The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Liang, Qiyao Song, Jinyeop Liu, Yizhou Gore, Jeff Fiete, Ila Miikkulainen, Risto Qiu, Xin |
| author_facet | Liang, Qiyao Song, Jinyeop Liu, Yizhou Gore, Jeff Fiete, Ila Miikkulainen, Risto Qiu, Xin |
| contents | Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., $N\!\approx\!30$), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00170 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective Liang, Qiyao Song, Jinyeop Liu, Yizhou Gore, Jeff Fiete, Ila Miikkulainen, Risto Qiu, Xin Machine Learning Artificial Intelligence Weight-perturbation evolution strategies (ES) can fine-tune billion-parameter language models with surprisingly small populations (e.g., $N\!\approx\!30$), contradicting classical zeroth-order curse-of-dimensionality intuition. We also observe a second seemingly separate phenomenon: under fixed hyperparameters, the stochastic fine-tuning reward often rises, peaks, and then degrades in both ES and GRPO. We argue that both effects reflect a shared geometric property of fine-tuning landscapes: they are low-dimensional in curvature. A small set of high-curvature dimensions dominates improvement, producing (i) heterogeneous time scales that yield rise-then-decay under fixed stochasticity, as captured by a minimal quadratic stochastic-ascent model, and (ii) degenerate improving updates, where many random perturbations share similar components along these directions. Using ES as a geometric probe on fine-tuning reward landscapes of GSM8K, ARC-C, and WinoGrande across Qwen2.5-Instruct models (0.5B--7B), we show that reward-improving perturbations remain empirically accessible with small populations across scales. Together, these results reconcile ES scalability with non-monotonic training dynamics and suggest that high-dimensional fine-tuning may admit a broader class of viable optimization methods than worst-case theory implies. |
| title | The Blessing of Dimensionality in LLM Fine-tuning: A Variance-Curvature Perspective |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.00170 |