Auxiliary Functional Separation Does Not Improve Prediction Under Fair Information Access: An Inversion Finding in Linear-Gaussian Regimes

**Ozone Archive Research Program**

**Paper ID:** O0-PAPER-002

**Underlying study:** O0-CRP-021

**Date:** 2026-07-29

**Version:** 1.0.0

**Record class:** SCIENTIFIC PAPER · single-study IMRAD wrapper

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Abstract

An auxiliary O/0 claim states that functional separation between an observer and its environment serves local prediction. We operationalize this in a partially-observable linear-Gaussian world and compare a Kalman filter (which maintains an explicit self/world separation) against a Vector Autoregression (VAR) model (which does not). We find that when the Kalman filter has *privileged* access to the correct system matrices, it outperforms VAR by 2–5% NMSE across 9 (regime × horizon) cells. When both models are trained on the same data with the same information budget, the direction *inverts*: unified VAR outperforms learned-Kalman by 3–24% NMSE across all tested regimes and horizons. The auxiliary claim that self/world separation *itself* improves prediction is UNSUPPORTED under fair comparison. The apparent advantage of separated architectures in prior demonstrations reflects privileged causal-structure knowledge, not the separation.

**Verdict:** INCONCLUSIVE (primary) / UNSUPPORTED (fair-comparison).

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1. Introduction

The proposition that "the observer maintains a functional boundary against its environment for local prediction" is a common auxiliary reading of O/0-adjacent philosophical claims. In the machine-learning literature the analog is the claim that structured, modular models outperform unstructured ones when the underlying world is decomposable. This paper tests the specific claim that maintaining an explicit self/world separation improves predictive accuracy in a partially-observable linear-Gaussian world.

2. Methods

**World.** A discrete-time linear-Gaussian state-space system with state dimension d ∈ {4, 8, 16}, observation dimension k ∈ {1, 2, 4, 8}, additive Gaussian dynamics noise, and additive Gaussian observation noise.

**Predictors.**

• **Kalman filter (K):** given correctly-specified system matrices A, C, Q, R. Maintains explicit internal state estimate and separate observation model.
• **Learned-Kalman (K′):** same architecture as K, but with matrices identified from training data via subspace identification.
• **VAR:** vector autoregression of order 2 on observations, no explicit internal state, no separation.
• **VAR(4):** VAR order 4.
• **Ridge-VAR:** VAR(2) with ridge regularization.
• **AR:** univariate AR(2) per observation channel (positive control lower bound).

**Design.** 3 regimes (fully observable, partially observable, minimally observable) × 30 seeds × 3 prediction horizons (τ=1, 5, 20). 1620 predictor evaluations total.

**Analysis.** Normalized mean squared error (NMSE) per predictor, per regime, per horizon. Paired-seed comparison to reduce variance.

3. Results

**Primary comparison (K with true matrices vs VAR):** K wins by 2–5% NMSE in 9 of 9 regime × horizon cells (p < 1e-10 in most).

**Fair comparison (K′ learned from same data as VAR):** VAR wins by 3–24% NMSE in 6 of 6 regimes at all 3 horizons.

**Effect direction inverts** when the information advantage is equalized. The largest VAR wins occur in the fully-observable regime (k/d = 1.0), where separation is least useful.

4. Discussion

The Kalman filter advantage in the primary comparison is real but reflects the model having been *given* correct causal structure. When both models must *learn* their parameters from the same finite data, the unified representation (VAR) is favored — likely because VAR estimates fewer distinct parameter blocks and generalizes better under data scarcity.

The auxiliary claim that functional separation intrinsically improves local prediction is UNSUPPORTED at fair comparison. Prior demonstrations of separation-advantage may reflect privileged causal-structure knowledge, not the separation.

**Adversarial interpretation.** A defender of the separation claim could argue that biological systems evolve their structural priors under selection, so the "fair comparison" is unrealistic. This is a valid limitation of the study — see Section 5.

5. Limitations

• Only tested in linear-Gaussian regimes. Nonlinear or non-Gaussian worlds may behave differently.
• All comparisons are within-model-family. Cross-family comparisons (e.g., neural-network vs Kalman) are not tested.
• Prediction is the only utility function tested. Separation may improve other criteria (interpretability, transferability, sample efficiency during learning).

6. Related studies

• **O0-CRP-029** — 6-regime replication of the fair-comparison finding. Confirms robustness across (d, k) grid.
• **O0-CRP-022** — Track 2 discriminability from inside. Companion to this Track 1 finding.
• **O0-SCOPE-002** — claim registry entry C009 (auxiliary functional-separation claim: NOT_SUPPORTED).

7. Data and code availability

• Full record: `research/studies/O0-CRP-021/scientific_record.md`
• Source code: `research/studies/O0-CRP-021/src/`
• Raw outputs: `research/studies/O0-CRP-021/data/`
• Preregistration: `research/studies/O0-CRP-021/preregistration.md`

8. References

• Kalman, R. E. (1960). "A New Approach to Linear Filtering and Prediction Problems." *J. Basic Eng.* 82(1):35–45.
• Van Overschee, P., & De Moor, B. (1996). *Subspace Identification for Linear Systems.* Kluwer.
• Lütkepohl, H. (2005). *New Introduction to Multiple Time Series Analysis.* Springer.