MesoNet: local-stability and conjecture checklist

coupled weight / plasticity system. negative plasticity-direction eigenvalue is only one piece; check the other slope + event updates too

source evolution: the earlier packet labels the central result a theorem; the later preprint labels Section 3.3 “MesoNet Central Conjecture.” Keep the later status when summarizing the overall claim.

Lyapunov heatmap

Dynamical-systems conjecture

proposed local model: coupled weight/plasticity dynamics are linearized around a fixed point. The displayed triangular Jacobian has one eigenvalue from the effective weight-direction slope and another -1/tau_d. Under that model, positive tau_d makes the plasticity-direction eigenvalue negative; the remaining local condition depends on the weight slope and attribution term.

assumptions that need checking: differentiability at the chosen STDP timing-error point; whether coupling terms really permit the stated triangular/block structure; a nonpositive derivative for the proposed Lyapunov-like function over the relevant domain; and a compact invariant set before invoking an invariance argument.

spectral extension: the document models fluctuations with a Wigner ensemble and shifts a semicircular spectrum. Its limitations section acknowledges that actual learned Jacobians may contain correlations that violate the assumed random-matrix structure. A local linearization or assumed spectrum is not automatically a global-convergence proof.

review question: compare the actual learned Jacobian's spectrum with the assumed distribution and keep the result separate from task accuracy. This is a research checklist, not a verification of the proof.

Mathematical model slide