ABSTRACT Library inventory is vital for collection management and reader satisfaction. Conventional manual methods cannot support real‐time updates, while existing automated solutions relying on centralized cloud computing suffer from bandwidth and latency limitations. To address these issues, we propose an edge‐cloud collaborative real‐time book inventory system. Spine detection and text recognition are executed on embedded edge devices, while the cloud handles rapid data retrieval to balance timeliness and accuracy. We design lightweight models for edge deployment, including the Library You Only Look Once (Lib‐YOLO) detector with a StarNet backbone, shared convolutional head, and dual‐scale hierarchical detection, supporting rotated objects for robust spine extraction. The optimized paddle practical optical character recognition (PP‐OCR) pipeline removes text rectification and integrates a filtering algorithm to reduce redundant computation and improve efficiency. Deployed on an NVIDIA Jetson Nano, the system achieves 73 ms spine detection latency, 191 ms text recognition latency, and 97.1% overall accuracy under simulated library conditions. The Lib‐YOLO model contains only 1.39 M parameters with 99% mean average precision (mAP), demonstrating the feasibility of precise, real‐time inventorying in resource‐constrained embedded environments.

Transformer-based models excel in various tasks but their generalization capabilities, especially in arithmetic reasoning, remain incompletely understood.Arithmetic tasks provide a controlled framework to explore these capabilities, yet performance anomalies persist, such as inconsistent effectiveness in multiplication and erratic generalization in modular addition (e.g., modulo 100 vs. 101).This paper develops a unified theoretical framework for understanding the generalization behaviors of transformers in arithmetic tasks, focusing on length generalization.Through detailed analysis of addition, multiplication, and modular operations, we reveal that translation invariance in addition aligns with relative positional encoding for robust generalization, while base mismatch in modular operations disrupts this alignment.Experiments across GPT-family models validate our framework, confirming its ability to predict generalization behaviors.Our work highlights the importance of task structure and training data distribution for achieving data-efficient and structure-aware training, providing a systematic approach to understanding of length generalization in transformers.