arXiv:2605.28961v1 Announce Type: cross Abstract: Existing theory of momentum assumes that gradients arrive at every parameter at a roughly constant rate, an assumption violated in practice by heavy-tailed data distributions and modern architectures. We theoretically analyze the dynamics of two tractable models of momentum under sparse updates: a least squares model with sparse inputs and a logistic regression model with a rare class. Both admit exact closed-form second-moment dynamics whose high-dimensional limits we characterize across three scaling exponents for sparsity, batch size, and mo
This research is emerging as AI model complexity increases and the practical challenges of training large models with non-ideal data distributions become more apparent, driving the need for more robust optimization theories.
Improved theoretical understanding of stochastic momentum under sparse updates can lead to more efficient and reliable training of large AI models, particularly in scenarios with imbalanced or heavy-tailed data.
The theoretical foundation for optimizing certain AI models is being refined, potentially enabling better performance and stability in specific, challenging real-world applications.
- · AI researchers and practitioners
- · Developers of large language models
- · Sparse data analytics platforms
- · Undifferentiated optimization algorithms
- · Resource-constrained AI training efforts relying on suboptimal methods
More stable and faster convergence for AI models trained with sparse, heavy-tailed data.
Potential for developing new, more specialized optimization algorithms that exploit sparsity patterns.
Reduced computational costs for certain AI applications, fostering wider adoption in resource-limited environments.
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Read at arXiv cs.LG