Efficient Adaptive Optimization via Subset-Norm and Subspace-Momentum: Fast, Memory-Reduced Training with Convergence Guarantees

• URL: http://arxiv.org/abs/2411.07120v1
• Date: Mon, 11 Nov 2024 16:48:07 GMT
• Title: Efficient Adaptive Optimization via Subset-Norm and Subspace-Momentum: Fast, Memory-Reduced Training with Convergence Guarantees
• Authors: Thien Hang Nguyen, Huy Le Nguyen,
• Abstract summary: We introduce two complementary techniques for memory optimization. One technique, Subset-Norm, reduces the momentum state's memory footprint by a low-dimensional subspace. The other technique, Subspace-Momentum, reduces the momentum state's memory footprint by a low-dimensional subspace.
• Score: 5.399838579600896
• License:
• Abstract: We introduce two complementary techniques for efficient adaptive optimization that reduce memory requirements while accelerating training of large-scale neural networks. The first technique, Subset-Norm adaptive step size, generalizes AdaGrad-Norm and AdaGrad(-Coordinate) by reducing the second moment term's memory footprint from $O(d)$ to $O(\sqrt{d})$ through step-size sharing, where $d$ is the model size. For non-convex smooth objectives under coordinate-wise sub-gaussian gradient noise, we prove a noise-adapted high-probability convergence guarantee showing improved dimensional dependence over existing methods. Our second technique, Subspace-Momentum, reduces the momentum state's memory footprint by operating in a low-dimensional subspace while applying standard SGD in the orthogonal complement. We establish high-probability convergence rates under similar relaxed assumptions. Empirical evaluation on LLaMA models from 60M to 1B parameters demonstrates the effectiveness of our methods, where combining subset-norm with subspace-momentum achieves Adam's validation perplexity in approximately half the training tokens (6.8B vs 13.1B) while using only 20% of the Adam's optimizer-states memory footprint and requiring minimal additional hyperparameter tuning.

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