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This paper unifies economic marginal utility theory with transformer mechanics, framing KV cache eviction and matrix factorization as constrained optimization problems to improve inference efficiency. The authors demonstrate a practical application in geo-mining document analysis, achieving high accuracy on a uranium-exploration corpus while significantly reducing latency compared to standard API calls. By linking latent representation spectra to utility schedules, the work offers a novel theoretical lens for optimizing memory allocation and model merging in specialized AI deployments.
Marginal utility, matrix factorization, and the Key-Value (KV) cache: a unified information-economic framework for sovereign geo-mining inference
arXiv:2609.20068v1 Announce Type: new Abstract: 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 collapse into a single allocation rule: retain the top dimensions whose eigenvalue exceeds the shadow price of the binding constraint. The framework is applied to the automated extraction of structured information from geo-mining documents, where it motivates a multi-pass inference protocol, a layer-wise TIES model merging procedure, and a selection policy combining extraction quality, localization drift and energy, scalarized with a Conditional Value-at-Risk term on drift. Two empirical contributions are reported. An 11.2-million-parameter hierarchical classifier, trained in about five minutes on a single GPU, reaches 90.0 per cent level-1 accuracy on a held-out test set from a 973-document uranium-exploration corpus, against 92.0 per cent for a proprietary model on a fifty-document human audit of the same corpus, at a latency of 2.62 ms per card against approximately 2,000 ms for the API and at negligible cost. A diagnostic of uniform-density TIES merging exposes a reproducible degenerate mode in which the merged model returns token-identical outputs across five geographically distinct districts while declaring high confidence; re-executing the merge under layer-wise calibrated densities removes that signature on the diagnostic sample. The full-scale extraction benchmark, including LoRA fine-tuning, is reported as projected rather than measured and remains an empirical extension of this work.
Abstract: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 collapse into a single allocation rule: retain the top dimensions whose eigenvalue exceeds the shadow price of the binding constraint. The framework is applied to the automated extraction of structured information from geo-mining documents, where it motivates a multi-pass inference protocol, a layer-wise TIES model merging procedure, and a selection policy combining extraction quality, localization drift and energy, scalarized with a Conditional Value-at-Risk term on drift. Two empirical contributions are reported. An 11.2-million-parameter hierarchical classifier, trained in about five minutes on a single GPU, reaches 90.0 per cent level-1 accuracy on a held-out test set from a 973-document uranium-exploration corpus, against 92.0 per cent for a proprietary model on a fifty-document human audit of the same corpus, at a latency of 2.62 ms per card against approximately 2,000 ms for the API and at negligible cost. A diagnostic of uniform-density TIES merging exposes a reproducible degenerate mode in which the merged model returns token-identical outputs across five geographically distinct districts while declaring high confidence; re-executing the merge under layer-wise calibrated densities removes that signature on the diagnostic sample. The full-scale extraction benchmark, including LoRA fine-tuning, is reported as projected rather than measured and remains an empirical extension of this work.
Version 11, 14 septembre 2026. 49 pages, 9 tables. Les valeurs de l'architecture souveraine sont projet{é}es et non mesur{é}es ; le calcul {à} grande {é}chelle est en cours. Soumission pr{é}vue {à} IEEE Transactions on Artificial Intelligence
Artificial Intelligence (cs.AI); Computation and Language (cs.CL)
arXiv:2609.20068 [cs.AI]
(or arXiv:2609.20068v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.20068 arXiv-issued DOI via DataCite (pending registration)
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