Finite-width fully connected neural networks with Gaussian-initialized weights deviate from their infinite-width Gaussian limit, exhibiting non-vanishing higher-order cumulants. We approximate these deviations, for a neural network evaluated in a finite number of inputs, using multidimensional Edgeworth expansions of arbitrary order $4m-1$, with $m\in\mathbb{N}$. Assuming that the corresponding Gaussian limit has an invertible covariance matrix and that the activation function is polynomially bounded, we establish a bound of order $n^{-m}$ on the total variation distance between the law of the true network output and its Edgeworth approximation, with matching lower bounds. As an application, we quantify the error in Bayesian posterior distributions when the prior is replaced by its Edgeworth expansion. Our results are more general and also apply to sequences of conditionally Gaussian vectors converging to a Gaussian vector with invertible covariance.

It consists of an image encoder with a Vision Transformer [17] architecture, a text encoder with a similar Transformer architecture, and heads that predict bounding boxes and label scores from provided images and text queries. Input(s) An image and a list of free-text object descriptions (queries).

Compared totheexisting sampling-based approaches, which are inapplicable to the infinite time horizon setting, wetrain aseparate deterministic neural networkthatservesasaninfinite timehorizon safety certificate.

One reason for this is the intractability of analyzing NNs, ODEs and hybrid systems.

Infrastructure-as-Code (IaC), an important component of cloud computing, allows the definition of cloud infrastructure in high-level programs.

Infrastructure-as-Code (IaC), an important component of cloud computing, allows the definition of cloud infrastructure in high-level programs.

Robust Document Layout Analysis (DLA) is critical for the automated processing and understanding of historical documents with complex page organizations. This paper benchmarks five state-of-the-art object detection architectures on three annotated datasets representing a spectrum of codicological complexity: The e-NDP, a corpus of Parisian medieval registers (1326-1504); CATMuS, a diverse multiclass dataset derived from various medieval and modern sources (ca.12th-17th centuries) and HORAE, a corpus of decorated books of hours (ca.13th-16th centuries). We evaluate two Transformer-based models (Co-DETR, Grounding DINO) against three YOLO variants (AABB, OBB, and YOLO-World). Our findings reveal significant performance variations dependent on model architecture, data set characteristics, and bounding box representation. In the e-NDP dataset, Co-DETR achieves state-of-the-art results (0.752 mAP@.50:.95), closely followed by YOLOv11X-OBB (0.721). Conversely, on the more complex CATMuS and HORAE datasets, the CNN-based YOLOv11x-OBB significantly outperforms all other models (0.564 and 0.568, respectively). This study unequivocally demonstrates that using Oriented Bounding Boxes (OBB) is not a minor refinement but a fundamental requirement for accurately modeling the non-Cartesian nature of historical manuscripts. We conclude that a key trade-off exists between the global context awareness of Transformers, ideal for structured layouts, and the superior generalization of CNN-OBB models for visually diverse and complex documents.