals on gaming desktop PCs, monitors, SSDs, and more.

Best early Black Friday gaming PC deals 2025: My favorite sales out early

Although Black Friday is still two weeks away, you can find great PlayStation deals now from across the internet. I've collected some of the best.

على الرغم من أن يوم الجمعة السوداء لا يزال بعيدًا لمدة أسبوعين، إلا أن هناك بالفعل عروض رائعة على بلاي ستيشن متاحة عبر الإنترنت. يبرز المقال أكثر من 20 عرضًا يمكن العثور عليها عبر منصات مختلفة، مما يوفر فرصة مبكرة للمتسوقين للاستفادة من الخصومات قبل التاريخ الرسمي ليوم الجمعة السوداء.

Aunque el Black Friday aún está a dos semanas de distancia, ya hay excelentes ofertas de PlayStation disponibles en línea. El artículo destaca más de 20 ventas que se pueden encontrar en varias plataformas, brindando una oportunidad anticipada para que los compradores aprovechen los descuentos antes de la fecha oficial del Black Friday.

Bien que le Black Friday soit encore dans deux semaines, il existe déjà d'excellentes offres PlayStation disponibles en ligne. L'article met en avant plus de 20 ventes que l'on peut trouver sur diverses plateformes, offrant ainsi une occasion précoce aux acheteurs de profiter des réductions avant la date officielle du Black Friday.

Although Black Friday is still two weeks away, there are already great PlayStation deals available online. The article highlights over 20 sales that can be found across various platforms, providing an early opportunity for shoppers to take advantage of discounts ahead of the official Black Friday date.

Best early Black Friday PlayStation deals 2025: 20+ sales out now

Black Friday is just over a week away, and you can already find great deals on TVs and home theater equipment from Samsung, Sony, and more.

Best early Black Friday TV deals 2025: Save on Samsung, TCL, and more

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arXiv:2511.06854v2 Announce Type: replace-cross 
Abstract: Irregularly sampled time series (ISTS), characterized by non-uniform time intervals with natural missingness, are prevalent in real-world applications. Existing approaches for ISTS modeling primarily rely on observed values to impute unobserved ones or infer latent dynamics. However, these methods overlook a critical source of learning signal: the reconstruction error inherently produced during model training. Such error implicitly reflects how well a model captures the underlying data structure and can serve as an informative proxy for unobserved values. To exploit this insight, we propose iTimER, a simple yet effective self-supervised pre-training framework for ISTS representation learning. iTimER models the distribution of reconstruction errors over observed values and generates pseudo-observations for unobserved timestamps through a mixup strategy between sampled errors and the last available observations. This transforms unobserved timestamps into noise-aware training targets, enabling meaningful reconstruction signals. A Wasserstein metric aligns reconstruction error distributions between observed and pseudo-observed regions, while a contrastive learning objective enhances the discriminability of learned representations. Extensive experiments on classification, interpolation, and forecasting tasks demonstrate that iTimER consistently outperforms state-of-the-art methods under the ISTS setting.

تُعتبر السلاسل الزمنية المأخوذة بشكل غير منتظم (ISTS) شائعة في التطبيقات الواقعية، حيث تتميز بفترات زمنية غير متساوية وغيابات طبيعية. تعتمد الأساليب الحالية لنمذجة ISTS بشكل أساسي على القيم المرصودة لاستنتاج القيم غير المرصودة، متجاهلة إشارة التعلم الناتجة عن خطأ إعادة البناء الذي يتم إنتاجه أثناء تدريب النموذج. يقترح الإطار المقترح iTimER استغلال هذا الخطأ في إعادة البناء لتحسين تعلم التمثيل من خلال توليد ملاحظات زائفة للعلامات الزمنية غير المرصودة، مما يحسن نمذجة ISTS.

Las series temporales muestreadas de manera irregular (ISTS) son comunes en aplicaciones del mundo real, caracterizadas por intervalos de tiempo no uniformes y ausencias naturales. Los métodos existentes para la modelización de ISTS suelen depender de valores observados para inferir los no observados, ignorando la señal de aprendizaje proveniente del error de reconstrucción generado durante el entrenamiento del modelo. El marco propuesto iTimER aprovecha este error de reconstrucción para mejorar el aprendizaje de la representación generando pseudo-observaciones para marcas de tiempo no observa…

Les séries temporelles échantillonnées de manière irrégulière (ISTS) sont courantes dans les applications réelles, caractérisées par des intervalles de temps non uniformes et des absences naturelles. Les méthodes traditionnelles de modélisation des ISTS s'appuient souvent sur des valeurs observées pour inférer celles non observées, négligeant le signal d'apprentissage provenant de l'erreur de reconstruction produite lors de l'entraînement du modèle. Le cadre proposé iTimER exploite cette erreur de reconstruction pour améliorer l'apprentissage de la représentation en générant des pseudo-observa…

Irregularly sampled time series (ISTS) are common in real-world applications, characterized by non-uniform time intervals and natural missingness. Traditional ISTS modeling methods often rely on observed values to infer unobserved ones, neglecting the learning signal from reconstruction error produced during model training. The proposed iTimER framework leverages this reconstruction error to enhance representation learning by generating pseudo-observations for unobserved timestamps, thus improving the modeling of ISTS.

