Humour Decomposition Mechanism (HDM)

• Humour Decomposition Mechanism (HDM) is a computational framework that analyzes dynamic, probabilistic interpretation and rapid error correction as the basis for humour.
• It models cognition by selecting optimal interpretation trajectories using probabilistic processing and neural network principles to simulate laughter triggers.
• HDM informs practical algorithms for managing ambiguity and memory constraints, offering actionable insights for AI, linguistics, and cognitive science research.

The Humour Decomposition Mechanism (HDM) is a class of computational models and algorithmic frameworks designed to systematically analyze, represent, and simulate the structure and emergence of humour during information processing. Originating in cognitive science and artificial intelligence research, HDM conceptualizes humour not as a simple additive or affective quality, but as an emergent effect of dynamic, probabilistic interpretation, error correction, and resolution of cognitive incongruity.

1. Probabilistic Trajectory Processing in Information Understanding

At the conceptual core of HDM lies a probabilistic model of how streams of symbols (e.g., words in text or utterances) are mapped to mental representations such as images or meanings stored in associative memory. Each input symbol $A_n$ corresponds to a set of possible images $\{B_n\}$, and understanding a text involves selecting a trajectory—$B_1^{(i_1)}, B_2^{(i_2)}, B_3^{(i_3)}, \ldots$—that best captures the intended meaning.

The processing pipeline proceeds as follows:

• Trajectory Construction: All feasible trajectories in the space of images are constructed.
• Probability Assignment: Each trajectory is assigned a probability based on memory-stored correlations, often using binary or $n$-ary probabilities. In the binary case:

$P(\text{trajectory}) = \prod_n p_{i_n i_{n+1}}$

• Decoding and Transmission: The most probable trajectory is selected as the “interpreted” meaning. For resource efficiency, only a limited number $M$ of probable trajectories are retained at any step, using a sliding-window approach for long texts.

The model thus links humour emergence to the management and selection of interpretation trajectories under resource and timing constraints (0711.2058).

2. Humour as a Malfunction: Error Correction and Version Switching

HDM characterizes the humorous effect as a specific malfunction in information processing. When there is a delay between the computation “front” (point of current analysis) and what is transmitted to consciousness, the system may prematurely commit to a probable but ultimately incorrect trajectory. If a superior trajectory is detected after transmission, the model calls for a rapid deletion and replacement of the originally accepted version with the corrected one.

This commutation between mutually incompatible interpretations is experienced psychologically as humour. The model formalizes this as follows:

• Processing delay ($\tau_{max}$): If processing lags behind output to consciousness, premature transmission can occur.
• Error Correction: When new evidence favors a previously less probable interpretation, rapid replacement is triggered.
• Subjective Effect: The switch between incompatible cognitive states produces the subjective humorous effect (0711.2058, 0711.2270).

This process generalizes to both simple verbal humour (e.g., puns) and more complex forms (involving layered or ambiguous meanings).

3. Emotional and Neural Correlates of Humorous Processing

The HDM links computational states to emotional evaluation:

• Emotion Formula: The strength of emotion is expressed as

$\mathcal{E} = \mathcal{N} (I - I_0)$

where $\mathcal{N}$ is a cognitive need, $I$ the quantity of information available (e.g., probability of a trajectory), and $I_0$ the information needed to satisfy the cognitive demand (0711.2270).

• Neural Mechanisms: The process of rapid deletion is modeled via Hopfield-type neural networks:

$$E = \sum_{\langle ij \rangle} J_{ij} \sigma_i \sigma_j$$

where $J_{ij}$ represents neuron connections and $\sigma_i$ the state variables. Forced de-excitation (akin to a strong “magnetic field” stimulus) dumps neural energy into motor areas, theorized as the physiological basis of laughter. This connects to classical views of laughter as nervous energy discharge (0711.2270).

• Emotional Dynamics: Certainty (high probability of interpretation) is felt as confidence or pleasure. Reversal or correction induces doubt and subsequently the humour response.

4. Algorithmic and Practical Instantiations

The HDM framework has been operationalized into practical algorithms:

• Correlation Matrix Learning: In implementation, a matrix $A_{ij}$ records co-occurrences of images or words:

$\Delta A_{ij} = 1 \quad \text{(when words $i$and$j$ appear together)}$

The probability of a trajectory is estimated by summing relevant entries:

$p = \sum_{i,j, i \ne j} A_{ij}$

This unsupervised, associative learning enables the system to automatically capture the structure underlying texts, making it feasible to adapt machine translation-like systems for humour processing (0711.3197).

• Ambiguity Management: Special strategies are developed for handling synonyms (by block structure in the matrix) and homonyms (which may require manual disambiguation).
• Resource Constraint Tactics: To avoid the exponential growth of possible trajectories, the mechanism employs fragment-based, most-probable-path retention, similar to beam search in sequence analysis.
• Empirical Testing: While primarily theoretical, the mechanism has been positioned for empirical validation via computational experiments, drawing analogies to established machine translation systems.

5. Biological and Evolutionary Function

According to the HDM, the sense of humour is not accidental but emerges as a biological optimization:

• Speed-Accuracy Trade-Off: Evolution has selected for fast, tentative information transmission with the acceptance of occasional misinterpretation, as delay can be more dangerous than error (e.g., in urgent decision-making).
• Efficient Memory Utilization: Transmission of tentative interpretations makes better use of limited operative memory. Corrections are less costly than delayed comprehension.
• Evolution of Social Laughter: The mechanism for rapidly “dumping” incorrect information, initially cognitive, becomes coupled with motor outputs (laughter) as a communication tool in social groups, supporting both internal and external information management (0711.2270).

6. Extensions to Multilevel, Ambiguous, and Complex Humour

HDM further encompasses advanced forms of humour:

• Higher-Level Gestalt Processing: Primary images can be combined into composite, secondary images, creating gestalt representations of meaning.
• Ambiguity and Contextual Layering: The mechanism accounts for coexisting interpretations in nested context layers. Timing and interdependency between processing streams can generate the ambiguity central to many complex jokes.
• Contextual and Delivery Effects: The model explains how timing, intonation, and the predictability of a joke modulate the likelihood and intensity of the humorous effect, and why hackneyed jokes lose their effect due to diminished incongruity.

7. Limitations and Outlook

The HDM, while offering a robust computational framework, is characterized by:

• Computational Complexity: Exponential growth of trajectories necessitates memory and processing constraints, requiring practical approximations.
• Semantic Depth: Simple forms of humour, such as wordplay and puns, are readily modeled, but more sophisticated humour demands comprehensive mapping of images and associations, which remains a significant challenge.
• Neural Implementation: Translating the mechanism into fully neural models emulating human timing and correction remains an open problem.
• Empirical Validation: Systematic testing in both artificial agents and human subjects is essential for tuning parameters (e.g., $\tau_{max}$) and confirming predictive value.

In summary, the Humour Decomposition Mechanism offers a comprehensive computational theory explaining humour as a byproduct of rapid, probabilistic interpretation, dynamic error correction, and the interplay between speed, accuracy, and cognitive resource management. The mechanism lays the groundwork for developing computer systems capable of detecting, generating, and potentially even expressing humour, linking linguistic ambiguity, emotional evaluation, and neural-level error correction within a unified theoretical and algorithmic framework.