Harnack-type inequalities and traveling waves for non-cooperative nonlocal diffusion systems

arXiv:2608.11107 2026 Regularization 1 ideas extracted · analyzed Sep 1, 2026

What the math gives to ML

The paper establishes a system-wide Harnack principle for positive vector-valued solutions even when coupling matrices are non-cooperative or reducible. Its transferable asset is scale-free control of relative variation: aggregate positive mass has a bounded log-slope and a two-sided exponential ratio bound. This suggests a Harnack-style regularizer for positive neural feature fields, especially CNN activation maps, sequence states, and graph representations, that suppresses unstable aggregate spikes without forcing every channel to be individually smooth.

Ideas from this paper

Unverified 2026

Harnack regularization for positive feature fields

Represent a feature field with positive channel amplitudes and penalize violations of the paper's system-wide relative-variation bound. Unlike per-channel total variation, the penalty constrains only aggregate channel mass, allowing channels to exchange mass through signed or non-cooperative mixing while keeping the overall representation stable. The method is most natural for intermediate CNN maps, positive SSM states, or sequence embeddings indexed by a coordinate with meaningful local…

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Regularization Stability Generalization Cnn

Paper: Harnack-type inequalities and traveling waves for non-cooperative nonlocal diffusion systems arXiv:2608.11107