Super Weights in LLMs and the Failure of Selective Training

Forum topic · 小凯 · 2026-07-13

Summary

This arXiv paper (2507.08699) examines Super Weights—individual parameters whose removal degrades LLM performance by orders of magnitude—and challenges the assumption that they are effective training targets. The authors show that pruning-induced degradation does not apply universally to all LLMs, and that training Super Weights in isolation (100 to 8,192 parameters) drops accuracy to random-guessing levels on OLMo-1B and OLMo-7B. Expanding training to local neighborhoods of up to 36K parameters provides no improvement. The failure is specific to Super Weight coordinates: training an equal number of randomly chosen positions in the same down_proj layers actually improves over the baseline, proving the collapse stems from targeting Super Weights rather than sparsity itself. In contrast, vanilla LoRA succeeds using only 0.16% of parameters by updating every position in attention weight matrices with low-rank structure, and applying the same low-rank updates to down_proj also works. Ablations across 10 random seeds confirm that restricting LoRA updates to Super Weight coordinates yields statistically indistinguishable results. The findings establish that parameter importance does not imply trainability in isolation—effective fine-tuning depends on structured decomposition of entire layers, not targeting individual important weights.

Paper Overview

Field: Machine Learning
Authors: Shreyas Subramanian, Adewale Akinfaderin, Akarsha Sehwag
Published: 2025-07-12
arXiv: 2507.08699

Abstract

Recent work identified Super Weights, individual parameters whose removal degrades model performance by orders of magnitude. We show that this degradation due to pruning Super Weights does not universally apply to all LLMs. Furthermore, if these parameters are so important, Super Weight-aware training should be effective. We show the opposite. Training Super Weights in isolation (100 to 8,192 parameters) drops accuracy to random-guessing levels on both OLMo-1B and OLMo-7B, and expanding to local neighborhoods of up to 36K parameters provides no improvement. The failure is specific to Super Weight coordinates: training an equal number of randomly chosen positions in the same down_proj layers instead improves over the baseline, so the collapse comes from targeting Super Weights, not from sparsity itself.

Key Findings

Pruning degradation is not universal: Performance loss from pruning Super Weights does not hold across all LLMs.
Isolated training fails: Fine-tuning only Super Weights (100–8,192 parameters) reduces accuracy to random-guessing levels on OLMo-1B and OLMo-7B.
Local neighborhoods don't help: Expanding training to up to 36K surrounding parameters gives no improvement.
The failure is coordinate-specific: Training equal numbers of randomly chosen positions in the same down_proj layers improves over the baseline—so collapse comes from targeting Super Weight coordinates, not sparsity itself.
LoRA succeeds: Vanilla LoRA updates every position in attention weight matrices via low-rank structure and works with only 0.16% of parameters; the same low-rank updates applied to down_proj also succeed.
Seed-robust result: Ablations across 10 random seeds confirm that restricting LoRA updates to Super Weight coordinates produces statistically indistinguishable results.

Conclusion

These findings establish that parameter importance does not imply the viability of training that parameter in isolation. Effective fine-tuning relies on structured decomposition across the whole layer, rather than targeting individual important weights.

Source: arXiv:2507.08699