Why Conclusions Diverge from the Same Observations: Formalizing World-Model Non-Identifiability via an Inference

TL;DR

This paper formalizes how non-identifiability in inference processes explains why different conclusions arise from the same observations, emphasizing the roles of inference settings and world models.

Contribution

It introduces an inference profile framework and categorizes non-identifiability into two levels, providing a new perspective on disagreement in inference and learning.

Findings

Disagreements can be due to inference setting differences or biases in data exposure.

The inference profile $ heta$ captures factors influencing divergent outputs.

Framework applies to deep learning, representation hierarchy, and AI regulation debates.

Abstract

When people share the same documents and observations yet reach different conclusions, the disagreement often shifts into a judgment that the other party is cognitively defective, irrational, or acting in bad faith. This paper argues that such divergence is better described as a form of non-identifiability inherent in inference and learning, rather than as a defect of the other party. We organize the phenomenon into two levels: (i) $\theta$-level non-identifiability, where conclusions diverge under the same world model $W$ because inference settings differ; and (ii) $W$-level non-identifiability, where repeated use of an inference setting $\theta$ biases data exposure and update rules, causing the learned world model $W$ itself to diverge. We introduce an inference profile $\theta = (R, E, S, D)$, consisting of Reference, Exploration, Stabilization, and Horizon, and show how outputs can split even for the same observation $o$ and the same $W$. We further explain why disagreements tend to project onto a small number of bases -- abstract versus concrete, externalizability, and order versus freedom -- as a consequence of general constraints on learning systems: computational, observational, and coordination constraints. Finally, we relate the framework to deep representation learning, including representation hierarchy, latent-state estimation, and regularization-exploration trade-offs, and illustrate the framework through a case study on AI regulation debates.