CVFeb 4, 2023
Semantic-Guided Generative Image Augmentation Method with Diffusion Models for Image ClassificationBohan Li, Xiao Xu, Xinghao Wang et al.
Existing image augmentation methods consist of two categories: perturbation-based methods and generative methods. Perturbation-based methods apply pre-defined perturbations to augment an original image, but only locally vary the image, thus lacking image diversity. In contrast, generative methods bring more image diversity in the augmented images but may not preserve semantic consistency, thus incorrectly changing the essential semantics of the original image. To balance image diversity and semantic consistency in augmented images, we propose SGID, a Semantic-guided Generative Image augmentation method with Diffusion models for image classification. Specifically, SGID employs diffusion models to generate augmented images with good image diversity. More importantly, SGID takes image labels and captions as guidance to maintain semantic consistency between the augmented and original images. Experimental results show that SGID outperforms the best augmentation baseline by 1.72% on ResNet-50 (from scratch), 0.33% on ViT (ImageNet-21k), and 0.14% on CLIP-ViT (LAION-2B). Moreover, SGID can be combined with other image augmentation baselines and further improves the overall performance. We demonstrate the semantic consistency and image diversity of SGID through quantitative human and automated evaluations, as well as qualitative case studies.
CLMay 28
Scaling Laws for Agent Harnesses via Effective Feedback ComputeXuanliang Zhang, Dingzirui Wang, Keyan Xu et al.
Agent harnesses increasingly determine the performance of language-model systems by deciding how models call tools, receive feedback, verify intermediate states, store memory, and revise solutions. Yet current test-time scaling analyses often parameterize this process by raw expenditure -- tokens, tool calls, operations, wall time, or cost -- which does not distinguish useful feedback from redundant or unstable interaction. We introduce \emph{Effective Feedback Compute} (EFC), a trace-level scaling coordinate that credits feedback only when it is informative, valid, non-redundant, and retained for subsequent decisions, and we normalize it by task demand when comparing tasks with different feedback requirements. Across synthetic controllable tasks, executable code tasks, real benchmark traces, held-out splits, and a prospective validation batch, EFC-based coordinates consistently predict failure rates better than raw-compute baselines and a strong multivariate SAS baseline. In controlled scaling, raw tokens and tool calls explain limited variation ($R^2=0.33$ and $0.42$), SAS reaches $0.88$, while Oracle-EFC and Estimated-EFC reach $0.94$ and Oracle-EFC/$D_{\mathrm{task}}$ reaches $0.99$. Matched-budget interventions show that improving feedback quality raises success from $0.27$ to $0.90$ while raw cost and tool calls are fixed. On mixed real traces, NRS-EFC/$D_{\mathrm{task}}$ reaches $R^2=0.92$ while raw compute has near-zero or negative fit, and it remains the best predictor in a prospective holdout ($R^2=0.85$). These results suggest that harness scaling is governed less by how much computation is spent than by how efficiently raw budget is converted into durable, task-sufficient feedback.
CLAug 16, 2024
FLEXTAF: Enhancing Table Reasoning with Flexible Tabular FormatsXuanliang Zhang, Dingzirui Wang, Longxu Dou et al.
The table reasoning task aims to answer the question according to the given table. Currently, using Large Language Models (LLMs) is the predominant method for table reasoning. Most existing methods employ a fixed tabular format to represent the table, which could limit the performance. Given that each instance requires different capabilities and models possess varying abilities, we assert that different instances and models suit different tabular formats. We prove the aforementioned claim through quantitative analysis of experimental results, where different instances and models achieve different performances using various tabular formats. Building on this discussion, we propose FLEXTAF-Single and FLEXTAF-Vote to enhance table reasoning performance by employing flexible tabular formats. Specifically, (i) FLEXTAF-Single trains a classifier to predict the most suitable tabular format based on the instance and the LLM. (ii) FLEXTAF-Vote integrates the results across different formats. Our experiments on WikiTableQuestions and TabFact reveal significant improvements, with average gains of 2.3% and 4.8% compared to the best performance achieved using a fixed tabular format with greedy decoding and self-consistency decoding, thereby validating the effectiveness of our methods.
CLAug 16, 2024
DAC: Decomposed Automation Correction for Text-to-SQLDingzirui Wang, Longxu Dou, Xuanliang Zhang et al.
