Weight-only post-training quantization (PTQ) for large language models (LLMs) typically ends with the projection of floating-point weights onto a uniform integer lattice, introducing structured output error due to non-zero activation means. Existing bias correction methods compensate for this shift by adding bias terms, which is incompatible with modern bias-less architectures such as LLaMA and Mistral and only addresses the error indirectly. We propose **Complementary Lattice Correction (CLC)**, a lightweight post-quantization method that corrects projection error directly on the integer lattice without modifying the model architecture. CLC performs a budget-constrained greedy descent that selectively flips quantized weights to adjacent lattice levels. We further show that CLC provably reduces the first-moment error and admits a worst-case bound on the layer-wise mean-squared error change, which certifies non-increase under a verifiable budget condition. Experiments across multiple models, quantizers, and bit widths show that CLC consistently improves perplexity and downstream accuracy with negligible overhead.

The integration of large language models (LLMs) into topic modeling has shown promise for improving topic interpretability and coherence, particularly by exploiting the generative capabilities of LLMs through instruction-based prompting. However, existing methods often incur substantial computational cost and inference complexity. To address these limitations, we propose **LLMFeed**, a novel framework that leverages **feed**back from an **LLM** to improve topic model optimization. Specifically, the LLM is used to **evaluate** topic quality, **identify** semantic meaning, and **recommend** representative topic words. These signals are then incorporated to (i) refine topic representations via Direct Preference Optimization (DPO), and (ii) guide contrastive learning for improved document-topic assignments. Extensive experiments show that **LLMFeed** achieves a 7.6% gain in topic coherence and over 10% improvement in doc-topic distributions on 20 Newsgroups dataset, while requiring only minutes to run, compared with hours for recent LLM-integrated topic modeling methods.