Mean-square linear stability of two-point ZO methods is governed by the full Hessian spectrum and admits explicit bounds in terms of trace and top eigenvalue; full-batch ZO-GD/GDM/Adam empirically operate at that boundary.
Type-ii saddles and probabilistic stability of stochastic gradient descent
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Zeroth-Order Optimization at the Edge of Stability
Mean-square linear stability of two-point ZO methods is governed by the full Hessian spectrum and admits explicit bounds in terms of trace and top eigenvalue; full-batch ZO-GD/GDM/Adam empirically operate at that boundary.