Learning Effective Interfaces from Opaque Stochastic Systems: Capacity, Selection, and Validation Limits

When can a model learned from restricted observations reliably replace an opaque stochastic system? This paper investigates the gap between an adequate model existing, a fitting procedure producing it, and a calibration rule selecting it.

The study presents a sequence of finite software investigations culminating in a comparison on 48 opaque synthetic systems. All compared methods use the same fitting and calibration records and are evaluated against complete interaction laws, including joint outputs, delayed effects and resource-sensitive behavior.

A portfolio of probabilistic automata and controlled hidden-state models passes 1,063 of 1,152 registered complete-law tests at a total-variation allowance of 0.15, compared with 970 for a passive tree control and 869 for a minimax tree bank. A prespecified secondary portfolio without the bespoke group-aware candidates reproduces the broad improvement, while mechanism-specific regressions remain.

A post-reveal capacity check establishes that every target fits the general 16-state instrument family. Nevertheless, under the original fitting budget, only 39 of the 48 systems receive an individually passing produced candidate, and only 37 receive one through calibration selection. Architectural capacity therefore does not guarantee successful finite-budget learning or selection.

A separately reported post-hoc sensitivity analysis increases fitting effort on the 11 original failures while retaining the same public data. The expanded portfolio contains a passing model for seven of these systems and selects one for five. Conditional diagnostics identify preparation-dependent response mixing in the challenge regressions. These findings show that fitting effort materially affects candidate production while selection and residual fitting failures persist.

The paper distinguishes model capacity, candidate production, calibration selection and validation coverage. It documents shared evaluation specifications, paired outcomes, source provenance and the limits of aggregate scores. The retrospective sensitivity analysis is outcome-selected and does not replace the original primary results or constitute an independent replication.

This computational preprint studies finite synthetic systems. It does not establish all-context adequacy, general superiority over untested learning methods, or empirical evidence of consciousness. It forms part of the broader Shadow Theory research programme while keeping its operational findings separate from phenomenal interpretation.

Author: Jeremy Rodgers, Independent Researcher
Website: https://everythingequation.com
Paper 3 DOI: 10.5281/zenodo.23075824

Related works:
Shadow Theory and Consciousness, Version 2: https://doi.org/10.5281/zenodo.22853774
Paper 2 — Relational Boundaries and Awareness Localization: Robustness, Composition, and Identification Limits: https://doi.org/10.5281/zenodo.23075822
Paper 4 — Identifying Binary Realizations from Intervention Laws: Certificates, Recoding Obstructions, and a Bounded SPC-2/IIT Comparison: https://doi.org/10.5281/zenodo.23075828