Beyond Observations: Reconstruction Error-Guided Irregularly Sampled Time Series Representation Learning

arXiv:2503.09887v2 Announce Type: replace-cross 
Abstract: We develop a novel semigroup stability analysis based on Lyapunov techniques and contraction coefficients to prove exponential convergence of Sinkhorn equations on weighted Banach spaces. This operator-theoretic framework yields exponential decays of Sinkhorn iterates towards Schr\"odinger bridges with respect to general classes of $\phi$-divergences and Kantorovich-type criteria, including the relative entropy, squared Hellinger integrals, $\alpha$-divergences as well as weighted total variation norms and Wasserstein distances. To the best of our knowledge, these contraction inequalities are the first results of this type in the literature on entropic transport and the Sinkhorn algorithm.
  We also provide Lyapunov contractions principles under minimal regularity conditions that allow to provide quantitative exponential stability estimates for a large class of Sinkhorn semigroups. We apply this novel framework in a variety of situations, ranging from polynomial growth potentials and heavy tailed marginals on general normed spaces to more sophisticated boundary state space models, including semi-circle transitions, Beta, Weibull, exponential marginals as well as semi-compact models. Last but not least, our approach also allows to consider statistical finite mixture of the above models, including kernel-type density estimators of complex data distributions arising in generative modeling.

On the contraction properties of Sinkhorn semigroups

arXiv:2511.13049v1 Announce Type: cross 
Abstract: We study a matrix completion problem where both the ground truth $R$ matrix and the unknown sampling distribution $P$ over observed entries are low-rank matrices, and \textit{share a common subspace}. We assume that a large amount $M$ of \textit{unlabeled} data drawn from the sampling distribution $P$ is available, together with a small amount $N$ of labeled data drawn from the same distribution and noisy estimates of the corresponding ground truth entries. This setting is inspired by recommender systems scenarios where the unlabeled data corresponds to `implicit feedback' (consisting in interactions such as purchase, click, etc. ) and the labeled data corresponds to the `explicit feedback', consisting of interactions where the user has given an explicit rating to the item. Leveraging powerful results from the theory of low-rank subspace recovery, together with classic generalization bounds for matrix completion models, we show error bounds consisting of a sum of two error terms scaling as $\widetilde{O}\left(\sqrt{\frac{nd}{M}}\right)$ and $\widetilde{O}\left(\sqrt{\frac{dr}{N}}\right)$ respectively, where $d$ is the rank of $P$ and $r$ is the rank of $M$. In synthetic experiments, we confirm that the true generalization error naturally splits into independent error terms corresponding to the estimations of $P$ and and the ground truth matrix $\ground$ respectively. In real-life experiments on Douban and MovieLens with most explicit ratings removed, we demonstrate that the method can outperform baselines relying only on the explicit ratings, demonstrating that our assumptions provide a valid toy theoretical setting to study the interaction between explicit and implicit feedbacks in recommender systems.

يتناول المقال مشكلة إكمال المصفوفات حيث تكون كل من مصفوفة الحقيقة الأساسية وتوزيع العينة غير المعروف مصفوفات منخفضة الرتبة تشترك في فضاء فرعي مشترك. يُفترض أن هناك كمية كبيرة من البيانات غير المعلّمة المتاحة، جنبًا إلى جنب مع كمية صغيرة من البيانات المعلّمة، مستلهمة من أنظمة التوصية. تستفيد الدراسة من نتائج استرداد الفضاءات الفرعية منخفضة الرتبة وحدود التعميم الكلاسيكية لإظهار حدود الخطأ، مما يساهم في التقدم في تقنيات التعلم شبه المراقب.

El artículo aborda un problema de completación de matrices donde tanto la matriz de verdad subyacente como la distribución de muestreo desconocida son matrices de bajo rango que comparten un subespacio común. Se asume que hay una gran cantidad de datos no etiquetados disponibles, junto con una pequeña cantidad de datos etiquetados, inspirado en sistemas de recomendación. El estudio aprovecha resultados de recuperación de subespacios de bajo rango y límites de generalización clásicos para demostrar límites de error, contribuyendo a los avances en técnicas de aprendizaje semi-supervisado.

L'article traite d'un problème de complétion de matrice où à la fois la matrice de vérité de base et la distribution d'échantillonnage inconnue sont des matrices de faible rang partageant un sous-espace commun. Il suppose qu'une grande quantité de données non étiquetées provenant de la distribution d'échantillonnage est disponible, ainsi qu'une petite quantité de données étiquetées, inspirée par les systèmes de recommandation. L'étude utilise des résultats de récupération de sous-espace de faible rang et des bornes de généralisation classiques pour démontrer des bornes d'erreur, contribuant au…

The article discusses a matrix completion problem where both the ground truth matrix and the unknown sampling distribution are low-rank matrices sharing a common subspace. It assumes a large amount of unlabeled data from the sampling distribution is available alongside a small amount of labeled data, inspired by recommender systems. The study leverages low-rank subspace recovery results and classic generalization bounds for matrix completion models to demonstrate error bounds, contributing to advancements in semi-supervised learning techniques.

A Malliavin calculus approach to score functions in diffusion generative models

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