Winner-take-all linear memory capacity scales as d² ~ n log n due to extreme values; listwise retrieval via Tail-Average Margin yields d² ~ n with exact asymptotic theory.
Gregor Bachmann and Vaishnavh Nagarajan
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Gradient descent reaches equal-weight superposition on Erdős-Rényi reachability via a Möbius attractor under S_n symmetry and Cascade Supervision, with a parameter-free decay law matching experimental cosines within 0.02.
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Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval
Winner-take-all linear memory capacity scales as d² ~ n log n due to extreme values; listwise retrieval via Tail-Average Margin yields d² ~ n with exact asymptotic theory.
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Emergence of Frontier Superposition: M\"obius attractor and Cascade Supervision
Gradient descent reaches equal-weight superposition on Erdős-Rényi reachability via a Möbius attractor under S_n symmetry and Cascade Supervision, with a parameter-free decay law matching experimental cosines within 0.02.