Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities
arXiv:2608.03685
2026
Dynamics
2 ideas extracted · analyzed Aug 31, 2026
What the math gives to ML
The paper identifies a nonstandard instability mechanism: a chemotactic cross-gradient flux can destabilize a homogeneous state even when the local reaction Jacobian is non-reactive and diffusion alone cannot produce a Turing instability. Linearization gives a mode-dependent, non-symmetric two-field operator whose off-diagonal chemotactic coupling grows with squared wave number. This yields a computable critical chemotactic strength and a preferred spatial frequency. The mechanism can be transferred to neural feature dynamics as a conservative cross-channel transport layer or as a spectral controller for learned spatial coupling.
Ideas from this paper
✗ Failed on benchmark
2026
Replace part of a CNN or continuous-depth feature block with two coupled feature fields. One field is transported up gradients of the other through a conservative cross-gradient flux, creating adaptive spatial organization that ordinary diffusion or symmetric convolution cannot produce. The coupling strength and dominant wavelength are controlled by a directly testable linear-instability boundary.
Useful7/10
Difficulty6/10
Novelty8/10
Unverified
2026
Use the mode-wise instability condition as a controller for a learned cross-channel transport gain. During training or inference, estimate the linearized feature dynamics and adjust the chemotactic strength to remain below a stability margin for robust processing, or deliberately cross the threshold during a controlled pattern-forming stage. This replaces blind gain tuning with a measurable dynamical criterion.
Useful6/10
Difficulty5/10
Novelty7/10