This paper builds a theoretical bridge between the economic notion of marginal utility and two machine‑learning constructs: matrix factorization and the key‑value (KV) cache of transformer language models. It shows that the singular‑value spectrum $\sigma_i$ of a rating matrix forms a diminishing marginal‑utility schedule for latent factors, while the eigenvalue spectrum $\lambda_i$ of the projected covariance operator represents the marginal‑utility schedule of a model’s learned representation. Under a fixed memory budget, cache eviction and low‑rank cache compression become instances of constrained utility maximization, leading to a single allocation rule: retain all dimensions whose eigenvalue exceeds the shadow price $\mu$ of the binding constraint, i.e., $\lambda_i > \mu$.
The framework is applied to automated extraction of structured information from geo‑mining documents. The implementation consists of three components: (1) a multi‑pass inference protocol that refines predictions layer by layer; (2) a layer‑wise TIES model merging procedure that uses calibrated densities to avoid a degenerate mode where merged models output identical tokens across distinct districts with inflated confidence; (3) a selection policy that scalarizes extraction quality, localization drift, and energy consumption, adding a Conditional Value‑at‑Risk (CVaR) term on drift to control extreme deviations.
Two empirical contributions are reported. First, an 11.2‑million‑parameter hierarchical classifier trained on a single GPU for about five minutes reaches 90.0% level‑1 accuracy on a held‑out test set of 973 uranium‑exploration documents. On a human‑audited subset of 50 documents, a proprietary model attains 92.0% accuracy but with a latency of roughly 2000 ms per API call, whereas the proposed model processes a card in 2.62 ms at negligible cost. Second, a diagnostic of uniform‑density TIES merging reveals a reproducible degenerate mode in which the merged model returns token‑identical outputs across five geographically distinct districts while reporting high confidence; re‑executing the merge with layer‑wise calibrated densities eliminates this signature on the diagnostic sample. The full‑scale extraction benchmark, including LoRA fine‑tuning, is presented as projected results rather than measured ones, leaving it as an empirical extension.
Review: By formalizing marginal utility as a principled criterion for feature and cache selection, the work offers a solid economic interpretation of KV cache management and demonstrates a practical trade‑off between efficiency and accuracy in geo‑mining document extraction, suggesting promising avenues for broader LLM deployment.