Language Models (LMs) are widely used in software engineering for code generation, but they may produce erroneous code. Rather than repairing outputs, a more thorough remedy is to address underlying model failures. LM repair offers a lightweight solution: it requires minimal data, lowers computational cost, and limits side effects. Unlike full retraining, LM repair focuses on applying tailored updates to targeted neurons, making it suitable for limited resources, high-performance demands, or strict safety requirements. In this paper, we propose Semantic Targeting for Analytical Repair (STAR), a novel semantic-based optimization method for repairing LLMs. STAR realizes the main operations of repairing LMs in an optimization process, including locating ``buggy neurons'', solving ``neuron patches'', and patching ``buggy neurons''. The neuron patches are computed with a solid semantic-based analytical formula, which directly bridges the changes to logits with the deltas of neurons, by steering latent representations. Compared to the prior work of LM repair (MINT) and standard optimization methods (SGD), STAR integrates their strengths while mitigating their limitations. By reformulating LM repair as an optimization process, STAR may solve multiple failures together, significantly improving the usefulness. Evaluated on coding tasks using popular code LMs, STAR demonstrates superior effectiveness compared with the state-of-the-art. Besides, STAR exhibits better efficiency. In terms of side effects, namely the balance between generalization and specificity, STAR outperforms prior work by a significant margin. Additionally, we conducted assessments on the overfitting risk of LM repair as well as the cumulative impact. Further, we analyzed the differences with pipeline-based methods and explained the reason why STAR is better and how it mitigated the common limitations of LM repair.

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