Text-to-SQL is an important task that helps people obtain information from databases by automatically generating SQL queries. Considering the brilliant performance, approaches based on Large Language Models (LLMs) become the mainstream for text-to-SQL. Among these approaches, automated correction is an effective approach that further enhances performance by correcting the mistakes in the generated results. The existing correction methods require LLMs to directly correct with generated SQL, while previous research shows that LLMs do not know how to detect mistakes, leading to poor performance. Therefore, in this paper, we propose to employ the decomposed correction to enhance text-to-SQL performance. We first demonstrate that decomposed correction outperforms direct correction since detecting and fixing mistakes with the results of the decomposed sub-tasks is easier than with SQL. Based on this analysis, we introduce Decomposed Automation Correction (DAC), which corrects SQL by decomposing text-to-SQL into entity linking and skeleton parsing. DAC first generates the entity and skeleton corresponding to the question and then compares the differences between the initial SQL and the generated entities and skeleton as feedback for correction. Experimental results show that our method improves performance by $3.7\%$ on average of Spider, Bird, and KaggleDBQA compared with the baseline method, demonstrating the effectiveness of DAC.
CLNov 14, 2025
DiscoX: Benchmarking Discourse-Level Translation task in Expert DomainsXiying Zhao, Zhoufutu Wen, Zhixuan Chen et al.
The evaluation of discourse-level translation in expert domains remains inadequate, despite its centrality to knowledge dissemination and cross-lingual scholarly communication. While these translations demand discourse-level coherence and strict terminological precision, current evaluation methods predominantly focus on segment-level accuracy and fluency. To address this limitation, we introduce DiscoX, a new benchmark for discourse-level and expert-level Chinese-English translation. It comprises 200 professionally-curated texts from 7 domains, with an average length exceeding 1700 tokens. To evaluate performance on DiscoX, we also develop Metric-S, a reference-free system that provides fine-grained automatic assessments across accuracy, fluency, and appropriateness. Metric-S demonstrates strong consistency with human judgments, significantly outperforming existing metrics. Our experiments reveal a remarkable performance gap: even the most advanced LLMs still trail human experts on these tasks. This finding validates the difficulty of DiscoX and underscores the challenges that remain in achieving professional-grade machine translation. The proposed benchmark and evaluation system provide a robust framework for more rigorous evaluation, facilitating future advancements in LLM-based translation.
CLNov 5, 2025
MME-CC: A Challenging Multi-Modal Evaluation Benchmark of Cognitive CapacityKaiyuan Zhang, Chenghao Yang, Zhoufutu Wen et al.
As reasoning models scale rapidly, the essential role of multimodality in human cognition has come into sharp relief, driving a growing need to probe vision-centric cognitive behaviors. Yet, existing multimodal benchmarks either overemphasize textual reasoning or fall short of systematically capturing vision-centric cognitive behaviors, leaving the cognitive capacity of MLLMs insufficiently assessed. To address this limitation, we introduce MME-CC (Multi-Modal Evaluation benchmark of Cognitive Capacity), a vision-grounded benchmark that organizes 11 representative reasoning tasks into three fundamental categories of visual information: spatial, geometric, and knowledge-based reasoning, and provides fine-grained analyses of MLLMs' cognitive capacity across these dimensions. Based on MME-CC, we conduct extensive experiments over 16 representative MLLMs. Our study reveals that closed-source models currently lead overall (e.g., 42.66 for Gemini-2.5-Pro vs. 30.45 for GLM-4.5V), while spatial and geometric reasoning remain broadly weak (less than or equal to 30%). We further identify common error patterns, including orientation mistakes, fragile cross-view identity persistence, and poor adherence to counterfactual instructions, and observe that Chain-of-Thought typically follows a three-stage process (extract -> reason -> verify) with heavy reliance on visual extraction. We hope this work catalyzes a shift toward treating the cognitive capacity of MLLMs as central to both evaluation and model design.
CLJul 8, 2025Code
A Survey on Latent ReasoningRui-Jie Zhu, Tianhao Peng, Tianhao Cheng et al.
Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, especially when guided by explicit chain-of-thought (CoT) reasoning that verbalizes intermediate steps. While CoT improves both interpretability and accuracy, its dependence on natural language reasoning limits the model's expressive bandwidth. Latent reasoning tackles this bottleneck by performing multi-step inference entirely in the model's continuous hidden state, eliminating token-level supervision. To advance latent reasoning research, this survey provides a comprehensive overview of the emerging field of latent reasoning. We begin by examining the foundational role of neural network layers as the computational substrate for reasoning, highlighting how hierarchical representations support complex transformations. Next, we explore diverse latent reasoning methodologies, including activation-based recurrence, hidden state propagation, and fine-tuning strategies that compress or internalize explicit reasoning traces. Finally, we discuss advanced paradigms such as infinite-depth latent reasoning via masked diffusion models, which enable globally consistent and reversible reasoning processes. By unifying these perspectives, we aim to clarify the conceptual landscape of latent reasoning and chart future directions for research at the frontier of LLM cognition. An associated GitHub repository collecting the latest papers and repos is available at: https://github.com/multimodal-art-projection/LatentCoT-Horizon/.
LGSep 16, 2025Code
FinSearchComp: Towards a Realistic, Expert-Level Evaluation of Financial Search and ReasoningLiang Hu, Jianpeng Jiao, Jiashuo Liu et al.
Search has emerged as core infrastructure for LLM-based agents and is widely viewed as critical on the path toward more general intelligence. Finance is a particularly demanding proving ground: analysts routinely conduct complex, multi-step searches over time-sensitive, domain-specific data, making it ideal for assessing both search proficiency and knowledge-grounded reasoning. Yet no existing open financial datasets evaluate data searching capability of end-to-end agents, largely because constructing realistic, complicated tasks requires deep financial expertise and time-sensitive data is hard to evaluate. We present FinSearchComp, the first fully open-source agent benchmark for realistic, open-domain financial search and reasoning. FinSearchComp comprises three tasks -- Time-Sensitive Data Fetching, Simple Historical Lookup, and Complex Historical Investigation -- closely reproduce real-world financial analyst workflows. To ensure difficulty and reliability, we engage 70 professional financial experts for annotation and implement a rigorous multi-stage quality-assurance pipeline. The benchmark includes 635 questions spanning global and Greater China markets, and we evaluate 21 models (products) on it. Grok 4 (web) tops the global subset, approaching expert-level accuracy. DouBao (web) leads on the Greater China subset. Experimental analyses show that equipping agents with web search and financial plugins substantially improves results on FinSearchComp, and the country origin of models and tools impact performance significantly.By aligning with realistic analyst tasks and providing end-to-end evaluation, FinSearchComp offers a professional, high-difficulty testbed for complex financial search and reasoning.
CLFeb 9
When Does Context Help? Error Dynamics of Contextual Information in Large Language ModelsDingzirui Wang, Xuanliang Zhang, Keyan Xu et al.
Contextual information at inference time, such as demonstrations, retrieved knowledge, or interaction history, can substantially improve large language models (LLMs) without parameter updates, yet its theoretical role remains poorly understood beyond specific settings such as in-context learning (ICL). We present a unified theoretical framework for analyzing the effect of arbitrary contextual information in Transformer-based LLMs. Our analysis characterizes contextual influence through output error dynamics. In a single-layer Transformer, we prove that the context-conditioned error vector decomposes additively into the baseline error vector and a contextual correction vector. This yields necessary geometric conditions for error reduction: the contextual correction must align with the negative baseline error and satisfy a norm constraint. We further show that the contextual correction norm admits an explicit upper bound determined by context-query relevance and complementarity. These results extend to multi-context and multi-layer Transformers. Experiments across ICL, retrieval-augmented generation, and memory evolution validate our theory and motivate a principled context selection strategy that improves performance by $0.6\%$.
CLFeb 9
How Do Language Models Understand Tables? A Mechanistic Analysis of Cell LocationXuanliang Zhang, Dingzirui Wang, Keyan Xu et al.
While Large Language Models (LLMs) are increasingly deployed for table-related tasks, the internal mechanisms enabling them to process linearized two-dimensional structured tables remain opaque. In this work, we investigate the process of table understanding by dissecting the atomic task of cell location. Through activation patching and complementary interpretability techniques, we delineate the table understanding mechanism into a sequential three-stage pipeline: Semantic Binding, Coordinate Localization, and Information Extraction. We demonstrate that models locate the target cell via an ordinal mechanism that counts discrete delimiters to resolve coordinates. Furthermore, column indices are encoded within a linear subspace that allows for precise steering of model focus through vector arithmetic. Finally, we reveal that models generalize to multi-cell location tasks by multiplexing the identical attention heads identified during atomic location. Our findings provide a comprehensive explanation of table understanding within Transformer architectures.
