Adaptive Optimization via Momentum on Variance-Normalized Gradients
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917266427215872 |
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| author | Patitucci, Francisco Mokhtari, Aryan |
| author_facet | Patitucci, Francisco Mokhtari, Aryan |
| contents | We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization. MVN-Grad scales each coordinate by an exponential moving average of gradient uncertainty and applies momentum to the resulting normalized gradients, eliminating the cross-time coupling between stale momentum and a stochastic normalizer present in standard Adam-type updates. We prove that this decoupling yields strictly smaller one-step conditional update variance than momentum-then-normalize variance methods under standard noise assumptions, and that MVN-Grad is robust to outliers: it has a uniformly bounded response to single gradient spikes.
In low-variance regimes, we further show variance normalization avoids sign-type collapse associated with second-moment scaling and can yield accelerated convergence. Across CIFAR-100 image classification and GPT-style language modeling benchmarks, MVN-Grad matches or outperforms Adam, AdaBelief, and LaProp, delivering smoother training and improved generalization with no added overhead. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10204 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Adaptive Optimization via Momentum on Variance-Normalized Gradients Patitucci, Francisco Mokhtari, Aryan Machine Learning Optimization and Control We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization. MVN-Grad scales each coordinate by an exponential moving average of gradient uncertainty and applies momentum to the resulting normalized gradients, eliminating the cross-time coupling between stale momentum and a stochastic normalizer present in standard Adam-type updates. We prove that this decoupling yields strictly smaller one-step conditional update variance than momentum-then-normalize variance methods under standard noise assumptions, and that MVN-Grad is robust to outliers: it has a uniformly bounded response to single gradient spikes. In low-variance regimes, we further show variance normalization avoids sign-type collapse associated with second-moment scaling and can yield accelerated convergence. Across CIFAR-100 image classification and GPT-style language modeling benchmarks, MVN-Grad matches or outperforms Adam, AdaBelief, and LaProp, delivering smoother training and improved generalization with no added overhead. |
| title | Adaptive Optimization via Momentum on Variance-Normalized Gradients |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2602.10204 |