Jul 2026· Advances in Engineering Technology Research· Vol 17, pp. 1461· 0 citations· 10 references
TL;DR
An activation steering method based on single-vector ablation is proposed to enhance mathematical reasoning by injecting a carefully constructed steering vector into the model’s residual stream by constructing the AS direction from the activation difference between mathematical and general-domain samples.
Abstract
Large Language Models (LLMs) often exhibit limited performance on mathematical reasoning tasks. This paper proposes an activation steering (AS) method based on single-vector ablation to enhance mathematical reasoning by injecting a carefully constructed steering vector into the model’s residual stream. Specifically, the AS direction is constructed from the activation difference between mathematical and general-domain samples and is injected into designated transformer layers during inference. Experiments on Llama-3-8B-Instruct demonstrate that the proposed method improves mathematical reasoning accuracy from 11.0% to 39.6%, while simultaneously enhancing general capabilities as well. However, transfer experiments on Qwen2.5-7B-Instruct fail to achieve comparable improvements, revealing the strong model dependency of the proposed approach. Furthermore, the effects of layer selection, steering coefficient, positional window, and steering vector construction are systematically investigated. This study provides both empirical evidence and theoretical insights regarding the application of activation steering methods.
Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing evaluation methods, which typically focus either on the final answer or on the intermediate reasoning steps, reduce mathematical reasoning to a shallow input–output mapping, overlooking its inherently multi-stage and multi-dimensional cognitive nature. Inspired by Pólya’s problem-solving theory, we propose SMART, a benchmark that decomposes mathematical problem-solving into four cognitive dimensions: S emantic Understanding, M athematical Reasoning, A rithmetic Computation, and R eflection & Refinemen t , and introduces dimension-specific tasks to measure the corresponding cognitive processes of LLMs. We apply SMART to 22 state-of-the-art open-and closed-source LLMs and uncover substantial discrepancies in their capabilities across dimensions. Our findings reveal genuine weaknesses in current models and motivate a new metric, the All-Pass Score, designed to better capture true problem-solving capability. Data is available at https://huggingface.co/datasets/ewdfd/SMART.
Yu-Heng Hou, Mei Wang, Yaoyao Zhong et al.· Annual Meeting of the Associ...· 0 citations
Reasoning failures in large language models (LLMs) are usually evaluated from final answers, but a wrong answer does not reveal why the model failed. The same incorrect output may reflect missing capability, an unstable reasoning trajectory, or a failure to activate a reasoning state that is already available in the frozen model. Existing prompting and benchmark-based evaluation methods mostly operate at the output level, while generic activation-steering methods typically apply global directions without diagnosing which examples require intervention. In this paper, we introduce SPARK, which uses hidden-state response to diagnose whether a model internally enters an effective reasoning state and to guide lightweight test-time steering. The key observation is that raw hidden-state susceptibility is strongly confounded by prompt length, especially in programmatic and algorithmic reasoning where harder serialized instances naturally become longer. SPARK therefore uses length-controlled susceptibility to separate input-scale effects from residual reasoning activation, and combines this signal with cross-layer coordination to select reasoning-active anchors and under-activated hard examples. We use FRONTIER-4.5K as a controlled programmatic reasoning suite for latent profiling and difficulty-aware analysis, and evaluate SPARK-Steering on GSM8K and MATH-500 with forward-only benchmark profiling. Our method improves Qwen3 series models consistently; on MATH-500, accuracy rises from 82.0% to 84.6% for Qwen3-4B and from 82.4% to 85.6% for Qwen3-8B. These results suggest that susceptibility can serve not only as a diagnostic signal for reasoning failures, but also as a practical guide for targeted test-time intervention.
Dongxu Zhang, Yiding Sun, Zihao Guo et al.· 0 citations
Large Language Models (LLMs) are predominantly assessed based on their common sense reasoning, language comprehension, and logical reasoning abilities. While models trained in specialized domains like mathematics or coding have demonstrated remarkable advancements in logical reasoning, there remains a significant gap in evaluating their code generation capabilities. Existing benchmark datasets fall short in pinpointing specific strengths and weaknesses, impeding targeted enhancements in models’ reasoning abilities to synthesize code.
