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Marginal utility, matrix factorization, and the Key-Value (KV) cache: a unified information-economic framework for sovereign geo-mining inference

arXiv · Artificial Intelligence · article · Sep 17, 2026 · UTC

This paper builds a theoretical bridge between the economic notion of marginal utility and two machine-learning constructs, matrix factorization and the Key--Value cache of transformer language models. The singular value spectrum of a rating matrix is shown to be a diminishing marginal utility schedule for latent factors, the eigenvalue spectrum of the projected covariance operator to be the marginal utility schedule of a model's learned representation, and cache eviction and low-rank cache compression to be instances of constrained utility maximization under a memory budget. The three collaps

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