CLFeb 13, 2024
A Survey of Table Reasoning with Large Language ModelsXuanliang Zhang, Dingzirui Wang, Longxu Dou et al.
Table reasoning, which aims to generate the corresponding answer to the question following the user requirement according to the provided table, and optionally a text description of the table, effectively improving the efficiency of obtaining information. Recently, using Large Language Models (LLMs) has become the mainstream method for table reasoning, because it not only significantly reduces the annotation cost but also exceeds the performance of previous methods. However, existing research still lacks a summary of LLM-based table reasoning works. Due to the existing lack of research, questions about which techniques can improve table reasoning performance in the era of LLMs, why LLMs excel at table reasoning, and how to enhance table reasoning abilities in the future, remain largely unexplored. This gap significantly limits progress in research. To answer the above questions and advance table reasoning research with LLMs, we present this survey to analyze existing research, inspiring future work. In this paper, we analyze the mainstream techniques used to improve table reasoning performance in the LLM era, and the advantages of LLMs compared to pre-LLMs for solving table reasoning. We provide research directions from both the improvement of existing methods and the expansion of practical applications to inspire future research.
CLFeb 16, 2024
Improving Demonstration Diversity by Human-Free Fusing for Text-to-SQLDingzirui Wang, Longxu Dou, Xuanliang Zhang et al.
Currently, the in-context learning method based on large language models (LLMs) has become the mainstream of text-to-SQL research. Previous works have discussed how to select demonstrations related to the user question from a human-labeled demonstration pool. However, human labeling suffers from the limitations of insufficient diversity and high labeling overhead. Therefore, in this paper, we discuss how to measure and improve the diversity of the demonstrations for text-to-SQL. We present a metric to measure the diversity of the demonstrations and analyze the insufficient of the existing labeled data by experiments. Based on the above discovery, we propose fusing iteratively for demonstrations (Fused) to build a high-diversity demonstration pool through human-free multiple-iteration synthesis, improving diversity and lowering label cost. Our method achieves an average improvement of 3.2% and 5.0% with and without human labeling on several mainstream datasets, which proves the effectiveness of Fused.
CLFeb 16, 2024
MURRE: Multi-Hop Table Retrieval with Removal for Open-Domain Text-to-SQLXuanliang Zhang, Dingzirui Wang, Longxu Dou et al.
The open-domain text-to-SQL task aims to retrieve question-relevant tables from massive databases and generate SQL. However, the performance of current methods is constrained by single-hop retrieval, and existing multi-hop retrieval of open-domain question answering is not directly applicable due to the tendency to retrieve tables similar to the retrieved ones but irrelevant to the question. Since the questions in text-to-SQL usually contain all required information, while previous multi-hop retrieval supplements the questions with retrieved documents. Therefore, we propose the multi-hop table retrieval with removal (MURRE), which removes previously retrieved information from the question to guide the retriever towards unretrieved relevant tables. Our experiments on two open-domain text-to-SQL datasets demonstrate an average improvement of 5.7% over the previous state-of-the-art results.
CLDec 16, 2024
SCITAT: A Question Answering Benchmark for Scientific Tables and Text Covering Diverse Reasoning TypesXuanliang Zhang, Dingzirui Wang, Baoxin Wang et al.
Scientific question answering (SQA) is an important task aimed at answering questions based on papers. However, current SQA datasets have limited reasoning types and neglect the relevance between tables and text, creating a significant gap with real scenarios. To address these challenges, we propose a QA benchmark for scientific tables and text with diverse reasoning types (SciTaT). To cover more reasoning types, we summarize various reasoning types from real-world questions. To involve both tables and text, we require the questions to incorporate tables and text as much as possible. Based on SciTaT, we propose a strong baseline (CaR), which combines various reasoning methods to address different reasoning types and process tables and text at the same time. CaR brings average improvements of 12.9% over other baselines on SciTaT, validating its effectiveness. Error analysis reveals the challenges of SciTaT, such as complex numerical calculations and domain knowledge.
CLMay 21, 2025
RoT: Enhancing Table Reasoning with Iterative Row-Wise TraversalsXuanliang Zhang, Dingzirui Wang, Keyan Xu et al.
