On Decision-Valued Maps and Representational Dependence

TL;DR

This paper introduces decision-valued maps to analyze how different data representations affect outcomes, and presents DecisionDB infrastructure for logging, replaying, and auditing these relationships, enhancing reproducibility and understanding of representation dependence.

Contribution

It formalizes decision-valued maps and develops DecisionDB, enabling deterministic replay and analysis of representation-dependent decision outcomes.

Findings

Decision-valued maps effectively capture representation effects.

DecisionDB allows precise logging and replay of decision relationships.

Representation space is partitioned into persistence regions and boundaries.

Abstract

A computational engine applied to different representations of the same data can produce different discrete outcomes, with some representations preserving the result and others changing it entirely. A decision-valued map records which representations preserve the outcome and which change it, associating each member of a declared representation family with the discrete result it produces. This paper formalizes decision-valued maps and describes DecisionDB, an infrastructure that logs, replays and audits these relationships using identifiers computed from content and artifacts stored in write-once form. Deterministic replay recovers each recorded decision identifier exactly from stored artifacts, with all three identifying fields matching their persisted values. The contribution partitions representation space into persistence regions and boundaries, and treats decision reuse as a mechanically checkable condition.