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.

The task of text-to-table receives widespread attention, yet its importance and difficulty are underestimated. Existing works use simple datasets similar to table-to-text tasks and employ methods that ignore domain structures. As a bridge between raw text and statistical analysis, the text-to-table task often deals with complex semi-structured texts that refer to specific domain topics in the real world with entities and events, especially from those of social sciences. In this paper, we analyze the limitations of benchmark datasets and methods used in the text-to-table literature and redefine the text-to-table task to improve its compatibility with long text-processing tasks. Based on this redefinition, we propose a new dataset called CPL (Chinese Private Lending), which consists of judgments from China and is derived from a real-world legal academic project. We further propose TKGT (Text-KG-Table), a two stages domain-aware pipeline, which firstly generates domain knowledge graphs (KGs) classes semi-automatically from raw text with the mixed information extraction (Mixed-IE) method, then adopts the hybrid retrieval augmented generation (Hybird-RAG) method to transform it to tables for downstream needs under the guidance of KGs classes. Experiment results show that TKGT achieves state-of-the-art (SOTA) performance on both traditional datasets and the CPL. Our data and main code are available at https://github.com/jiangpw41/TKGT.