To bridge this gap, this thesis introduces two novel contributions: CodeEval and CodeQual. CodeEval is an innovative, pedagogical benchmarking method that mirrors the evaluation processes encountered in academic programming courses. It comprises a multi-dimensional benchmark dataset of 602 hand-crafted problems designed to rigorously evaluate LLMs across 24 distinct aspects of Python programming, covering three proficiency levels—beginner, intermediate, and advanced—and includes both class-based and function-based problem types with detailed problem specifications and comprehensive test suites achieving 99.1% coverage. To facilitate widespread adoption, we developed RunCodeEval, an open-source execution framework that provides researchers with a ready-to-use evaluation pipeline. Our evaluation of 15 state-of-the-art LLMs revealed consistent performance degradation with increasing complexity (validated statistically, Cohen’s d = 0.790) and universal struggles with advanced concepts like concurrency.
Code quality is inherently subjective, encompassing dimensions like readability, efficiency, and adherence to language idioms that traditional static metrics fail to capture adequately. While large language models can assess these subjective qualities, lightweight models offer practical advantages: seamless CI/CD pipeline integration, lower operational costs, and full control over model behavior. We investigate whether such models can learn to assess code quality by training on synthetic LLM annotations. We introduce CodeQual, a dataset of 5,819 code samples derived from five established sources spanning diverse domains—competitive programming, pedagogical problems, software engineering, and general benchmarks—scored by LLMs across five quality dimensions, with 655 human-annotated samples for evaluation. Our fine-tuned model, CodeQualBERT, not only matches LLM performance but exceeds inter-human agreement on all five dimensions, achieving 16–100% improvement over the inter-human agreement baseline.
Together, these contributions provide a comprehensive framework for evaluating and improving LLMs in software engineering contexts, encompassing both functional correctness assessment and subjective code quality evaluation.
Experimental results show that PD-CoTD significantly enhances the mathematical reasoning abilities of SLMs and provides an effective solution for deploying powerful reasoning in resource-constrained environments.
Zhe Wang, Long Zhang, Fengbo Zheng et al.· International journal of sof...· 0 citations
Transformer-based large language models (LLMs) continue to achieve state-of-the-art performance across various natural language processing tasks. However, their subpar performance on seemingly elementary problems, such as basic arithmetic, raises concerns about model reliability, safety, and ethical deployment. In this study, we demonstrate that the performance of a vanilla Transformer model trained on integer arithmetic tasks can be improved using methods effective for human learners. We begin by decomposing the arithmetic task into well-defined subtasks and conducting loss convergence order analysis together with ablation studies for each subtask. Our findings reveal that LLMs exhibit learning patterns similar to those of human learners, with a faster learning speed for simpler subtasks compared to more complex ones. In addition, we successfully improved the accuracy of LLMs by applying problem-solving strategies and cognitive empowerment methods shown to enhance the performance of human learners. This suggests that transformer-based LLMs may share cognitive processes with human learners in arithmetic. Lastly, we provide a comprehensive demonstration of our method's effectiveness, including significant accuracy improvement experiments, visualization verification, and explanation-based analysis to illuminate the intricacies of LLMs in arithmetic learning. In general, this work explores the potential similarities between transformer-based LLMs and human learners, supported by explainable AI (XAI) verifications, ultimately fostering trust in LLMs for critical and high-stakes applications.
Luyu Qiu, Jianing Li, Hwanhee Kim et al.· 0 citations
This work proposes StrategyBench, which selects strategy-inducible tasks from BIG-Bench, constructs reference strategies, and defines evaluation metrics along two dimensions: strategy quality and downstream utility, and experiments show that explicit strategy utility differs substantially across task categories and depends on both strategy generation and execution conditions.
Jinghan Tan, Yuanzheng Wang, Lu Chen et al.· 0 citations