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This paper introduces a novel training methodology that enables a Transformer model to generalize the addition of two-digit numbers to numbers with unseen lengths of digits. The proposed approach employs an autoregressive generation technique, processing from right to left, which mimics a common manual method for adding large numbers. To the best of my knowledge, this methodology has not been previously explored in the literature. All results are reproducible, and the corresponding R code is available at github.com/AGPatriota/ALGA-R/.

This paper introduces Fetch-A-Set (FAS), a comprehensive benchmark tailored for legislative historical document analysis systems, addressing the challenges of large-scale document retrieval in historical contexts. The benchmark comprises a vast repository of documents dating back to the XVII century, serving both as a training resource and an evaluation benchmark for retrieval systems. It fills a critical gap in the literature by focusing on complex extractive tasks within the domain of cultural heritage. The proposed benchmark tackles the multifaceted problem of historical document analysis, including text-to-image retrieval for queries and image-to-text topic extraction from document fragments, all while accommodating varying levels of document legibility. This benchmark aims to spur advancements in the field by providing baselines and data for the development and evaluation of robust historical document retrieval systems, particularly in scenarios characterized by wide historical spectrum.

This paper presents Neural Visibility Field (NVF), a novel uncertainty quantification method for Neural Radiance Fields (NeRF) applied to active mapping. Our key insight is that regions not visible in the training views lead to inherently unreliable color predictions by NeRF at this region, resulting in increased uncertainty in the synthesized views. To address this, we propose to use Bayesian Networks to composite position-based field uncertainty into ray-based uncertainty in camera observations. Consequently, NVF naturally assigns higher uncertainty to unobserved regions, aiding robots to select the most informative next viewpoints. Extensive evaluations show that NVF excels not only in uncertainty quantification but also in scene reconstruction for active mapping, outperforming existing methods.

This paper presents a novel approach to visual simultaneous localization and mapping (SLAM) using multiple RGB-D cameras. The proposed method, Multicam-SLAM, significantly enhances the robustness and accuracy of SLAM systems by capturing more comprehensive spatial information from various perspectives. This method enables the accurate determination of pose relationships among multiple cameras without the need for overlapping fields of view. The proposed Muticam-SLAM includes a unique multi-camera model, a multi-keyframes structure, and several parallel SLAM threads. The multi-camera model allows for the integration of data from multiple cameras, while the multi-keyframes and parallel SLAM threads ensure efficient and accurate pose estimation and mapping. Extensive experiments in various environments demonstrate the superior accuracy and robustness of the proposed method compared to conventional single-camera SLAM systems. The results highlight the potential of the proposed Multicam-SLAM for more complex and challenging applications. Code is available at \url{//github.com/AlterPang/Multi_ORB_SLAM}.

This paper proposes a composite inner-product computation unit based on left-to-right (LR) arithmetic for the acceleration of convolution neural networks (CNN) on hardware. The efficacy of the proposed L2R-CIPU method has been shown on the VGG-16 network, and assessment is done on various performance metrics. The L2R-CIPU design achieves 1.06x to 6.22x greater performance, 4.8x to 15x more TOPS/W, and 4.51x to 53.45x higher TOPS/mm2 than prior architectures.

This letter studies a distribution-free, finite-sample data perturbation (DP) method, the Residual-Permuted Sums (RPS), which is an alternative of the Sign-Perturbed Sums (SPS) algorithm, to construct confidence regions. While SPS assumes independent (but potentially time-varying) noise terms which are symmetric about zero, RPS gets rid of the symmetricity assumption, but assumes i.i.d. noises. The main idea is that RPS permutes the residuals instead of perturbing their signs. This letter introduces RPS in a flexible way, which allows various design-choices. RPS has exact finite sample coverage probabilities and we provide the first proof that these permutation-based confidence regions are uniformly strongly consistent under general assumptions. This means that the RPS regions almost surely shrink around the true parameters as the sample size increases. The ellipsoidal outer-approximation (EOA) of SPS is also extended to RPS, and the effectiveness of RPS is validated by numerical experiments, as well.

The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the theory of matrix-variate regression and instrumental variable methods to construct distribution-free confidence regions for the state-space matrices. Both direct and indirect identification are studied, and the exactness as well as the strong consistency of the construction are proved. Furthermore, a new, computationally efficient ellipsoidal outer-approximation algorithm for the confidence regions is proposed. The new construction results in a semidefinite optimization problem which has an order-of-magnitude smaller number of constraints, as if one applied the ellipsoidal outer-approximation after vectorization. The effectiveness of the approach is also demonstrated empirically via a series of numerical experiments.

This paper presents LogiCode, a novel framework that leverages Large Language Models (LLMs) for identifying logical anomalies in industrial settings, moving beyond traditional focus on structural inconsistencies. By harnessing LLMs for logical reasoning, LogiCode autonomously generates Python codes to pinpoint anomalies such as incorrect component quantities or missing elements, marking a significant leap forward in anomaly detection technologies. A custom dataset "LOCO-Annotations" and a benchmark "LogiBench" are introduced to evaluate the LogiCode's performance across various metrics including binary classification accuracy, code generation success rate, and precision in reasoning. Findings demonstrate LogiCode's enhanced interpretability, significantly improving the accuracy of logical anomaly detection and offering detailed explanations for identified anomalies. This represents a notable shift towards more intelligent, LLM-driven approaches in industrial anomaly detection, promising substantial impacts on industry-specific applications.

We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a commonly used model for the unknown parameter is a random field. We make use of the circulant embedding procedure for sampling from the aforementioned coefficient. To improve the computational complexity of the MLMC estimator in the case of highly oscillatory random fields, we devise and implement a smoothing technique integrated into the circulant embedding method. This allows to choose the coarsest mesh on the first level of MLMC independently of the correlation length of the covariance function of the random field, leading to considerable savings in computational cost. We illustrate this with numerical experiments, where we see a saving of factor 5-10 in computational cost for accuracies of practical interest.