Research Shows Edge of Stability Phenomenon Selectively Affects Learning Across Training Data Groups
A new machine learning study finds that the edge of stability—a phenomenon in neural network training—does not affect all data groups equally, instead redistributing learning progress across the training distribution. The research identifies two conditions necessary for a group to benefit: alignment of its aggregate gradient with the top Hessian eigenvector and sustained non-vanishing gradient magnitude. The findings suggest the edge of stability functions as a mechanism governing how learning is allocated across different subsets of data, with implications for understanding neural network training dynamics.
Researchers have demonstrated that the edge of stability (EoS), a known phenomenon in neural network optimization, selectively shapes learning across different subsets of the training distribution rather than acting as a purely global property. Using a branching intervention technique that allows entry and exit from the EoS regime from identical training states, the authors causally establish a trade-off where some data groups experience amplified learning progress while others are suppressed. The study identifies two necessary conditions for groups to benefit from EoS: first, the group's aggregate gradient must align with the top Hessian eigenvector, which the researchers confirm through controlled perturbations that randomize direction while preserving distance; second, the group must maintain non-vanishing gradient magnitude over time. Under cross-entropy loss, this mechanism causes gradient saturation in confidently classified groups, shifting learning advantages to output-outliers whose gradients remain active. These findings reframe the edge of stability from a simple stability boundary to a more complex mechanism governing the distribution of learning across data.
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- arXiv cs.LGCenter
Edge of Stability Selectively Shapes Learning Across the Data Distribution
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