Branching stochastic mechanics. II. Relative localization and collective poles from Bohm/Fisher feedback
arXiv:2609.02520
2026
Dynamics
1 ideas extracted · analyzed Sep 3, 2026
What the math gives to ML
The paper develops a reciprocal forward/backward field theory in which Bohm quantum-potential, equivalently Fisher-information, feedback acts on a connected relative sector. Its transferable mechanism is state-dependent curvature feedback: the density formed by two reciprocal fields generates a second-derivative potential that can localize relative activity, while the dressed theory suppresses secular and ultraviolet growth. A practical neural-network translation is a two-stream reciprocal layer whose feature density produces Bohm/Fisher feedback, implemented as an unrolled dynamical module with an explicit resolution-dependent stability limit.
Ideas from this paper
Unverified
2026
Replace a single recurrent hidden state by reciprocal forward and backward feature fields whose product defines a positive feature density. Feed the associated Bohm/Fisher potential back into both streams, creating adaptive curvature feedback that suppresses sharp incoherent relative structure and can localize the learned representation.
Useful6/10
Difficulty6/10
Novelty8/10