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This work connects Adam loss spikes to both the mismatch between momentum timescales and finite-scale superquadratic loss geometry beyond the Hessian, and shows that confident cross-entropy losses develop a core--wall landscape comprising a narrow quadratic core followed by a steep wall, which produces effective superquadratic behavior at the scale of an optimizer update.
Local mismatches in dialogue can paradoxically lead to stronger preservation of prior beliefs rather than immediate revisions, challenging conventional assumptions about listener behavior.
