Why Smaller Is Slower? Dimensional Misalignment in Compressed LLMs

Post-training compression reduces LLM parameter counts but often produces irregular tensor dimensions that degrade GPU performance – a phenomenon we call \emph{dimensional misalignment}. We present a full-stack analysis tracing root causes at three levels: framework, library, and hardware. The key insight is that model inference becomes slower because the resulting dimensions are unfriendly with the GPU execution stack. For example, compressing Llama-3-8B with activation-aware singular value decomposition (ASVD) has 15% fewer parameters yet runs no faster than the uncompressed baseline, because 95% of its dimensions are misaligned. We propose $\mathbf{\text{GAC}}$ (GPU-Aligned Compression), a new compression paradigm that wraps any dimension-reducing compressor and re-selects hardware-aligned dimensions via multi-choice knapsack optimization under the same parameter budget. We evaluate GAC on Llama-3-8B with ASVD and LLM-Pruner, achieving 100% alignment and recovering up to 1.5$\times$ speedup while preserving model quality.