Only relative ranks matter in weight-clustered large language models

• URL: http://arxiv.org/abs/2603.17917v1
• Date: Wed, 18 Mar 2026 16:55:13 GMT
• Title: Only relative ranks matter in weight-clustered large language models
• Abstract summary: Large language models (LLMs) contain billions of parameters, yet many exact values are not essential.<n>We show that what matters most is the relative rank of weights-whether one connection is stronger or weaker than another-rather than precise magnitudes.<n>For Llama 3.1-8B-Instruct and SmolLM2-135M, reducing each matrix to only 16-64 distinct values preserves strong accuracy without retraining.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large language models (LLMs) contain billions of parameters, yet many exact values are not essential. We show that what matters most is the relative rank of weights-whether one connection is stronger or weaker than another-rather than precise magnitudes. To reduce the number of unique weight values, we apply weight clustering to pretrained models, replacing every weight matrix with K shared values from K-means. For Llama 3.1-8B-Instruct and SmolLM2-135M, reducing each matrix to only 16-64 distinct values preserves strong accuracy without retraining, providing a simple, training-free method to compress LLMs on disk. Optionally fine-tuning only the cluster means (centroids) recovers 30-40 percent of the remaining accuracy gap at minimal cost. We then systematically randomize cluster means while keeping assignments fixed. Scrambling the relative ranks of the clusters degrades quality sharply-perplexity can increase by orders of magnitude-even when global statistics such as mean and variance are preserved. In contrast, rank-preserving randomizations cause almost no loss at mid and late layers. On the other hand, when many layers are perturbed simultaneously, progressive layer-by-layer replacement reveals that scale drift-not rank distortion-is the dominant collapse mechanism; however, an affine correction w' = aw + b with a > 0 (which preserves both rank order and overall weight distribution) can substantially delay this drift. This rank-based perspective offers a new lens on model compression and robustness.

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