When Does Sparsity Mitigate the Curse of Depth in LLMs

Dilxat Muhtar, Xinyuan Song, Sebastian Pokutta, Max Zimmer, Nico Pelleriti, Thomas Hofmann, Shiwei Liu

Keywords: Curse of Depth, Variance Propagation, Layer Effectiveness, LLMs

TL;DR: Model sparsity is key to regularizing variance growth in deep neural networks and overcoming the curse of depth

Abstract: Recent work has demonstrated the curse of depth in large language models (LLMs), where later layers contribute less to learning and representation than earlier layers. Such under-utilization is linked to the accumulated growth of variance in Pre-Layer Normalization, which can push deep blocks toward near-identity behavior. In this paper, we demonstrate that, sparsity, beyond enabling efficiency, acts as a regulator of variance propagation and thereby improves depth utilization. Our investigation covers two sources of sparsity: (i) implicit sparsity, which emerges from training and data conditions, including weight sparsity induced by weight decay and attention sparsity induced by long-context inputs; and (ii) explicit sparsity, which is enforced by architectural design, including key/value-sharing sparsity in Grouped-Query Attention and expert-activation sparsity in Mixture-of-Experts. Our claim is thoroughly supported by controlled depth-scaling experiments and targeted layer effectiveness interventions. Across settings, we observe a consistent relationship: sparsity improves layer utilization by reducing output variance and promoting functional differentiation. We eventually distill our findings into a practical rule-of-thumb recipe for training depth-effective LLMs, yielding a notable 4.6% accuracy improvement on downstream tasks. Our results reveal sparsity, arising naturally from standard design choices, as a key yet previously overlooked mechanism for effective depth scaling in LLMs.

Submission Number: 73