Sharp constants in the one-sided John-Nirenberg inequality for functions of bounded lower oscillation
arXiv:2608.10892
2026
Regularization
2 ideas extracted · analyzed Sep 1, 2026
What the math gives to ML
The paper gives a sharp one-sided concentration law for functions whose average exceeds their local essential infimum by at most a bounded lower-oscillation norm. The transferable asset is the explicit tail envelope with optimal constants: relative to a local lower baseline, the fraction of values exceeding height lambda is at most e exp(-lambda/B), where B is the BLO norm. This suggests controlling activation or attention-logit spikes with a local-minimum-relative regularizer, and deriving adaptive clipping thresholds from a target exceedance probability rather than arbitrary percentile or norm clipping.
Ideas from this paper
Unverified
2026
Use the sharp exponential tail bound to set a local clipping threshold from a desired exceedance probability. Instead of globally clipping activations at a fixed value or percentile, clip each local window at its minimum plus B log(e/delta), where delta is the tolerated fraction of clipped entries.
Useful5/10
Difficulty3/10
Novelty7/10
Unverified
2026
Regularize hidden activations or attention logits by their local mean excess above the local minimum, rather than by symmetric variance or absolute magnitude. The penalty specifically suppresses upper-tail spikes while remaining invariant to adding a constant offset to every value in a local window.
Useful5/10
Difficulty4/10
Novelty8/10