Necessity and refinement of stabilization methods for active nematic training

Determine whether the stabilization mechanisms used during training of activity fields in active nematics—namely, eligibility trace gating based on free energy peaks, spatial gating based on defect–target proximity, and clamping/thresholding of the activity magnitude—are strictly necessary, and develop refined or minimal stabilization strategies that prevent unwanted defect nucleation while preserving learning performance.

Background

To prevent nucleation of new defects during learning with the local update rule, the authors introduce three practical stabilizations: (i) an eligibility trace z(r,t) that weights updates near defects, (ii) spatial gating that restricts learning to when the defect is within a window of the target position, and (iii) clamping and global limits on the activity magnitude. These measures enabled successful training in their tests but may not be minimal or optimal.

The authors explicitly note that it is unresolved whether all these stabilizations are needed or how they could be improved, motivating a systematic paper to determine necessity and to design refined alternatives.