Precision Scoping

Claim Type: mechanism_hypothesis
Scope: Tau-scoped precision separation and update rules
Depends On: INV-008, ARC-004
Status: provisional
Claim ID: MECH-003

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Source: docs/processed/legacy_tree/architecture/precision_scoping.md

τ-Scoped Precision: Update Rules and Separation

Overview

REE treats precision and confidence as the same control variable operating at different temporal depths (τ). To prevent pathological coupling, precision MUST be τ-scoped, with explicit, lossy projections between τ bands.

There is no global precision scalar in REE.

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Definitions

Let: • \tau \in {\gamma, \beta, \theta, \delta} be temporal depth • \varepsilon_\tau be prediction error at depth τ • \pi_\tau be precision (gain / confidence weight) at depth τ • z_\tau be the state estimate at depth τ

A τ-scoped state token is:

\langle z \mid \tau, \rho, \phi, \pi_\tau \rangle

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Core Rule (Normative)

Precision values at different τ depths MUST be stored, updated, and applied independently.

Formally:

\pi_\gamma \neq \pi_\beta \neq \pi_\theta \neq \pi_\delta

No module may: • directly overwrite another τ’s precision • aggregate precisions without a projection operator • treat precision as τ-agnostic metadata

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Local Precision Update (Phasic-like)

At each τ depth, precision updates locally from error statistics:

\pi_\tau(t+1) = (1 - \alpha_\tau)\,\pi_\tau(t) + \alpha_\tau\,f(

\varepsilon_\tau(t)

, context)

Where: • \alpha_\tau is τ-specific (γ ≫ β ≫ θ ≫ δ) • f is bounded and saturating • update is event-locked at γ/β and slowly integrated at θ/δ

Interpretation: • γ / β precision behaves phasically (fast, sharp) • θ / δ precision behaves tonically (slow, stabilising)

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Precision Application

Precision modulates influence, not truth.

At each τ depth:

\Delta z_\tau \propto \pi_\tau \cdot \varepsilon_\tau

Crucially: • γ precision weights sensory/motor corrections • β precision weights action–outcome learning • θ precision weights trajectory relevance • δ precision weights model persistence and narrative stability

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Cross-τ Projection (Explicit and Lossy)

Cross-τ influence MUST pass through a projection operator:

\pi_{\tau_j} \leftarrow \mathcal{P}{\tau_i \rightarrow \tau_j}(\pi{\tau_i}, history, context)

Properties of \mathcal{P}: • Slow (many samples required) • Directional (usually short → long τ only) • Lossy (cannot preserve sharp spikes) • Context-gated (φ-dependent)

Examples: • repeated β-scale precision → gradual θ-scale confidence • sustained θ-scale confidence → very slow δ-scale belief stability • γ-scale precision never projects directly to δ

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Prohibited Operations (Hard Constraints)

The following are architectural violations: • using γ-scale surprise to directly raise δ-scale certainty • collapsing πγ…πδ into a single “attention” scalar • letting E3 read untyped precision • allowing precision to bypass φ gating

These violations correspond to known failure modes: • impulsivity • delusional certainty • manic over-commitment • reward hacking

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Biological Correspondence (Non-normative note)

This separation mirrors: • phasic dopamine → πγ / πβ • tonic dopamine → πθ / πδ • anatomical separation enforcing τ isolation

REE encodes this by design, not by accident.

Expected vs unexpected uncertainty should be treated as separate control inputs (ACh‑like vs NE‑like), rather than collapsed into a single precision signal.

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Summary (for quick reference) • Precision is one variable, many τ-scoped registers • Phasic vs tonic = short-τ vs long-τ integration • Cross-τ effects require explicit, slow projection • Precision modulates influence, not truth —

Open Questions

None noted in preserved sources.

Related Claims (IDs)

• MECH-003

References / Source Fragments

• docs/processed/legacy_tree/architecture/precision_scoping.md