ABSTRACT
This paper investigates the computational complexity of magnitude calculation for skew finite subsets in high-dimensional spaces, proposing an approximation framework that achieves O(n2logn) complexity with provable error bounds.
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Key findings
Magnitude computation for skew finite subsets is tractable even in high dimensions.
A novel approximation algorithm is proposed, achieving O(n2logn) complexity with approximation guarantees.
Empirical evidence suggests magnitude-based regularization is feasible for neural network training in high dimensions.
Limitations & open questions
The theoretical complexity landscape for structured subsets in high dimensions is still incompletely understood.