EMA-Nesterov: Stabilizing Nesterov's Lookahead for Accelerated Deep Learning Optimization
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918520956125184 |
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| author | Yau, Chung-Yiu Li, Dawei Glentis, Athanasios Boreiko, Valentyn Wai, Hoi-To Hong, Mingyi |
| author_facet | Yau, Chung-Yiu Li, Dawei Glentis, Athanasios Boreiko, Valentyn Wai, Hoi-To Hong, Mingyi |
| contents | Lookahead-based acceleration methods, such as Nesterov's momentum, are widely used in optimization, but they often become unreliable in deep learning training mainly due to stochastic gradient noise and non-convex loss landscapes. In particular, standard lookahead relies on short-horizon update signals (e.g., differences between consecutive iterates), which are inherently noisy and can lead to unstable extrapolation directions. This work revisits Nesterov's acceleration from a trajectory perspective and argues that effective acceleration in deep learning should harness the low-frequency trends of optimization trajectories rather than extrapolating noisy one-step updates. Leveraging this insight, we propose EMA-Nesterov, a simple modification that replaces the standard Nesterov's lookahead direction with an exponential moving average (EMA) of parameter updates. This yields a stabilized lookahead direction that captures and harnesses the evolving trend of the training trajectory through a low-pass filter, while remaining adaptive to progressive changes via the geometric weighting structure of EMA. We show that EMA-Nesterov retains a theoretical accelerated convergence rate in convex problems that is analogous to Nesterov's accelerated gradient method. Furthermore, we provide empirical evidence on language model pre-training to verify that EMA-Nesterov is broadly applicable across a range of fine-tuned base optimizers, including Adam, SOAP, Muon, as well as complex optimizers that achieve state-of-the-art performance on optimization benchmarks (NanoGPT). Compared to prior lookahead methods, EMA-Nesterov achieves better performance by avoiding the instability of short-horizon lookahead and the non-adaptivity of long-horizon lookahead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_25395 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | EMA-Nesterov: Stabilizing Nesterov's Lookahead for Accelerated Deep Learning Optimization Yau, Chung-Yiu Li, Dawei Glentis, Athanasios Boreiko, Valentyn Wai, Hoi-To Hong, Mingyi Machine Learning Optimization and Control Lookahead-based acceleration methods, such as Nesterov's momentum, are widely used in optimization, but they often become unreliable in deep learning training mainly due to stochastic gradient noise and non-convex loss landscapes. In particular, standard lookahead relies on short-horizon update signals (e.g., differences between consecutive iterates), which are inherently noisy and can lead to unstable extrapolation directions. This work revisits Nesterov's acceleration from a trajectory perspective and argues that effective acceleration in deep learning should harness the low-frequency trends of optimization trajectories rather than extrapolating noisy one-step updates. Leveraging this insight, we propose EMA-Nesterov, a simple modification that replaces the standard Nesterov's lookahead direction with an exponential moving average (EMA) of parameter updates. This yields a stabilized lookahead direction that captures and harnesses the evolving trend of the training trajectory through a low-pass filter, while remaining adaptive to progressive changes via the geometric weighting structure of EMA. We show that EMA-Nesterov retains a theoretical accelerated convergence rate in convex problems that is analogous to Nesterov's accelerated gradient method. Furthermore, we provide empirical evidence on language model pre-training to verify that EMA-Nesterov is broadly applicable across a range of fine-tuned base optimizers, including Adam, SOAP, Muon, as well as complex optimizers that achieve state-of-the-art performance on optimization benchmarks (NanoGPT). Compared to prior lookahead methods, EMA-Nesterov achieves better performance by avoiding the instability of short-horizon lookahead and the non-adaptivity of long-horizon lookahead. |
| title | EMA-Nesterov: Stabilizing Nesterov's Lookahead for Accelerated Deep Learning Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2605.25395 |