Coherence-Aware AGI Metric

• The paper introduces a coherence-aware AGI measure using generalized means and AUC to penalize compensability and reveal domain weaknesses.
• It replaces conventional arithmetic scoring with a continuum of p-values to expose inter-domain dependencies and critical performance gaps.
• The methodology provides a multidimensional diagnostic tool that guides improvements by emphasizing balanced, robust cognitive evaluations.

A coherence-aware measure of AGI seeks to rigorously quantify an agent’s balanced competence and integration across cognitive domains, addressing both inter-domain dependency and robustness under variable compensability assumptions. This paradigm is technically motivated by the limitations of conventional aggregate scoring approaches, and is formalized via generalized means and area-under-curve (AUC) metrics, as detailed in recent CHC-based AGI assessment frameworks.

1. Limitations of Arithmetic Mean and Compensability

The prevailing baseline for AGI measurement evaluates proficiency by aggregating normalized domain scores—most notably via the arithmetic mean, as formalized in CHC-based frameworks. Here, for n domains with scores $s_i \in [0,1]$, the global score is given by:

$AGI_1 = \frac{1}{n} \sum_{i=1}^n s_i$

This method assumes full compensability: exceptional scores in one domain can offset weak or even zero performance in others. Such compensability is problematic from both psychometric and systems-theoretic perspectives. Cognitive domains are interdependent; catastrophic failure in memory or reasoning undermines overall general intelligence, even if other faculties are unimpaired.

The arithmetic mean therefore tends to reward specialization and disguises deep asymmetries—a system with null scores in a few critical areas may retain a deceptively high global score. This suggests that standard aggregate approaches overstate general competence and fail to capture the requirement for balanced, robust, and mutually supporting intelligence across domains (Fourati, 23 Oct 2025).

2. Generalized Mean Formalism

To address the limitations of compensability, the coherence-aware framework introduces the generalized mean (power mean):

• For $p \neq 0$:

$$AGI_p = \left( \frac{1}{n} \sum_{i=1}^n \max(s_i, \epsilon)^p \right)^{1/p}$$

• For $p = 0$ (geometric mean):

$$AGI_0 = \left( \prod_{i=1}^n \max(s_i, \epsilon) \right)^{1/n}$$

where $\epsilon > 0$ prevents collapse in the event any $s_i = 0$.

The parameter $p$ tunes the compensability regime:

• $p = 1$ (arithmetic mean): fully compensatory (standard aggregate measure).
• $p = 0$ (geometric mean): penalizes imbalance, yields zero if any domain score vanishes.
• $p = -1$ (harmonic mean): maximally non-compensatory; dominated by lowest scores.

By varying $p$ across a continuum $[p_{min}, p_{max}]$, coherence can be assessed under a spectrum of compensatory assumptions.

3. Area-Under-the-Curve (AUC) Coherence Metric

Recognizing that the true character of general intelligence is reflected in performance under variable compensability, the paper defines a coherence-aware measure as the area under the curve (AUC) of $AGI_p$:

$$AGI_{AUC} = \frac{1}{p_{max} - p_{min}} \int_{p_{min}}^{p_{max}} AGI_p\, dp$$

This metric penalizes imbalances, honoring the principle of “coherent sufficiency”: robust competence across all essential domains. It also captures inter-domain dependencies, since harm in one area proportionally depresses the entire curve.

In practice, integration is performed over $p \in [-1, 1]$. A high $AGI_{AUC}$ indicates resilience—elevated scores persist even as compensability is reduced—while a low value exposes brittleness or domain gaps.

Domain Score Table

Model	Arithmetic Mean $AGI_1$	Geometric Mean $AGI_0$	Coherence-AUC ($AGI_{AUC}$)
GPT-4	27%	~0%	~7%
GPT-5	58%	~0%	~24%

Note: Values reflect aggregation over CHC-based cognitive domains. Near-zero geometric means indicate at least one critical domain is missing or highly deficient; coherence-AUC exposes this masked shortfall even when arithmetic scores are high.

4. Mathematical and Interpretive Properties

The coherence-aware construction possesses several important properties:

• Strictness: As $p$ decreases, the metric becomes less tolerant of imbalance—single deficiencies cause sublinear depression.
• Interpretability: Reporting the full $AGI_p$ curve and $AGI_{AUC}$ provides a transparent, multidimensional diagnostic rather than a single “magic number.”
• Inter-domain dependency: Penalization reflects systems-theoretic bottlenecks—failure in one domain bounds overall effective intelligence.
• Metric pluralism: The framework supports simultaneous reporting of arithmetic, geometric, harmonic means, and $AGI_{AUC}$, enabling richer analysis.

This suggests that incremental improvement in weak domains, even if modest, can disproportionately increase overall coherence, and directs focus toward domain bottlenecks rather than artificial specialization.

5. Implications for AGI Evaluation and Advancement

The coherence-aware measure fundamentally alters both interpretation and research priorities:

• It eschews specialization in favor of resilient, interdependent domain competence.
• It informs benchmarking and model development, steering optimization toward balanced, robust cognitive machinery.
• It challenges overoptimistic claims of progress toward AGI based solely on aggregate metrics.

Applied to published scores for leading models, the AUC analysis reveals persistent deficits (such as in long-term memory and real-time reasoning) even when average proficiency appears substantial. This richer metric thus provides a more principled and stricter foundation for AGI measurement, aligning evaluation closer to the ideal of coherent, sufficiency-based general intelligence (Fourati, 23 Oct 2025).

6. Context within Broader AGI Frameworks

The coherence-aware framework extends and refines prior CHC-based AGI definitions, addressing shortcomings in snapshot-based or equally weighted scoring approaches (Hendrycks et al., 21 Oct 2025). Whereas earlier methods may produce “jagged” cognitive profiles and mask critical failures, the integrated generalized mean surfaces these gaps, pushing model construction and assessment toward genuinely holistic intelligence.

A plausible implication is that future AGI systems will be incentivized to close interdependent bottlenecks and ensure competence across all domains—not only for competitive assessment, but as a structural necessity for robust intelligent action. The metric admits future refinement, such as adaptive domain weighting, nonlinear scaling, or further integration with cluster-based and stability indices.

7. Summary

A coherence-aware measure of AGI is defined as the area under the generalized mean curve of domain scores, penalizing imbalance and rewarding robust, interdependent competence. This approach provides a strict, interpretable, and multidimensional evaluation methodology, revealing deep bottlenecks masked by aggregate scores and guiding principled progress toward genuine artificial general intelligence.