Intuition-Method Layered Model

• Intuition-Method Layered Model is a reasoning framework in AI that integrates rapid, experience-based intuition with methodical, transferable strategies for handling novel problem scenarios.
• It employs a dual-process structure where the Intuition Layer quickly maps past experiences to current tasks and the Method Layer systematically decouples reasoning into reusable, modular solutions enhanced by vertical, horizontal, temporal, and spatial extensions.
• Empirical evaluations show improved efficiency and robustness in uncertain conditions, with an entropy metric quantifying the diversity and independence of extension strategies for adaptable problem-solving.

The Intuition-Method Layered Model describes a reasoning framework in artificial intelligence and cognitive systems that integrates rapid, experience-driven intuition with systematic, transferable method-based reasoning. Initially developed to simulate human-like intuition in AI systems and subsequently extended across logic-based architectures, visual cognition, multimodal reasoning, and LLMs, this paradigm aims to efficiently handle direct, indirect, and previously unseen problem scenarios by combining quick, reflexive responses with modular, adaptable reasoning units. Modern extensions incorporate scope-broadening mechanisms such as vertical (causal), horizontal (parallel/generalization), temporal, and spatial expansions, with a formal entropy-based metric to evaluate the system's ability to solve novel and complex problems.

1. Dual-Process Structure: Intuition and Method Layers

The foundational architecture consists of two distinct layers:

• Intuition Layer: This component is designed to generate rapid, “first-reaction” responses by mapping the current problem instance to a stored set of past experiences. Technically, the intuition process (IP) overlays a mapping mechanism onto the standard logic-based process (NP). The activation and contribution of intuition are modelled by weighted scores for importance, priority (of experience match), probability of process activation $P(\frac{IP}{NP})$, and external change factors. The mathematical form is:

$$f(x)_t = \text{MappingFn}(f(x)_t) + \text{Adjustment Factor}$$

$$\text{MappingFn}(f(x)_t) = \left[P\left(\frac{IP}{NP}\right) \times \text{Importance}(IP) + \text{Priority}(E)\right] + E + P(\text{External Changes})$$

where $E$ denotes the experience value (Dundas et al., 2011).

• Method Layer: When intuition alone is insufficient, the question–answer pair is decoupled into reusable “methods.” Each method is defined as $(q, y)$, with $q$ as the question and $y$ the solution. This modularity supports the transfer of reasoning units to new, related scenarios, enabling systematic logical deduction, probabilistic computation, or algorithmic solution construction.

The model is explicitly layered, with intuition supporting method-based reasoning especially when time and computational resources are constrained. In critical applications, intuition can yield “good enough” estimates rapidly, while subsequent methodical processing refines the output if resources permit (Dundas et al., 2011).

2. Mathematical Formalisms and Architectural Abstractions

The integration and behaviour of layered reasoning are formalised both in logic-based settings and general software architecture:

• Layer Denotation: Each layer is abstracted as $(I, O, f)$—$I$ input ports, $O$ output ports, $f: val(I) \rightarrow \mathcal{P}(val(O))$ mapping input valuations to output sets (Marmsoler et al., 2015).
• Layer Composition: Layers are connected via an attachment relation $A$, which formally links output ports to input ports in higher layers. The semantics are built as relational compositions, producing a hierarchical dependency graph.
• Dependency Formalism:
  • Syntactic dependency is defined by wire-level connectivity: $l \to_s l'$ if at least one output of $l$ feeds an input of $l'$.
  • Semantic dependency is defined by the effect of altering one layer’s behaviour on another’s output. The two coincide under "usability"—if every open input port admits at least one valuation, semantic and syntactic dependencies match via the reflexive–transitive closure (Marmsoler et al., 2015).
• Scope Extension: The extended model tracks not only direct mappings $(p(y|q))$, but augmented forms:
  • Vertical (cause)-extension: $p(y|q) \rightarrow p(y|q, c)$
  • Horizontal (parallel/generalization): $p(y|q) \rightarrow p(y|q, N(q))$ with $N(q)$ as similar questions; generalization via mapping $g(q)$.
  • Temporal extension: $X' = X \cup H \cup F$, where $H$ and $F$ are history and future states.
  • Spatial extension: $X' = \mathcal{E}_{spatial}(X), X \subset X'$ broadens input context (Su, 12 Oct 2025).

