Standard Intelligence Model

Updated 11 April 2026

Standard Intelligence Model is a unified framework that formalizes intelligence using explicit mathematical structures, hierarchical processes, and performance-based metrics.
It bridges various AI paradigms by integrating key operations like knowledge input, innovation, and output, enabling clear abstraction and comparison.
The model supports practical benchmarking through standardized IQ tests, abstraction hierarchies, and extended architectures to evaluate both natural and artificial agents.

A Standard Intelligence Model provides a unified, formal framework for describing the structural, functional, and quantitative features of intelligence in both natural and artificial systems. It aims to bridge disparate traditions in AI by defining common abstractions for input, storage, innovation, and output, often formalized mathematically, and offers tools for benchmarking and comparing diverse intelligent agents. This overview synthesizes the principal Standard Intelligence Models developed in contemporary research, spanning mathematical system models, axiomatizations, hierarchical information-processing frameworks, and performance-based metrics.

1. Formal Structural Models of Intelligence

Several Standard Intelligence Models define intelligence in terms of explicit sets, mappings, and system architectures.

Abstract Mathematical Description

Liu & Shi’s model formalizes a “standard intelligent system” as the 11-tuple:

$M = \{ K,\; K_s,\; K_m,\; K_n,\; Q,\; Q_i,\; Q_o,\; I,\; O,\; C,\; N \}$

Where:

$K$ is the universe of knowledge;
$K_s$ is the public, shared cloud subset;
$K_m$ is the system’s mastered knowledge;
$K_n$ is newly innovated knowledge;
$Q$ denotes all possible knowledge forms;
$Q_i$ / $Q_o$ are input/output form subsets;
$I$ is the input function, mapping elements and forms to update $K_m$ ;
$K$ 0 is the output function, placing new elements into $K$ 1;
$K$ 2 is knowledge manipulation within $K$ 3;
$K$ 4 is innovation, generating $K$ 5.

All knowledge acquisition, manipulation, and innovation are thus explicit function mappings on these sets (Liu et al., 2015).

Axiomatic and Categorical Model

An alternative, set-theoretic approach axiomatizes intelligence as a subset $K$ 6 of a universal set, equipped with structures for input, internal processing, and output. At each time step, input/output are modeled as subset transfers between $K$ 7 and its complement $K$ 8, with temporal evolution formalized by bijections $K$ 9 and structural changes within $K_s$ 0 (Itoh, 20 Apr 2025). These structures are extended categorically, with functors capturing time evolution and imitation mappings across classes of intelligent systems.

These formalizations provide an unambiguous mathematical canvas for describing both biological and artificial intelligences: from neural networks to reflex arcs.

2. Hierarchical and Abstraction-Based Frameworks

A dominant theme in standard models is the decomposition of intelligence into hierarchical levels of abstraction and bidirectional information flow.

Three-Layer Abstraction Hierarchy

Yaworsky and others describe intelligence as a layered process:

Physical Level: Raw, high-dimensional, fast-varying sensory signals (pixel arrays, waveforms).
Information Level: Structured, interpretable intermediate representations (feature maps, symbolic frames).
Abstract Level: Time-invariant conceptual representations (beliefs, rules) (Yaworsky, 2018, Yaworsky, 2018).

The core cognitive flow is bidirectional:

Bottom-up (learning/abstraction): Mapping many lower-level signals into fewer, higher-level representations; increasing abstraction with each layer.
Top-down (recall or reasoning): High-level abstractions constrain, activate, or interpret lower-level information and sensory signals, supporting attention, prediction, and decision.

Formally, these models describe both spatial abstraction (mapping $K_s$ 1) and temporal abstraction (mapping over time sequences to invariant constructs).

Concept Graphs and World-Self Models

Other models focus on the organization of knowledge as networks of “concepts,” incorporating a “self” node. Each concept is a vector incorporating activation, symbolic content, and a set of weighted, typed relations to other concepts. The World-Self Model (WSM) manages both world concepts and self-concept in a unified directed graph, with activation and inference propagating across weighted edges and behaviors triggered by goal-driven losses (Yue, 2022). This graph structure allows the explicit unification of connectionist (learning), symbolic (concept manipulation), and behaviorist (goal/action) paradigms.

3. Functional and Performance-Based Metrics

A crucial property of a Standard Intelligence Model is the ability to provide quantitative assessment and comparison.

Multifactor IQ and Capability Grading

Liu & Shi propose a 15-subtest IQ system, weighted across four abilities: acquisition (10%), mastery (15%), innovation (65%), and feedback (10%). Scores are normalized, resulting in absolute and deviation IQ metrics (Liu et al., 2015). A related grading system classifies agents from grade 0 (trivial, fixed systems) through grade 5 (creative, fully human) and up to hypothetical omnipotent grade 6, based on which of the core abilities they manifest and whether they support dynamical growth or cloud knowledge-sharing (Liu et al., 2017). AlphaGo, for example, is classified as grade 3, lacking dynamic creativity and full cloud integration.

