SHIFT-LLM: Distribution Shift Correction in Depth-Pruned LLMs

Depth pruning removes entire Transformer blocks to reduce the inference cost of large language models, but disrupts the hidden-state distributions expected by downstream layers, leading to significant accuracy loss. We introduce SHIFT-LLM, a training-free post-pruning correction framework that inserts a Linear Residual Adapter (LRA) at each pruning site. Each LRA preserves the identity pathway of the original residual block and adds a lightweight affine residual correction. This correction is calibrated via closed-form least-squares regression on a small held-out set, without gradient computation, to approximate the missing residual update produced by the pruned block. Together with the preserved identity pathway, the resulting LRA output approximates the hidden state produced by the original block, thereby mitigating the distributional mismatch introduced by layer removal while avoiding the expensive attention and feed-forward computations of the removed blocks. The resulting LRAs support low-rank factorization and exact merging across consecutive pruned layers for additional compression, and combine naturally with parameter-efficient fine-tuning for further recovery beyond fine-tuning the pruned model alone. Experiments on five model families, six layer-selection criteria, and seven zero-shot benchmarks show that SHIFT-LLM consistently recovers accuracy lost to depth pruning across most configurations, achieving gains up to +15.7 points on Llama-3.1-8B-Instruct while requiring only a few hundred calibration samples and no gradient computation.