These formalisms provide a technology-agnostic and systematic baseline for constructing, verifying, and adapting layered reasoning architectures in software and AI systems (Marmsoler et al., 2015).

3. Scope Extension: Multidimensional Reasoning Expansion

Recognizing the limitations of intuition and method layers for unseen or indirected problems, the scope extension mechanism is introduced to broaden applicability:

• Vertical Extension identifies underlying causal factors or explanatory dimensions otherwise omitted in direct mappings.
• Horizontal Extension expands the reasoning context by integrating related, parallel, or more generalized versions of the problem. Sibling nodes in a knowledge tree represent extensions to other scenarios, while parent nodes aggregate broader generalizations.
• Temporal and Spatial Extensions (first-systematic inclusion (Su, 12 Oct 2025)) allow the model to reason over time-evolving states and larger spatial contexts, essential for problems where localized evidence is insufficient. For example, spatial extension may incorporate global environment data to resolve ambiguities, while temporal extension uses dynamic data histories to forecast or backtrack causal links.

These extensions are systematically organized into knowledge trees—hierarchical structures linking questions, solutions, and extension operations. Shared nodes create knowledge networks, resulting in increased adaptability and reasoning power (Su, 12 Oct 2025).

4. Quantitative Evaluation: Entropy of Method Extension

To evaluate the capacity of the layered model to resolve unseen issues, an entropy metric for method extension is proposed:

$H(E) = -\sum_{i=1}^{n} p(e_i) \log p(e_i)$

where $E = \{e_1, e_2, \ldots, e_n\}$ represents the set of extension strategies/methods and $p(e_i)$ is the normalized contribution of $e_i$. High entropy reflects diversity and independence of extension paths—critical for robust reasoning on indirected problems. When extensions are highly dependent or coupled, entropy declines, indicating limited adaptability (Su, 12 Oct 2025).

This framework permits the quantitative assessment of an LLM’s or reasoning system's extensibility, supporting principled selection and design in real-world scenarios.

5. Comparative and Empirical Analysis

The Intuition-Method Layered Model has been empirically compared to conventional logic-based models, neural architectures, and statistical reasoning systems:

• Poker Hand Dataset: In untrained settings,
  • Neural Networks: 30–40% failure
  • Hidden Markov Models: 20–30% failure
  • Intuition-based Layered Model: 10–15% failure
• Car Evaluation Dataset: The intuition-based approach is robust against mixing anomalous and unknown entities; its accuracy remains constant as logic-based approaches degrade in disturbed environments (Dundas et al., 2011).

Despite its strengths in rapid approximation and handling uncertainty, the intuition process is not a substitute for careful logic-based reasoning in unconstrained time/resource settings. Its gains in efficiency are offset by sensitivity to the mapping quality (via priority/importance weights), and may produce unexpected results if misassigned (Dundas et al., 2011).

6. Practical Implications and Future Directions

This layered paradigm finds application in AI reasoning under time, resource, and knowledge constraints, especially when indirected or out-of-distribution scenarios arise. Key implications:

• Rapid First-Response: Intuition delivers immediate, experience-based answers under severe temporal or computational limitations.
• Systematic Adaptation: Method-based reasoning and scope extension provide systematic, adaptable pathways for problem resolution when intuition fails.
• Knowledge Tree and Network Construction: Systematic organization of extensions ensures that parallel, causal, temporal, and spatial reasoning paths are accessible for transfer and generalization.
• Formal Entropy Evaluation: Entropy of method extension enables rigorous assessment and tracking of the system’s evolving capability to meet new challenges.

Current extensions posit scope-broadening as central to effective LLM deployment and general AI reasoning. Techniques for constructing and optimizing knowledge trees/networks, as well as adaptive scaling of intuition-method balancing, are active areas of research.

7. Context within Layered and Modular Architectures

The Intuition–Method Layered Model generalizes principles from layered architecture in software engineering, interpretable neural networks, and multimodal cognitive systems. It is distinguished by:

• Hierarchical, modular decomposition (from ports and services to reasoning strategies).
• Rigorous definitions of dependency and effect propagation (syntactic and semantic).
• Explicit recognition of the dynamic interplay between rapid, experiential processing and slow, systematic deduction.
• Evaluation frameworks adaptable across logic, vision, language, and multimodal learning domains (Marmsoler et al., 2015, Su, 12 Oct 2025).

The model defines a robust base for extensible, adaptable reasoning in LLMs and AI systems, anchored by precise mathematical and architectural principles.