Abstract
We present \LegoLM{}, a structured weight-sharing compression framework for large language models grounded in a systematic study of why global weight sharing fails and how to fix it. We identify two distinct failure modes. Distributional mismatch: for vector blocks of dimension d <= 2, transformer layers with heterogeneous weight scales impose a scale-mismatch penalty that grows linearly with d and cannot be resolved by increasing K, producing perplexity in the millions.Outlier dominance: for scalar blocks, a fraction ~1/K of weights lies beyond the outermost Lloyd-Max decision threshold and cannot be represented by any centroid; their misrepresentation accumulates across layers, causing catastrophic quality loss. \LegoLM{} resolves both failure modes via three data-free adaptations: 1 scalar-block encoding to eliminate the d-linear mismatch component, 2 percentile-selective replacement that identifies and preserves outlier weights verbatim, and 3 boundary-layer protection for the first and last transformer blocks. Across GPT-2 small (124M) and Mistral-7B, \LegoLM{} achieves +0.03% PPL degradation at 4.41X compression on Mistral-7B - outperforming PTQ-8bit in both quality and compression ratio - and -0.02% at 2.67X. Downstream evaluation on LAMBADA and HellaSwag confirms that \LegoLM{} at K=64, p=99% preserves accuracy within noise at 5.12 X compression, exceeding PTQ-8bit's compression ratio while matching its accuracy. We further discover that outlier dominance grows with model scale: full replacement at K=128 degrades GPT-2 small by only +23% but catastrophically degrades Mistral-7B by +1,134,279%, while selective replacement at p=99% rescues both models to under +15%. A controlled ablation confirms that selective replacement is the dominant mechanism: adding it to per-layer K-means also yields near-lossless quality, matching \LegoLM{} within 0.02%.
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Recent SVD based compression methods for large language models like SVD LLM and Basis Sharing can be unified under one optimization problem. While mathematical proofs and tests on Pythia models show this unified approach improves weight reconstruction error by up to 46% percent it fails in practical tasks. Downstream metrics like perplexity and accuracy severely degrade compared to standard per layer SVD LLM. The authors explain this failure mechanistically. Although the bundle method mathematically couples adjacent layers the transformer residual stream actually decouples them during forward passes. Thus per layer optimality matters more than joint cross layer optimization. The paper concludes that weight space reconstruction is a flawed objective for cross layer compression and future methods must focus on per layer activation reconstruction instead.
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