Intelligence as Information Processing

The Theory of Intelligences (TIS) models intelligence as a multi-step information-processing operator that differentiates, correlates, and integrates information to reduce uncertainty and accomplish goals. The model defines explicit indices:

Solving Index ( $K_s$ 2): Mean uncertainty reduction for subgoals of a task.
Planning Index ( $K_s$ 3): Efficiency and completeness of path selection toward goal achievement.
Combined Intelligence Index ( $K_s$ 4): A convex combination of solving and planning, with tunable task weighting (Hochberg, 2023).

Difficulty is rigorously defined as intrinsic task complexity over system ability, and intelligence can be scaled by this metric to compare performance across a spectrum of tasks and agent types.

4. Generalization, Unity, and the Intelligence Space

Standard Intelligence Models aim for interoperability across natural and artificial agents, and for robust, scalable measurement.

Nested Hierarchies and Intelligence Space

A unifying structure is the three-level nested hierarchy:

Immediate Intelligence ( $K_s$ 5): Rational agent optimizing actions for current states.
Cumulative Intelligence ( $K_s$ 6): Agents with continuous, lifelong learning.
Full-Spectrum Intelligence ( $K_s$ 7): Addition of situatedness, awareness, projectivity, generality, affect, purpose, language, collaboration, socialization, education (Rosenbloom, 2023).

The “intelligence space” is spanned by these levels, with agents mapped to points or regions according to the degree of approximation to these ideals, quantified by capability measurement functions $K_s$ 8. Natural human intelligence occupies a region near the all-ones corner of the $K_s$ 9 space; existing AIs generally inhabit lower-level regions.

Unified Functional Paradigm

Several models advocate for unification across paradigms by mapping connectionist (neural), symbolic, and behaviorist architectures into a common formal and information-processing framework, with explicit bridging mechanisms (e.g., concept graphs, loss functions, goal-driven self-world loops).

5. Architectural Extensions and Practical Benchmarks

Foundational computer architectures are extended in Standard Intelligence Models to capture key cognitive capacities.

From Von Neumann to Extended Architectures

Standard models adapt and augment the five-block Von Neumann architecture, adding:

Innovation Generator: For the creation of new knowledge or rules.
Cloud Memory: For shared, externalized, collective knowledge, enabling synchronization and distributed learning between agents (Liu et al., 2015, Liu et al., 2017).

This facilitates principled benchmarking: natural and artificial agents can be tested with the same subtests, and comparative scores situate each system within the model’s defined intelligence space and capability hierarchy.

6. Theoretical Limitations and Directions for Unification

Despite their generality, Standard Intelligence Models confront several challenges:

Quantitative comparison often requires additional measures, such as explicit utility, reward, or goal structures.
Formal scalar metrics (e.g., IQ) are not standard across all frameworks and may miss qualitative differences in agent behavior or architecture.
Extensions to category theory provide avenues for high-level abstraction and comparison between classes of intelligent systems.
The structural models are compatible, in principle, with performance-based universal intelligence metrics, but mappings between subset transfers, activity, and reward remain an open research area (Itoh, 20 Apr 2025).

7. Conclusion and Comparative Table

The table below contrasts principal Standard Intelligence Models along key axes:

Model / Author	Structure / Formalism	Key Features
Liu & Shi (2015, 2017)	11-tuple, functional; IQ test	Explicit abilities, mathematical IQ, cloud, innovation generator (Liu et al., 2015, Liu et al., 2017)
Yaworsky (2018); SIM	3-level hierarchy (physical, info, abstract)	Abstraction hierarchy, bidirectional flow, generality (Yaworsky, 2018, Yaworsky, 2018)
Rosenbloom & Lord (2023)	3-level intelligence space	Immediate, cumulative, full-spectrum, continuous measures (Rosenbloom, 2023)
TIS (2023); Cohen	Information calculus, indices	Solving/planning index, goal difficulty, evolutionary proxies (Hochberg, 2023)
WSM (2022)	Concept graph (world+self)	Symbolic, connectionist, behaviorist unification; activation, inference, learning (Yue, 2022)
Itoh (2025)	Axiomatic (set, category theory)	Input/process/output structures, categorical time, universal and activity-centric (Itoh, 20 Apr 2025)

Each model captures core operations and attributes required for intelligent behavior, codifies criteria for comparison, and supports both the mathematical study and empirical benchmarking of AI and biological systems within a comprehensive standard framework.