WUSPruner: Second-Moment-Optimal Transforms for Structured Pruning

The effectiveness of structured pruning depends on the basis in which model dimensions are removed. This raises a central question: how should a transformation be chosen to make coordinate deletion preserve the original computation? We introduce WUSPruner, a transform-based framework for structured pruning of large language models. We characterize the optimal invertible transformation for a local linear reconstruction objective and show that, under positive-definite second moments, the WUS transform attains the minimum deletion error. In this basis, the error decomposes into coordinate-wise contributions determined by a singular-value spectrum, providing a principled rule for truncation. Guided by this result, we construct a practical pruning method using blockwise polar factors of WUS, with coordinate importance recomputed in the resulting orthogonal bases. Experiments on Llama and Qwen models from 8B to 72B parameters show higher average accuracy than baselines across six knowledge and commonsense benchmarks and lower perplexity on PTB and C4. These findings demonstrate the value of designing the transformation around the coordinate-deletion objective for structured LLM pruning.