The table reasoning task, crucial for efficient data acquisition, aims to answer questions based on the given table. Recently, reasoning large language models (RLLMs) with Long Chain-of-Thought (Long CoT) significantly enhance reasoning capabilities, leading to brilliant performance on table reasoning. However, Long CoT suffers from high cost for training and exhibits low reliability due to table content hallucinations. Therefore, we propose Row-of-Thought (RoT), which performs iteratively row-wise table traversal, allowing for reasoning extension and reflection-based refinement at each traversal. Scaling reasoning length by row-wise traversal and leveraging reflection capabilities of LLMs, RoT is training-free. The sequential traversal encourages greater attention to the table, thus reducing hallucinations. Experiments show that RoT, using non-reasoning models, outperforms RLLMs by an average of 4.3%, and achieves state-of-the-art results on WikiTableQuestions and TableBench with comparable models, proving its effectiveness. Also, RoT outperforms Long CoT with fewer reasoning tokens, indicating higher efficiency.
CLJun 29, 2025
V-SYNTHESIS: Task-Agnostic Synthesis of Consistent and Diverse In-Context Demonstrations from Scratch via V-EntropyDingzirui Wang, Xuanliang Zhang, Keyan Xu et al.
High labeling cost for in-context learning (ICL) demonstrations motivates using large language models (LLMs) for synthesis to reduce overhead. However, existing synthesis methods are mainly task-specific or rely on pre-existing demonstrations. So this paper focuses on synthesizing demonstrations from scratch for arbitrary tasks. A major challenge in synthesizing from scratch is ensuring consistency with the target task, as the lack of labeling guidance could lead to synthesis bias. We first propose a consistency metric called V-Score, which has higher performance and lower computation cost compared with the metrics based on grams or embedding vectors. Furthermore, we introduce V-Synthesis, which leverages V-Score for proportional sampling to ensure both high consistency and diversity of synthesized demonstrations. Experimental results demonstrate that V-Synthesis yields an average performance improvement of 2.0% compared to existing synthesis methods confirming the effectiveness of V-Synthesis.
CLJun 29, 2025
Format-Adapter: Improving Reasoning Capability of LLMs by Adapting Suitable FormatDingzirui Wang, Xuanliang Zhang, Rongyu Cao et al.
Generating and voting multiple answers is an effective method to mitigate reasoning inconsistencies of large language models (LLMs). Prior works have shown that multiple reasoning formats outperform a single format when generating multiple answers. However, previous works using multiple formats rely on formats labeled by humans, which could be unsuitable for all tasks and have high labeling costs. To address this issue, we adapt suitable formats to the given tasks by generating and selecting formats. We first propose how to measure the reasoning error when generating multiple answers. Then, we introduce Format-Adapter, which utilizes LLMs to generate and select suitable reasoning formats by minimizing the error measurement we present. We conduct experiments on math and commonsense reasoning tasks, where Format-Adapter achieves a 4.3% performance improvement on average over previous works, demonstrating the effectiveness.
CLJun 29, 2025
Learning-to-Context Slope: Evaluating In-Context Learning Effectiveness Beyond Performance IllusionsDingzriui Wang, Xuanliang Zhang, Keyan Xu et al.
In-context learning (ICL) has emerged as an effective approach to enhance the performance of large language models (LLMs). However, its effectiveness varies significantly across models and tasks, posing challenges for practitioners to determine when ICL reliably improves performance. Current evaluation approaches, reliant on performance change after applying ICL, suffer from low reliability, poor attribution, and impracticality in data-insufficient scenarios. We propose the Learning-to-Context Slope (LCS), a novel metric that quantifies ICL effectiveness by modeling the slope between learning gain (loss decrease from demonstrations) and contextual relevance (demonstration-input relevance). LCS addresses key limitations of performance-based metrics: (1) it captures continuous loss changes even when outputs are incorrect, improving reliability; (2) its formulation attributes ICL failures to weak contextual alignment (inability to adapt inputs to demonstrations) or strong output calibration (self-verification of correctness); and (3) it minimizes reliance on labeled data via synthetic evaluation. Extensive experiments demonstrate that LCS strongly correlates with performance improvements in labeled settings and reliably reflects true effectiveness in biased or data-scarce scenarios. Further analysis reveals actionable thresholds for LCS and identifies model capabilities critical to ICL success.
CLApr 14, 2025
Abacus-SQL: A Text-to-SQL System Empowering Cross-Domain and Open-Domain Database RetrievalKeyan Xu, Dingzirui Wang, Xuanliang Zhang et al.
The existing text-to-SQL systems have made significant progress in SQL query generation, but they still face numerous challenges. Existing systems often lack retrieval capabilities for open-domain databases, requiring users to manually filter relevant databases. Additionally, their cross-domain transferability is limited, making it challenging to accommodate diverse query requirements. To address these issues, we propose Abacus-SQL. Abacus-SQL utilizes database retrieval technology to accurately locate the required databases in an open-domain database environment. It also enhances the system cross-domain transfer ability through data augmentation methods. Moreover, Abacus-SQL employs Pre-SQL and Self-debug methods, thereby enhancing the accuracy of SQL queries. Experimental results demonstrate that Abacus-SQL performs excellently in multi-turn text-to-SQL tasks, effectively validating the approach's effectiveness. Abacus-SQL is publicly accessible at https://huozi.8wss.com/abacus-sql/.
CLFeb 24, 2025
MULTITAT: Benchmarking Multilingual Table-and-Text Question AnsweringXuanliang Zhang, Dingzirui Wang, Keyan Xu et al.
Question answering on the hybrid context of tables and text (TATQA) is a critical task, with broad applications in data-intensive domains. However, existing TATQA datasets are limited to English, leading to several drawbacks: (i) They overlook the challenges of multilingual TAT-QA and cannot assess model performance in the multilingual setting. (ii) They do not reflect real-world scenarios where tables and texts frequently appear in non-English languages. To address the limitations, we propose the first multilingual TATQA dataset (MULTITAT). Specifically, we sample data from 3 mainstream TATQA datasets and translate it into 10 diverse languages. To align the model TATQA capabilities in English with other languages, we develop a baseline, Ours. Experimental results reveal that the performance on non-English data in MULTITAT drops by an average of 19.4% compared to English, proving the necessity of MULTITAT. We further analyze the reasons for this performance gap. Furthermore, Ours outperforms other baselines by an average of 3.3, demonstrating its effectiveness.
CLFeb 16, 2024
Enhancing Numerical Reasoning with the Guidance of Reliable Reasoning ProcessesDingzirui Wang, Longxu Dou, Xuanliang Zhang et al.
Numerical reasoning is an essential ability for NLP systems to handle numeric information. Recent research indicates that fine-tuning a small-scale model to learn generating reasoning processes alongside answers can significantly enhance performance. However, current methods have the limitation that most methods generate reasoning processes with large language models (LLMs), which are "unreliable" since such processes could contain information unrelated to the answer. To address this limitation, we introduce Enhancing NumeriCal reasOning with Reliable procEsses (Encore), which derives the reliable reasoning process by decomposing the answer formula, ensuring which fully supports the answer. Nevertheless, models could lack enough data to learn the reasoning process generation adequately, since our method generates only one single reasoning process for one formula. To overcome this difficulty, we present a series of pre-training tasks to help models learn the reasoning process generation with synthesized data. The experiments show that Encore yields improvement on all five experimental datasets with an average of 1.8%, proving the effectiveness of our method.
CLSep 25, 2025
Bounds of Chain-of-Thought Robustness: Reasoning Steps, Embed Norms, and BeyondDingzirui Wang, Xuanliang Zhang, Keyan Xu et al.
Existing research indicates that the output of Chain-of-Thought (CoT) is significantly affected by input perturbations. Although many methods aim to mitigate such impact by optimizing prompts, a theoretical explanation of how these perturbations influence CoT outputs remains an open area of research. This gap limits our in-depth understanding of how input perturbations propagate during the reasoning process and hinders further improvements in prompt optimization methods. Therefore, in this paper, we theoretically analyze the effect of input perturbations on the fluctuation of CoT outputs. We first derive an upper bound for input perturbations under the condition that the output fluctuation is within an acceptable range, based on which we prove that: (i) This upper bound is positively correlated with the number of reasoning steps in the CoT; (ii) Even an infinitely long reasoning process cannot eliminate the impact of input perturbations. We then apply these conclusions to the Linear Self-Attention (LSA) model, which can be viewed as a simplified version of the Transformer. For the LSA model, we prove that the upper bound for input perturbation is negatively correlated with the norms of the input embedding and hidden state vectors. To validate this theoretical analysis, we conduct experiments on three mainstream datasets and four mainstream models. The experimental results align with our theoretical analysis, empirically demonstrating the correctness of our findings.